Julia_AI_ML_HighPerformance_Reference.jl

# JULIA AI/MACHINE LEARNING - Comprehensive Reference - by Richard Rembert
# Julia for high-performance scientific computing, machine learning, and AI
# with focus on speed, parallelism, and mathematical computing excellence

# ═══════════════════════════════════════════════════════════════════════════════
#                           1. SETUP AND PROJECT STRUCTURE
# ═══════════════════════════════════════════════════════════════════════════════

# Julia Installation and Setup:
# 1. Download Julia from https://julialang.org/downloads/
# 2. Install Julia packages using Pkg manager
# 3. Set up VS Code with Julia extension or use Jupyter notebooks
# 4. Configure environment for optimal performance

using Pkg

# Essential Package Installation
essential_packages = [
    # Core Data Science and ML
    "DataFrames", "CSV", "Statistics", "StatsBase", "StatsPlots",
    
    # Machine Learning
    "MLJ", "MLJModels", "MLJLinearModels", "MLJDecisionTreeInterface",
    "MLJXGBoostInterface", "MLJFlux", "ScikitLearn",
    
    # Deep Learning and Neural Networks
    "Flux", "MLUtils", "CUDA", "Zygote", "ChainRules",
    
    # Linear Algebra and Mathematics
    "LinearAlgebra", "SparseArrays", "Random", "Distributions",
    
    # Optimization
    "Optim", "JuMP", "Ipopt", "GLPK",
    
    # Parallel Computing
    "Distributed", "SharedArrays", "ThreadsX", "FLoops",
    
    # Data Visualization
    "Plots", "PlotlyJS", "StatsPlots", "Makie", "GLMakie",
    
    # Time Series and Signal Processing
    "DSP", "TimeseriesTools", "StateSpaceModels",
    
    # Text Processing and NLP
    "TextAnalysis", "Languages", "WordTokenizers",
    
    # Scientific Computing
    "DifferentialEquations", "ForwardDiff", "FiniteDiff",
    
    # Data Import/Export
    "JSON", "BSON", "HDF5", "FileIO", "JLD2",
    
    # Benchmarking and Performance
    "BenchmarkTools", "ProfileView", "TimerOutputs",
    
    # Utilities
    "ProgressMeter", "Dates", "Printf", "Logging"
]

# Install packages if not already installed
for package in essential_packages
    try
        eval(Meta.parse("using $package"))
        println("✓ $package already installed")
    catch
        println("Installing $package...")
        Pkg.add(package)
    end
end

# Load essential packages
using DataFrames, CSV, Statistics, StatsBase
using LinearAlgebra, Random, Distributions
using Plots, StatsPlots
using MLJ, MLJModels
using Flux
using BenchmarkTools
using ProgressMeter
using Printf

# Set random seed for reproducibility
Random.seed!(42)

# Configure plotting backend
plotlyjs()

# ═══════════════════════════════════════════════════════════════════════════════
#                           2. PERFORMANCE OPTIMIZATION SETUP
# ═══════════════════════════════════════════════════════════════════════════════

"""
Performance optimization utilities for Julia AI/ML applications.
"""
module PerformanceOptimizer

using CUDA, Distributed, SharedArrays, ThreadsX
using BenchmarkTools, TimerOutputs

export setup_parallel_environment, optimize_blas, benchmark_system, check_gpu_availability

"""
Set up parallel computing environment with optimal thread and process configuration.
"""
function setup_parallel_environment()
    # Configure threading
    num_threads = Threads.nthreads()
    println("Available Julia threads: $num_threads")
    
    if num_threads == 1
        println("⚠️  Warning: Running on single thread. Set JULIA_NUM_THREADS for better performance.")
    end
    
    # Set up distributed computing if needed
    if nprocs() == 1
        addprocs(min(4, Sys.CPU_THREADS ÷ 2))
        println("Added $(nprocs() - 1) worker processes")
    end
    
    @everywhere using SharedArrays, ProgressMeter
    
    return (threads=num_threads, processes=nprocs())
end

"""
Optimize BLAS configuration for mathematical operations.
"""
function optimize_blas()
    # Set optimal BLAS thread count
    BLAS.set_num_threads(min(8, Sys.CPU_THREADS))
    
    println("BLAS Configuration:")
    println("  Vendor: $(BLAS.vendor())")
    println("  Threads: $(BLAS.get_num_threads())")
    
    # Linear algebra performance test
    n = 1000
    A = randn(n, n)
    B = randn(n, n)
    
    blas_time = @belapsed $A * $B
    println("  Matrix multiplication benchmark (1000×1000): $(round(blas_time * 1000, digits=2)) ms")
    
    return blas_time
end

"""
Check GPU availability and configure CUDA if available.
"""
function check_gpu_availability()
    if CUDA.functional()
        devices = CUDA.devices()
        println("GPU Configuration:")
        println("  CUDA functional: ✓")
        println("  Available devices: $(length(devices))")
        
        for (i, device) in enumerate(devices)
            CUDA.device!(device)
            props = CUDA.properties(device)
            mem_info = CUDA.MemoryInfo()
            
            println("  Device $i: $(props.name)")
            println("    Compute capability: $(props.major).$(props.minor)")
            println("    Memory: $(round(mem_info.total / 1024^3, digits=1)) GB")
            println("    Free memory: $(round(mem_info.free / 1024^3, digits=1)) GB")
        end
        
        return true
    else
        println("GPU Configuration: CUDA not available")
        return false
    end
end

"""
Comprehensive system benchmark for ML workloads.
"""
function benchmark_system()
    println("=== Julia ML System Benchmark ===")
    
    # CPU benchmark
    println("\n1. CPU Performance:")
    cpu_result = @benchmark sum(randn(10^6))
    println("   Vector sum (1M elements): $(round(median(cpu_result.times) / 1e6, digits=2)) ms")
    
    # Memory bandwidth
    println("\n2. Memory Performance:")
    n = 10^7
    x = randn(n)
    mem_result = @benchmark copy($x)
    bandwidth = (n * sizeof(Float64) * 2) / (median(mem_result.times) / 1e9) / 1024^3
    println("   Memory bandwidth: $(round(bandwidth, digits=1)) GB/s")
    
    # Matrix operations
    println("\n3. Linear Algebra:")
    n = 2000
    A = randn(n, n)
    B = randn(n, n)
    matmul_result = @benchmark $A * $B
    println("   Matrix multiplication (2000×2000): $(round(median(matmul_result.times) / 1e6, digits=0)) ms")
    
    # Eigenvalue decomposition
    n = 1000
    A_sym = Symmetric(randn(n, n))
    eigen_result = @benchmark eigvals($A_sym)
    println("   Eigenvalue decomposition (1000×1000): $(round(median(eigen_result.times) / 1e6, digits=0)) ms")
    
    return (cpu=cpu_result, memory=mem_result, matmul=matmul_result, eigen=eigen_result)
end

end # module PerformanceOptimizer

# Initialize performance optimizations
using .PerformanceOptimizer
setup_info = setup_parallel_environment()
blas_time = optimize_blas()
gpu_available = check_gpu_availability()

# ═══════════════════════════════════════════════════════════════════════════════
#                           3. DATA STRUCTURES AND PREPROCESSING
# ═══════════════════════════════════════════════════════════════════════════════

"""
High-performance data preprocessing module optimized for Julia's type system.
"""
module DataPreprocessing

using DataFrames, Statistics, StatsBase
using LinearAlgebra, Random
using ProgressMeter

export DataProcessor, preprocess_pipeline, feature_engineering, split_data

"""
Advanced data preprocessing with Julia's type system and performance optimizations.
"""
struct DataProcessor{T<:Real}
    data::DataFrame
    target_column::Union{String, Symbol, Nothing}
    categorical_columns::Vector{String}
    numerical_columns::Vector{String}
    preprocessing_steps::Vector{String}
    scalers::Dict{String, Any}
    encoders::Dict{String, Any}
    
    function DataProcessor{T}(data::DataFrame, target_column=nothing) where T<:Real
        # Identify column types
        categorical_cols = String[]
        numerical_cols = String[]
        
        for col in names(data)
            if eltype(data[!, col]) <: Union{String, AbstractString} || 
               eltype(data[!, col]) <: CategoricalValue
                push!(categorical_cols, string(col))
            elseif eltype(data[!, col]) <: Real
                push!(numerical_cols, string(col))
            end
        end
        
        # Remove target from feature columns
        if target_column !== nothing
            target_str = string(target_column)
            filter!(x -> x != target_str, categorical_cols)
            filter!(x -> x != target_str, numerical_cols)
        end
        
        new{T}(data, target_column, categorical_cols, numerical_cols, 
                String[], Dict{String, Any}(), Dict{String, Any}())
    end
end

# Convenient constructor
DataProcessor(data::DataFrame, target_column=nothing) = DataProcessor{Float64}(data, target_column)

"""
Handle missing values with various strategies optimized for Julia.
"""
function handle_missing_values!(processor::DataProcessor{T}, 
                               strategy::Symbol=:median, 
                               threshold::Float64=0.5) where T
    
    data = processor.data
    n_rows = nrow(data)
    
    # Remove columns with too many missing values
    cols_to_remove = String[]
    for col in names(data)
        missing_ratio = count(ismissing, data[!, col]) / n_rows
        if missing_ratio > threshold
            push!(cols_to_remove, col)
        end
    end
    
    if !isempty(cols_to_remove)
        select!(data, Not(cols_to_remove))
        println("Removed $(length(cols_to_remove)) columns with >$(threshold*100)% missing values")
    end
    
    # Handle missing values in remaining columns
    for col in names(data)
        if any(ismissing, data[!, col])
            if col in processor.numerical_columns
                if strategy == :median
                    replacement = median(skipmissing(data[!, col]))
                elseif strategy == :mean
                    replacement = mean(skipmissing(data[!, col]))
                elseif strategy == :mode
                    replacement = mode(skipmissing(data[!, col]))
                else
                    replacement = zero(T)
                end
                
                data[!, col] = coalesce.(data[!, col], replacement)
            elseif col in processor.categorical_columns
                replacement = mode(skipmissing(data[!, col]))
                data[!, col] = coalesce.(data[!, col], replacement)
            end
        end
    end
    
    push!(processor.preprocessing_steps, "Missing values handled with $strategy strategy")
    return processor
end

"""
Detect and handle outliers using IQR or Z-score methods.
"""
function handle_outliers!(processor::DataProcessor{T}, 
                         method::Symbol=:iqr, 
                         threshold::Float64=1.5) where T
    
    data = processor.data
    outlier_count = 0
    
    for col in processor.numerical_columns
        if col in names(data)
            values = data[!, col]
            
            if method == :iqr
                q1, q3 = quantile(values, [0.25, 0.75])
                iqr = q3 - q1
                lower_bound = q1 - threshold * iqr
                upper_bound = q3 + threshold * iqr
                
                # Cap outliers instead of removing
                outliers = (values .< lower_bound) .| (values .> upper_bound)
                outlier_count += sum(outliers)
                
                data[!, col] = clamp.(values, lower_bound, upper_bound)
                
            elseif method == :zscore
                μ, σ = mean(values), std(values)
                z_scores = abs.((values .- μ) ./ σ)
                outliers = z_scores .> threshold
                outlier_count += sum(outliers)
                
                # Cap at threshold standard deviations
                data[values .> μ + threshold*σ, col] .= μ + threshold*σ
                data[values .< μ - threshold*σ, col] .= μ - threshold*σ
            end
        end
    end
    
    push!(processor.preprocessing_steps, 
          "Outliers handled using $method method ($(outlier_count) outliers capped)")
    return processor
end

"""
Encode categorical variables using one-hot or ordinal encoding.
"""
function encode_categorical!(processor::DataProcessor{T}, 
                           method::Symbol=:onehot,
                           max_categories::Int=10) where T
    
    data = processor.data
    
    for col in processor.categorical_columns
        if col in names(data)
            unique_vals = unique(skipmissing(data[!, col]))
            n_unique = length(unique_vals)
            
            if n_unique <= max_categories
                if method == :onehot
                    # One-hot encoding
                    for val in unique_vals
                        new_col = "$(col)_$(val)"
                        data[!, new_col] = Int.(data[!, col] .== val)
                    end
                    # Remove original column
                    select!(data, Not(col))
                    
                elseif method == :ordinal
                    # Ordinal encoding
                    val_to_int = Dict(val => i for (i, val) in enumerate(unique_vals))
                    data[!, col] = [get(val_to_int, val, 0) for val in data[!, col]]
                end
                
                processor.encoders[col] = unique_vals
            end
        end
    end
    
    push!(processor.preprocessing_steps, "Categorical variables encoded using $method method")
    return processor
end

"""
Scale numerical features using standardization or normalization.
"""
function scale_features!(processor::DataProcessor{T}, method::Symbol=:standardize) where T
    data = processor.data
    
    for col in processor.numerical_columns
        if col in names(data)
            values = data[!, col]
            
            if method == :standardize
                μ, σ = mean(values), std(values)
                if σ > 0
                    data[!, col] = (values .- μ) ./ σ
                    processor.scalers[col] = (mean=μ, std=σ, method=:standardize)
                end
                
            elseif method == :normalize
                min_val, max_val = minimum(values), maximum(values)
                if max_val > min_val
                    data[!, col] = (values .- min_val) ./ (max_val - min_val)
                    processor.scalers[col] = (min=min_val, max=max_val, method=:normalize)
                end
                
            elseif method == :robust
                med_val = median(values)
                mad_val = median(abs.(values .- med_val))
                if mad_val > 0
                    data[!, col] = (values .- med_val) ./ mad_val
                    processor.scalers[col] = (median=med_val, mad=mad_val, method=:robust)
                end
            end
        end
    end
    
    push!(processor.preprocessing_steps, "Features scaled using $method method")
    return processor
end

"""
Advanced feature engineering with polynomial and interaction features.
"""
function create_polynomial_features!(processor::DataProcessor{T}, degree::Int=2) where T
    data = processor.data
    original_cols = copy(processor.numerical_columns)
    
    # Polynomial features
    for col in original_cols[1:min(5, length(original_cols))]
        if col in names(data)
            values = data[!, col]
            
            for d in 2:degree
                new_col = "$(col)_poly$(d)"
                data[!, new_col] = values .^ d
                push!(processor.numerical_columns, new_col)
            end
        end
    end
    
    push!(processor.preprocessing_steps, "Polynomial features created up to degree $degree")
    return processor
end

"""
Create interaction features between numerical variables.
"""
function create_interaction_features!(processor::DataProcessor{T}, max_interactions::Int=10) where T
    data = processor.data
    original_cols = copy(processor.numerical_columns)
    interactions_created = 0
    
    for i in 1:min(5, length(original_cols))
        for j in (i+1):min(5, length(original_cols))
            if interactions_created >= max_interactions
                break
            end
            
            col1, col2 = original_cols[i], original_cols[j]
            if col1 in names(data) && col2 in names(data)
                new_col = "$(col1)_x_$(col2)"
                data[!, new_col] = data[!, col1] .* data[!, col2]
                push!(processor.numerical_columns, new_col)
                interactions_created += 1
            end
        end
        
        if interactions_created >= max_interactions
            break
        end
    end
    
    push!(processor.preprocessing_steps, "Created $interactions_created interaction features")
    return processor
end

"""
Complete preprocessing pipeline with optimal defaults.
"""
function preprocess_pipeline(data::DataFrame, target_column=nothing; 
                           missing_strategy::Symbol=:median,
                           outlier_method::Symbol=:iqr,
                           encoding_method::Symbol=:onehot,
                           scaling_method::Symbol=:standardize,
                           create_polynomials::Bool=false,
                           create_interactions::Bool=false) :: DataProcessor
    
    println("Starting preprocessing pipeline...")
    
    processor = DataProcessor(copy(data), target_column)
    
    # Apply preprocessing steps
    handle_missing_values!(processor, missing_strategy)
    handle_outliers!(processor, outlier_method)
    encode_categorical!(processor, encoding_method)
    
    if create_polynomials
        create_polynomial_features!(processor)
    end
    
    if create_interactions
        create_interaction_features!(processor)
    end
    
    scale_features!(processor, scaling_method)
    
    println("Preprocessing completed. Applied $(length(processor.preprocessing_steps)) steps:")
    for (i, step) in enumerate(processor.preprocessing_steps)
        println("  $i. $step")
    end
    
    return processor
end

"""
Efficient train-validation-test split with stratification support.
"""
function split_data(X::AbstractMatrix{T}, y::AbstractVector; 
                   train_ratio::Float64=0.7, 
                   val_ratio::Float64=0.15,
                   stratify::Bool=false,
                   random_state::Int=42) where T
    
    Random.seed!(random_state)
    n = size(X, 1)
    
    if stratify && eltype(y) <: Union{String, Symbol, Integer}
        # Stratified split for classification
        unique_classes = unique(y)
        train_indices = Int[]
        val_indices = Int[]
        test_indices = Int[]
        
        for class in unique_classes
            class_indices = findall(==(class), y)
            n_class = length(class_indices)
            
            # Shuffle class indices
            shuffle!(class_indices)
            
            # Calculate splits
            n_train = round(Int, n_class * train_ratio)
            n_val = round(Int, n_class * val_ratio)
            
            append!(train_indices, class_indices[1:n_train])
            append!(val_indices, class_indices[n_train+1:n_train+n_val])
            append!(test_indices, class_indices[n_train+n_val+1:end])
        end
        
        # Shuffle the final indices
        shuffle!(train_indices)
        shuffle!(val_indices)
        shuffle!(test_indices)
        
    else
        # Random split
        indices = shuffle(1:n)
        
        n_train = round(Int, n * train_ratio)
        n_val = round(Int, n * val_ratio)
        
        train_indices = indices[1:n_train]
        val_indices = indices[n_train+1:n_train+n_val]
        test_indices = indices[n_train+n_val+1:end]
    end
    
    # Create splits
    X_train, X_val, X_test = X[train_indices, :], X[val_indices, :], X[test_indices, :]
    y_train, y_val, y_test = y[train_indices], y[val_indices], y[test_indices]
    
    println("Data split complete:")
    println("  Training: $(length(train_indices)) samples")
    println("  Validation: $(length(val_indices)) samples") 
    println("  Test: $(length(test_indices)) samples")
    
    return (X_train, X_val, X_test, y_train, y_val, y_test)
end

end # module DataPreprocessing

# ═══════════════════════════════════════════════════════════════════════════════
#                           4. MACHINE LEARNING ALGORITHMS
# ═══════════════════════════════════════════════════════════════════════════════

"""
High-performance machine learning implementations leveraging Julia's speed.
"""
module MachineLearning

using LinearAlgebra, Statistics, Random
using MLJ, MLJModels, MLJLinearModels
using DataFrames
using ProgressMeter
using Distributions

export LinearRegression, LogisticRegression, RandomForest, GradientBoosting
export KMeans, PCA, SVM, NeuralNetwork
export cross_validate, hyperparameter_tune, ensemble_predict

"""
High-performance linear regression with analytical solution.
"""
struct LinearRegression{T<:Real}
    coefficients::Vector{T}
    intercept::T
    fitted::Bool
    
    LinearRegression{T}() where T = new{T}(T[], zero(T), false)
end

LinearRegression() = LinearRegression{Float64}()

function fit!(model::LinearRegression{T}, X::AbstractMatrix{T}, y::AbstractVector{T}) where T
    # Add intercept column
    X_with_intercept = hcat(ones(T, size(X, 1)), X)
    
    # Analytical solution: θ = (X'X)^(-1)X'y
    θ = (X_with_intercept' * X_with_intercept) \ (X_with_intercept' * y)
    
    model.intercept = θ[1]
    model.coefficients = θ[2:end]
    model.fitted = true
    
    return model
end

function predict(model::LinearRegression{T}, X::AbstractMatrix{T}) where T
    @assert model.fitted "Model must be fitted before prediction"
    return X * model.coefficients .+ model.intercept
end

"""
Logistic regression with gradient descent optimization.
"""
mutable struct LogisticRegression{T<:Real}
    coefficients::Vector{T}
    intercept::T
    learning_rate::T
    max_iterations::Int
    tolerance::T
    fitted::Bool
    
    function LogisticRegression{T}(; learning_rate::T=T(0.01), 
                                  max_iterations::Int=1000,
                                  tolerance::T=T(1e-6)) where T
        new{T}(T[], zero(T), learning_rate, max_iterations, tolerance, false)
    end
end

LogisticRegression(; kwargs...) = LogisticRegression{Float64}(; kwargs...)

sigmoid(z::T) where T = one(T) / (one(T) + exp(-z))

function fit!(model::LogisticRegression{T}, X::AbstractMatrix{T}, y::AbstractVector{T}) where T
    n, p = size(X)
    
    # Initialize parameters
    model.coefficients = zeros(T, p)
    model.intercept = zero(T)
    
    @showprogress "Training logistic regression..." for iter in 1:model.max_iterations
        # Forward pass
        z = X * model.coefficients .+ model.intercept
        predictions = sigmoid.(z)
        
        # Compute cost
        cost = -mean(y .* log.(predictions .+ eps(T)) .+ 
                    (one(T) .- y) .* log.(one(T) .- predictions .+ eps(T)))
        
        # Compute gradients
        error = predictions .- y
        grad_coef = (X' * error) ./ n
        grad_intercept = mean(error)
        
        # Update parameters
        model.coefficients .-= model.learning_rate .* grad_coef
        model.intercept -= model.learning_rate * grad_intercept
        
        # Check convergence
        if norm(grad_coef) < model.tolerance && abs(grad_intercept) < model.tolerance
            println("Converged after $iter iterations")
            break
        end
    end
    
    model.fitted = true
    return model
end

function predict_proba(model::LogisticRegression{T}, X::AbstractMatrix{T}) where T
    @assert model.fitted "Model must be fitted before prediction"
    z = X * model.coefficients .+ model.intercept
    return sigmoid.(z)
end

function predict(model::LogisticRegression{T}, X::AbstractMatrix{T}) where T
    proba = predict_proba(model, X)
    return Int.(proba .> 0.5)
end

"""
K-Means clustering with K-means++ initialization.
"""
mutable struct KMeans{T<:Real}
    n_clusters::Int
    centroids::Matrix{T}
    labels::Vector{Int}
    max_iterations::Int
    tolerance::T
    fitted::Bool
    
    function KMeans{T}(n_clusters::Int; max_iterations::Int=300, tolerance::T=T(1e-4)) where T
        new{T}(n_clusters, Matrix{T}(undef, 0, 0), Int[], max_iterations, tolerance, false)
    end
end

KMeans(n_clusters::Int; kwargs...) = KMeans{Float64}(n_clusters; kwargs...)

"""
K-means++ initialization for better convergence.
"""
function kmeans_plus_plus_init(X::AbstractMatrix{T}, k::Int) where T
    n, d = size(X)
    centroids = zeros(T, k, d)
    
    # Choose first centroid randomly
    centroids[1, :] = X[rand(1:n), :]
    
    # Choose remaining centroids
    for i in 2:k
        # Compute distances to nearest centroid
        distances = zeros(T, n)
        for j in 1:n
            min_dist = Inf
            for c in 1:i-1
                dist = sum((X[j, :] .- centroids[c, :]) .^ 2)
                min_dist = min(min_dist, dist)
            end
            distances[j] = min_dist
        end
        
        # Choose next centroid with probability proportional to squared distance
        probs = distances ./ sum(distances)
        cumsum_probs = cumsum(probs)
        r = rand()
        next_idx = findfirst(x -> x >= r, cumsum_probs)
        centroids[i, :] = X[next_idx, :]
    end
    
    return centroids
end

function fit!(model::KMeans{T}, X::AbstractMatrix{T}) where T
    n, d = size(X)
    
    # Initialize centroids with K-means++
    model.centroids = kmeans_plus_plus_init(X, model.n_clusters)
    model.labels = zeros(Int, n)
    
    @showprogress "K-means clustering..." for iter in 1:model.max_iterations
        old_centroids = copy(model.centroids)
        
        # Assign points to nearest centroids
        for i in 1:n
            min_dist = Inf
            best_cluster = 1
            
            for k in 1:model.n_clusters
                dist = sum((X[i, :] .- model.centroids[k, :]) .^ 2)
                if dist < min_dist
                    min_dist = dist
                    best_cluster = k
                end
            end
            
            model.labels[i] = best_cluster
        end
        
        # Update centroids
        for k in 1:model.n_clusters
            cluster_points = X[model.labels .== k, :]
            if size(cluster_points, 1) > 0
                model.centroids[k, :] = mean(cluster_points, dims=1)[:]
            end
        end
        
        # Check convergence
        if norm(model.centroids - old_centroids) < model.tolerance
            println("K-means converged after $iter iterations")
            break
        end
    end
    
    model.fitted = true
    return model
end

function predict(model::KMeans{T}, X::AbstractMatrix{T}) where T
    @assert model.fitted "Model must be fitted before prediction"
    
    n = size(X, 1)
    labels = zeros(Int, n)
    
    for i in 1:n
        min_dist = Inf
        best_cluster = 1
        
        for k in 1:model.n_clusters
            dist = sum((X[i, :] .- model.centroids[k, :]) .^ 2)
            if dist < min_dist
                min_dist = dist
                best_cluster = k
            end
        end
        
        labels[i] = best_cluster
    end
    
    return labels
end

"""
Principal Component Analysis with SVD for numerical stability.
"""
mutable struct PCA{T<:Real}
    n_components::Int
    components::Matrix{T}
    explained_variance::Vector{T}
    explained_variance_ratio::Vector{T}
    mean::Vector{T}
    fitted::Bool
    
    function PCA{T}(n_components::Int) where T
        new{T}(n_components, Matrix{T}(undef, 0, 0), T[], T[], T[], false)
    end
end

PCA(n_components::Int) = PCA{Float64}(n_components)

function fit!(model::PCA{T}, X::AbstractMatrix{T}) where T
    n, p = size(X)
    
    # Center the data
    model.mean = mean(X, dims=1)[:]
    X_centered = X .- model.mean'
    
    # Perform SVD
    U, S, V = svd(X_centered)
    
    # Store components and explained variance
    n_comp = min(model.n_components, p, n-1)
    model.components = V[:, 1:n_comp]'
    
    # Calculate explained variance
    total_var = sum(S .^ 2) / (n - 1)
    model.explained_variance = (S[1:n_comp] .^ 2) ./ (n - 1)
    model.explained_variance_ratio = model.explained_variance ./ total_var
    
    model.fitted = true
    
    println("PCA fitted: $(sum(model.explained_variance_ratio) * 100)% variance explained by $n_comp components")
    return model
end

function transform(model::PCA{T}, X::AbstractMatrix{T}) where T
    @assert model.fitted "Model must be fitted before transformation"
    X_centered = X .- model.mean'
    return X_centered * model.components'
end

function fit_transform!(model::PCA{T}, X::AbstractMatrix{T}) where T
    fit!(model, X)
    return transform(model, X)
end

"""
Cross-validation with multiple performance metrics.
"""
function cross_validate(model_constructor, X::AbstractMatrix{T}, y::AbstractVector, 
                       cv_folds::Int=5; metrics=[:accuracy], random_state::Int=42) where T
    
    Random.seed!(random_state)
    n = size(X, 1)
    fold_size = n ÷ cv_folds
    indices = shuffle(1:n)
    
    results = Dict(metric => Float64[] for metric in metrics)
    
    @showprogress "Cross-validation..." for fold in 1:cv_folds
        # Create train/test split for this fold
        test_start = (fold - 1) * fold_size + 1
        test_end = fold == cv_folds ? n : fold * fold_size
        
        test_indices = indices[test_start:test_end]
        train_indices = setdiff(indices, test_indices)
        
        X_train, X_test = X[train_indices, :], X[test_indices, :]
        y_train, y_test = y[train_indices], y[test_indices]
        
        # Train model
        model = model_constructor()
        fit!(model, X_train, y_train)
        
        # Make predictions
        if hasmethod(predict_proba, (typeof(model), typeof(X_test)))
            y_pred_proba = predict_proba(model, X_test)
            y_pred = Int.(y_pred_proba .> 0.5)
        else
            y_pred = predict(model, X_test)
        end
        
        # Calculate metrics
        for metric in metrics
            if metric == :accuracy
                score = mean(y_pred .== y_test)
            elseif metric == :mse
                score = mean((y_pred .- y_test) .^ 2)
            elseif metric == :mae
                score = mean(abs.(y_pred .- y_test))
            elseif metric == :r2
                ss_res = sum((y_test .- y_pred) .^ 2)
                ss_tot = sum((y_test .- mean(y_test)) .^ 2)
                score = 1 - ss_res / ss_tot
            end
            
            push!(results[metric], score)
        end
    end
    
    # Print results
    println("\nCross-validation results:")
    for metric in metrics
        scores = results[metric]
        println("  $(metric): $(round(mean(scores), digits=4)) ± $(round(std(scores), digits=4))")
    end
    
    return results
end

end # module MachineLearning

# ═══════════════════════════════════════════════════════════════════════════════
#                           5. DEEP LEARNING WITH FLUX.jl
# ═══════════════════════════════════════════════════════════════════════════════

"""
High-performance deep learning implementations using Flux.jl.
"""
module DeepLearning

using Flux, MLUtils
using CUDA
using Statistics, Random
using ProgressMeter
using Plots

export NeuralNetwork, ConvolutionalNetwork, RecurrentNetwork, Autoencoder
export train_model!, evaluate_model, create_optimizer, plot_training_history

"""
Flexible neural network architecture builder.
"""
struct NeuralNetwork
    model::Chain
    optimizer
    loss_function
    metrics::Vector{Function}
    training_history::Dict{String, Vector{Float64}}
    
    function NeuralNetwork(input_dim::Int, hidden_dims::Vector{Int}, output_dim::Int;
                          activation=relu, output_activation=identity,
                          dropout_rate::Float64=0.0, use_batch_norm::Bool=false)
        
        layers = []
        
        # Input to first hidden layer
        push!(layers, Dense(input_dim, hidden_dims[1], activation))
        if use_batch_norm
            push!(layers, BatchNorm(hidden_dims[1]))
        end
        if dropout_rate > 0
            push!(layers, Dropout(dropout_rate))
        end
        
        # Hidden layers
        for i in 1:length(hidden_dims)-1
            push!(layers, Dense(hidden_dims[i], hidden_dims[i+1], activation))
            if use_batch_norm
                push!(layers, BatchNorm(hidden_dims[i+1]))
            end
            if dropout_rate > 0
                push!(layers, Dropout(dropout_rate))
            end
        end
        
        # Output layer
        push!(layers, Dense(hidden_dims[end], output_dim, output_activation))
        
        model = Chain(layers...)
        optimizer = Adam(0.001)
        loss_function = Flux.mse
        metrics = [mse_metric]
        training_history = Dict("train_loss" => Float64[], "val_loss" => Float64[])
        
        new(model, optimizer, loss_function, metrics, training_history)
    end
end

# Metric functions
mse_metric(ŷ, y) = mean((ŷ .- y) .^ 2)
mae_metric(ŷ, y) = mean(abs.(ŷ .- y))
accuracy_metric(ŷ, y) = mean(Flux.onecold(ŷ) .== Flux.onecold(y))

"""
Convolutional Neural Network for image data.
"""
struct ConvolutionalNetwork
    model::Chain
    optimizer
    loss_function
    training_history::Dict{String, Vector{Float64}}
    
    function ConvolutionalNetwork(input_shape::Tuple, num_classes::Int;
                                conv_layers::Vector{Tuple{Int,Int}}=[(32,3), (64,3), (128,3)],
                                dense_layers::Vector{Int}=[128, 64])
        
        layers = []
        
        # Convolutional layers
        in_channels = input_shape[3]  # Assuming (height, width, channels, batch)
        
        for (out_channels, kernel_size) in conv_layers
            push!(layers, Conv((kernel_size, kernel_size), in_channels => out_channels, relu))
            push!(layers, BatchNorm(out_channels))
            push!(layers, MaxPool((2, 2)))
            in_channels = out_channels
        end
        
        # Flatten
        push!(layers, Flux.flatten)
        
        # Calculate flattened size (approximate)
        flattened_size = div(input_shape[1], 2^length(conv_layers)) * 
                        div(input_shape[2], 2^length(conv_layers)) * in_channels
        
        # Dense layers
        prev_size = flattened_size
        for hidden_size in dense_layers
            push!(layers, Dense(prev_size, hidden_size, relu))
            push!(layers, Dropout(0.5))
            prev_size = hidden_size
        end
        
        # Output layer
        if num_classes == 1
            push!(layers, Dense(prev_size, 1, sigmoid))  # Binary classification
        else
            push!(layers, Dense(prev_size, num_classes))  # Multi-class
        end
        
        model = Chain(layers...)
        optimizer = Adam(0.001)
        loss_function = num_classes == 1 ? Flux.binarycrossentropy : Flux.crossentropy
        training_history = Dict("train_loss" => Float64[], "val_loss" => Float64[], 
                               "train_acc" => Float64[], "val_acc" => Float64[])
        
        new(model, optimizer, loss_function, training_history)
    end
end

"""
Recurrent Neural Network for sequence data.
"""
struct RecurrentNetwork
    model::Chain
    optimizer
    loss_function
    training_history::Dict{String, Vector{Float64}}
    
    function RecurrentNetwork(input_size::Int, hidden_size::Int, output_size::Int, seq_length::Int;
                            cell_type::Symbol=:LSTM, num_layers::Int=2, dropout_rate::Float64=0.2)
        
        layers = []
        
        # Recurrent layers
        for i in 1:num_layers
            in_size = i == 1 ? input_size : hidden_size
            
            if cell_type == :LSTM
                push!(layers, LSTM(in_size, hidden_size))
            elseif cell_type == :GRU
                push!(layers, GRU(in_size, hidden_size))
            else
                push!(layers, RNN(in_size, hidden_size))
            end
            
            if dropout_rate > 0 && i < num_layers
                push!(layers, Dropout(dropout_rate))
            end
        end
        
        # Output layer
        push!(layers, Dense(hidden_size, output_size))
        
        model = Chain(layers...)
        optimizer = Adam(0.001)
        loss_function = Flux.mse
        training_history = Dict("train_loss" => Float64[], "val_loss" => Float64[])
        
        new(model, optimizer, loss_function, training_history)
    end
end

"""
Autoencoder for dimensionality reduction and feature learning.
"""
struct Autoencoder
    encoder::Chain
    decoder::Chain
    optimizer
    loss_function
    training_history::Dict{String, Vector{Float64}}
    
    function Autoencoder(input_dim::Int, encoding_dims::Vector{Int};
                        activation=relu, final_activation=sigmoid)
        
        # Encoder
        encoder_layers = []
        prev_dim = input_dim
        for dim in encoding_dims
            push!(encoder_layers, Dense(prev_dim, dim, activation))
            prev_dim = dim
        end
        encoder = Chain(encoder_layers...)
        
        # Decoder (reverse of encoder)
        decoder_layers = []
        for i in length(encoding_dims):-1:2
            push!(decoder_layers, Dense(encoding_dims[i], encoding_dims[i-1], activation))
        end
        push!(decoder_layers, Dense(encoding_dims[1], input_dim, final_activation))
        decoder = Chain(decoder_layers...)
        
        optimizer = Adam(0.001)
        loss_function = Flux.mse
        training_history = Dict("train_loss" => Float64[], "val_loss" => Float64[])
        
        new(encoder, decoder, optimizer, loss_function, training_history)
    end
end

# Forward pass for autoencoder
(ae::Autoencoder)(x) = ae.decoder(ae.encoder(x))

"""
Generic training function for all network types.
"""
function train_model!(network, train_data, val_data=nothing; 
                     epochs::Int=100, batch_size::Int=32, 
                     verbose::Bool=true, early_stopping::Bool=true,
                     patience::Int=10, min_delta::Float64=1e-4)
    
    # Setup for GPU if available
    device = gpu_available ? gpu : cpu
    
    if isa(network, NeuralNetwork)
        model = network.model |> device
    elseif isa(network, Union{ConvolutionalNetwork, RecurrentNetwork})
        model = network.model |> device
    elseif isa(network, Autoencoder)
        encoder = network.encoder |> device
        decoder = network.decoder |> device
        model = Chain(encoder, decoder) |> device
    end
    
    # Create data loaders
    train_loader = DataLoader(train_data, batchsize=batch_size, shuffle=true)
    val_loader = val_data !== nothing ? DataLoader(val_data, batchsize=batch_size) : nothing
    
    # Training state
    best_val_loss = Inf
    patience_counter = 0
    
    # Training loop
    progress = Progress(epochs, desc="Training epochs...")
    
    for epoch in 1:epochs
        # Training phase
        train_losses = Float64[]
        
        for (x_batch, y_batch) in train_loader
            x_batch, y_batch = x_batch |> device, y_batch |> device
            
            # Forward and backward pass
            loss, grads = Flux.withgradient(model) do m
                ŷ = m(x_batch)
                network.loss_function(ŷ, y_batch)
            end
            
            # Update parameters
            Flux.update!(network.optimizer, model, grads[1])
            
            push!(train_losses, loss)
        end
        
        train_loss = mean(train_losses)
        push!(network.training_history["train_loss"], train_loss)
        
        # Validation phase
        if val_loader !== nothing
            val_losses = Float64[]
            
            for (x_batch, y_batch) in val_loader
                x_batch, y_batch = x_batch |> device, y_batch |> device
                ŷ = model(x_batch)
                loss = network.loss_function(ŷ, y_batch)
                push!(val_losses, loss)
            end
            
            val_loss = mean(val_losses)
            push!(network.training_history["val_loss"], val_loss)
            
            # Early stopping check
            if early_stopping
                if val_loss < best_val_loss - min_delta
                    best_val_loss = val_loss
                    patience_counter = 0
                else
                    patience_counter += 1
                    if patience_counter >= patience
                        println("\nEarly stopping at epoch $epoch")
                        break
                    end
                end
            end
            
            if verbose && epoch % 10 == 0
                println("Epoch $epoch: Train Loss = $(round(train_loss, digits=4)), Val Loss = $(round(val_loss, digits=4))")
            end
        else
            if verbose && epoch % 10 == 0
                println("Epoch $epoch: Train Loss = $(round(train_loss, digits=4))")
            end
        end
        
        next!(progress)
    end
    
    # Move model back to CPU for compatibility
    if isa(network, NeuralNetwork)
        network.model = network.model |> cpu
    elseif isa(network, Union{ConvolutionalNetwork, RecurrentNetwork})
        network.model = network.model |> cpu
    elseif isa(network, Autoencoder)
        network.encoder = network.encoder |> cpu
        network.decoder = network.decoder |> cpu
    end
    
    return network
end

"""
Evaluate model performance on test data.
"""
function evaluate_model(network, test_data; batch_size::Int=32)
    device = gpu_available ? gpu : cpu
    
    if isa(network, NeuralNetwork)
        model = network.model |> device
    elseif isa(network, Union{ConvolutionalNetwork, RecurrentNetwork})
        model = network.model |> device
    elseif isa(network, Autoencoder)
        encoder = network.encoder |> device
        decoder = network.decoder |> device
        model = Chain(encoder, decoder) |> device
    end
    
    test_loader = DataLoader(test_data, batchsize=batch_size)
    
    total_loss = 0.0
    total_samples = 0
    predictions = []
    targets = []
    
    for (x_batch, y_batch) in test_loader
        x_batch, y_batch = x_batch |> device, y_batch |> device
        
        ŷ = model(x_batch)
        loss = network.loss_function(ŷ, y_batch)
        
        batch_size_actual = size(x_batch)[end]
        total_loss += loss * batch_size_actual
        total_samples += batch_size_actual
        
        # Store predictions and targets for additional metrics
        push!(predictions, ŷ |> cpu)
        push!(targets, y_batch |> cpu)
    end
    
    avg_loss = total_loss / total_samples
    
    # Concatenate all predictions and targets
    all_predictions = vcat(predictions...)
    all_targets = vcat(targets...)
    
    # Calculate additional metrics
    metrics = Dict("loss" => avg_loss)
    
    # For regression tasks
    if size(all_predictions, 1) == 1 || length(size(all_predictions)) == 1
        mse = mean((all_predictions .- all_targets) .^ 2)
        mae = mean(abs.(all_predictions .- all_targets))
        
        # R-squared
        ss_res = sum((all_targets .- all_predictions) .^ 2)
        ss_tot = sum((all_targets .- mean(all_targets)) .^ 2)
        r2 = 1 - ss_res / ss_tot
        
        metrics["mse"] = mse
        metrics["mae"] = mae
        metrics["r2"] = r2
    else
        # For classification tasks
        predicted_classes = Flux.onecold(all_predictions)
        true_classes = Flux.onecold(all_targets)
        accuracy = mean(predicted_classes .== true_classes)
        metrics["accuracy"] = accuracy
    end
    
    return metrics
end

"""
Plot training history for visualization.
"""
function plot_training_history(network; save_path::String="")
    history = network.training_history
    
    if haskey(history, "val_loss")
        # Plot training and validation loss
        p1 = plot(history["train_loss"], label="Training Loss", 
                 title="Model Loss", xlabel="Epoch", ylabel="Loss")
        plot!(p1, history["val_loss"], label="Validation Loss")
        
        if haskey(history, "train_acc")
            # Plot training and validation accuracy
            p2 = plot(history["train_acc"], label="Training Accuracy",
                     title="Model Accuracy", xlabel="Epoch", ylabel="Accuracy")
            plot!(p2, history["val_acc"], label="Validation Accuracy")
            
            final_plot = plot(p1, p2, layout=(2,1), size=(800, 600))
        else
            final_plot = p1
        end
    else
        # Plot only training loss
        final_plot = plot(history["train_loss"], label="Training Loss",
                         title="Training Loss", xlabel="Epoch", ylabel="Loss")
    end
    
    if !isempty(save_path)
        savefig(final_plot, save_path)
        println("Training history plot saved to: $save_path")
    end
    
    return final_plot
end

"""
Create optimizers with different configurations.
"""
function create_optimizer(optimizer_type::Symbol; learning_rate::Float64=0.001, kwargs...)
    if optimizer_type == :adam
        return Adam(learning_rate)
    elseif optimizer_type == :sgd
        momentum = get(kwargs, :momentum, 0.9)
        return Momentum(learning_rate, momentum)
    elseif optimizer_type == :rmsprop
        return RMSProp(learning_rate)
    elseif optimizer_type == :adagrad
        return AdaGrad(learning_rate)
    else
        throw(ArgumentError("Unknown optimizer type: $optimizer_type"))
    end
end

end # module DeepLearning

# ═══════════════════════════════════════════════════════════════════════════════
#                           6. PARALLEL AND DISTRIBUTED COMPUTING
# ═══════════════════════════════════════════════════════════════════════════════

"""
Parallel computing utilities for scaling ML algorithms.
"""
module ParallelComputing

using Distributed, SharedArrays, ThreadsX
using Statistics, Random
using ProgressMeter

export parallel_cross_validation, distributed_grid_search, parallel_bootstrap
export threaded_matrix_operations, distributed_kmeans

"""
Parallel cross-validation with distributed computing.
"""
function parallel_cross_validation(model_func, X, y, cv_folds::Int=5; 
                                 metrics=[:accuracy], random_state::Int=42)
    
    Random.seed!(random_state)
    n = size(X, 1)
    fold_size = n ÷ cv_folds
    indices = shuffle(1:n)
    
    # Create fold indices
    fold_ranges = [(i-1)*fold_size+1 : (i==cv_folds ? n : i*fold_size) for i in 1:cv_folds]
    
    # Distribute data to workers
    @everywhere X_shared = $X
    @everywhere y_shared = $y
    @everywhere model_func_shared = $model_func
    @everywhere indices_shared = $indices
    
    # Parallel execution of CV folds
    results = @distributed (append!) for fold in 1:cv_folds
        # Get test indices for this fold
        test_indices = indices_shared[fold_ranges[fold]]
        train_indices = setdiff(indices_shared, test_indices)
        
        # Split data
        X_train = X_shared[train_indices, :]
        X_test = X_shared[test_indices, :]
        y_train = y_shared[train_indices]
        y_test = y_shared[test_indices]
        
        # Train model
        model = model_func_shared()
        fit!(model, X_train, y_train)
        
        # Make predictions and calculate metrics
        y_pred = predict(model, X_test)
        
        fold_results = Dict()
        for metric in metrics
            if metric == :accuracy
                score = mean(y_pred .== y_test)
            elseif metric == :mse
                score = mean((y_pred .- y_test) .^ 2)
            elseif metric == :mae
                score = mean(abs.(y_pred .- y_test))
            end
            fold_results[metric] = score
        end
        
        [fold_results]
    end
    
    # Aggregate results
    aggregated = Dict()
    for metric in metrics
        scores = [result[metric] for result in results]
        aggregated[metric] = (mean=mean(scores), std=std(scores), scores=scores)
    end
    
    return aggregated
end

"""
Distributed grid search for hyperparameter optimization.
"""
function distributed_grid_search(model_func, param_grid::Dict, X, y; 
                                cv_folds::Int=3, scoring::Symbol=:accuracy,
                                verbose::Bool=true)
    
    # Generate parameter combinations
    param_names = collect(keys(param_grid))
    param_values = collect(values(param_grid))
    param_combinations = vec(collect(Iterators.product(param_values...)))
    
    n_combinations = length(param_combinations)
    println("Grid search with $n_combinations parameter combinations")
    
    # Distribute data and functions
    @everywhere X_grid = $X
    @everywhere y_grid = $y
    @everywhere model_func_grid = $model_func
    @everywhere param_names_grid = $param_names
    
    # Parallel grid search
    results = @distributed (append!) for i in 1:n_combinations
        params = param_combinations[i]
        param_dict = Dict(zip(param_names_grid, params))
        
        # Create model with current parameters
        model = model_func_grid(; param_dict...)
        
        # Perform cross-validation
        cv_results = parallel_cross_validation(() -> model_func_grid(; param_dict...),
                                             X_grid, y_grid, cv_folds, 
                                             metrics=[scoring])
        
        score = cv_results[scoring].mean
        
        [(params=param_dict, score=score, cv_std=cv_results[scoring].std)]
    end
    
    # Find best parameters
    best_idx = argmax([r.score for r in results])
    best_result = results[best_idx]
    
    if verbose
        println("Best parameters: $(best_result.params)")
        println("Best cross-validation score: $(round(best_result.score, digits=4)) ± $(round(best_result.cv_std, digits=4))")
    end
    
    return (best_params=best_result.params, best_score=best_result.score, all_results=results)
end

"""
Parallel bootstrap sampling for statistical inference.
"""
function parallel_bootstrap(statistic_func, data, n_bootstrap::Int=1000; 
                          confidence_level::Float64=0.95, random_state::Int=42)
    
    Random.seed!(random_state)
    n_samples = size(data, 1)
    
    # Generate bootstrap sample indices
    bootstrap_indices = [rand(1:n_samples, n_samples) for _ in 1:n_bootstrap]
    
    @everywhere data_bootstrap = $data
    @everywhere statistic_func_bootstrap = $statistic_func
    
    # Parallel bootstrap computation
    bootstrap_stats = @distributed (append!) for indices in bootstrap_indices
        bootstrap_sample = data_bootstrap[indices, :]
        stat = statistic_func_bootstrap(bootstrap_sample)
        [stat]
    end
    
    # Calculate confidence intervals
    α = 1 - confidence_level
    lower_percentile = (α/2) * 100
    upper_percentile = (1 - α/2) * 100
    
    ci_lower = percentile(bootstrap_stats, lower_percentile)
    ci_upper = percentile(bootstrap_stats, upper_percentile)
    
    return (
        statistic=mean(bootstrap_stats),
        ci_lower=ci_lower,
        ci_upper=ci_upper,
        bootstrap_distribution=bootstrap_stats
    )
end

"""
Threaded matrix operations for improved performance.
"""
function threaded_matrix_multiply(A::AbstractMatrix{T}, B::AbstractMatrix{T}) where T
    m, k = size(A)
    k2, n = size(B)
    @assert k == k2 "Matrix dimensions must match"
    
    C = zeros(T, m, n)
    
    ThreadsX.foreach(1:m) do i
        for j in 1:n
            for l in 1:k
                C[i, j] += A[i, l] * B[l, j]
            end
        end
    end
    
    return C
end

"""
Threaded element-wise operations.
"""
function threaded_map(f, arrays...)
    result = similar(arrays[1])
    ThreadsX.map!(f, result, arrays...)
    return result
end

"""
Distributed K-means clustering for large datasets.
"""
function distributed_kmeans(X::AbstractMatrix{T}, k::Int; 
                          max_iterations::Int=300, tolerance::T=T(1e-4),
                          n_init::Int=10) where T
    
    n, d = size(X)
    best_centroids = nothing
    best_inertia = Inf
    
    # Try multiple initializations in parallel
    @everywhere X_kmeans = $X
    @everywhere k_kmeans = $k
    @everywhere max_iterations_kmeans = $max_iterations
    @everywhere tolerance_kmeans = $tolerance
    
    results = @distributed (append!) for init in 1:n_init
        # K-means++ initialization
        centroids = kmeans_plus_plus_init(X_kmeans, k_kmeans)
        
        # Lloyd's algorithm
        for iter in 1:max_iterations_kmeans
            old_centroids = copy(centroids)
            
            # Assign points to nearest centroids (parallel)
            labels = ThreadsX.map(1:size(X_kmeans, 1)) do i
                min_dist = Inf
                best_cluster = 1
                
                for j in 1:k_kmeans
                    dist = sum((X_kmeans[i, :] .- centroids[j, :]) .^ 2)
                    if dist < min_dist
                        min_dist = dist
                        best_cluster = j
                    end
                end
                
                best_cluster
            end
            
            # Update centroids
            for j in 1:k_kmeans
                cluster_points = X_kmeans[labels .== j, :]
                if size(cluster_points, 1) > 0
                    centroids[j, :] = mean(cluster_points, dims=1)[:]
                end
            end
            
            # Check convergence
            if norm(centroids - old_centroids) < tolerance_kmeans
                break
            end
        end
        
        # Calculate inertia
        inertia = 0.0
        for i in 1:size(X_kmeans, 1)
            min_dist = Inf
            for j in 1:k_kmeans
                dist = sum((X_kmeans[i, :] .- centroids[j, :]) .^ 2)
                min_dist = min(min_dist, dist)
            end
            inertia += min_dist
        end
        
        [(centroids=centroids, inertia=inertia)]
    end
    
    # Select best result
    best_idx = argmin([r.inertia for r in results])
    best_result = results[best_idx]
    
    return (centroids=best_result.centroids, inertia=best_result.inertia)
end

end # module ParallelComputing

# ═══════════════════════════════════════════════════════════════════════════════
#                           7. TIME SERIES ANALYSIS AND FORECASTING
# ═══════════════════════════════════════════════════════════════════════════════

"""
Advanced time series analysis with Julia's performance advantages.
"""
module TimeSeriesAnalysis

using Statistics, LinearAlgebra, Random
using DSP, Distributions
using Plots
using ProgressMeter

export TimeSeriesModel, ARIMA, ExponentialSmoothing, StateSpaceModel
export seasonal_decompose, detect_changepoints, forecast_accuracy

"""
Time series decomposition using STL (Seasonal and Trend decomposition using Loess).
"""
function seasonal_decompose(y::Vector{T}, period::Int; 
                          trend_window::Union{Int,Nothing}=nothing,
                          seasonal_window::Union{Int,Nothing}=nothing) where T<:Real
    
    n = length(y)
    
    # Default parameters
    if trend_window === nothing
        trend_window = ceil(Int, 1.5 * period / (1 - 1.5/period))
    end
    if seasonal_window === nothing
        seasonal_window = 7  # Default seasonal smoothing
    end
    
    # Initialize components
    trend = zeros(T, n)
    seasonal = zeros(T, n)
    remainder = zeros(T, n)
    
    # Simple trend extraction using moving average
    half_window = trend_window ÷ 2
    for i in (half_window+1):(n-half_window)
        trend[i] = mean(y[(i-half_window):(i+half_window)])
    end
    
    # Extrapolate trend at boundaries
    trend[1:half_window] .= trend[half_window+1]
    trend[(n-half_window+1):n] .= trend[n-half_window]
    
    # Detrend the series
    detrended = y .- trend
    
    # Extract seasonal component
    seasonal_matrix = reshape(detrended[1:(period * (n ÷ period))], period, n ÷ period)
    seasonal_pattern = vec(mean(seasonal_matrix, dims=2))
    
    # Repeat seasonal pattern
    for i in 1:n
        seasonal[i] = seasonal_pattern[((i-1) % period) + 1]
    end
    
    # Calculate remainder
    remainder = y .- trend .- seasonal
    
    return (trend=trend, seasonal=seasonal, remainder=remainder, original=y)
end

"""
ARIMA model implementation with maximum likelihood estimation.
"""
mutable struct ARIMA{T<:Real}
    p::Int  # AR order
    d::Int  # Differencing order
    q::Int  # MA order
    ar_params::Vector{T}
    ma_params::Vector{T}
    intercept::T
    sigma2::T
    fitted_values::Vector{T}
    residuals::Vector{T}
    aic::T
    bic::T
    fitted::Bool
    
    function ARIMA{T}(p::Int, d::Int, q::Int) where T<:Real
        new{T}(p, d, q, T[], T[], zero(T), zero(T), T[], T[], 
               T(Inf), T(Inf), false)
    end
end

ARIMA(p::Int, d::Int, q::Int) = ARIMA{Float64}(p, d, q)

"""
Difference a time series to achieve stationarity.
"""
function difference_series(y::Vector{T}, d::Int) where T<:Real
    result = copy(y)
    for _ in 1:d
        result = diff(result)
    end
    return result
end

"""
Fit ARIMA model using conditional sum of squares.
"""
function fit!(model::ARIMA{T}, y::Vector{T}) where T<:Real
    n = length(y)
    
    # Apply differencing
    y_diff = difference_series(y, model.d)
    n_diff = length(y_diff)
    
    # Initialize parameters
    initial_params = [zeros(T, model.p); zeros(T, model.q); mean(y_diff)]
    
    # Define log-likelihood function
    function log_likelihood(params)
        ar_params = params[1:model.p]
        ma_params = params[model.p+1:model.p+model.q]
        intercept = params[end]
        
        # Initialize residuals and fitted values
        residuals = zeros(T, n_diff)
        fitted_vals = zeros(T, n_diff)
        
        # Calculate residuals using recursive approach
        for t in max(model.p, model.q)+1:n_diff
            # AR component
            ar_term = sum(ar_params[i] * y_diff[t-i] for i in 1:model.p)
            
            # MA component
            ma_term = sum(ma_params[i] * residuals[t-i] for i in 1:model.q)
            
            fitted_vals[t] = intercept + ar_term + ma_term
            residuals[t] = y_diff[t] - fitted_vals[t]
        end
        
        # Calculate log-likelihood
        sigma2 = var(residuals[max(model.p, model.q)+1:end])
        valid_residuals = residuals[max(model.p, model.q)+1:end]
        n_valid = length(valid_residuals)
        
        if sigma2 <= 0
            return T(Inf)
        end
        
        ll = -0.5 * n_valid * log(2π * sigma2) - 0.5 * sum(valid_residuals.^2) / sigma2
        return -ll  # Return negative for minimization
    end
    
    # Optimize parameters (simple grid search for demonstration)
    best_params = initial_params
    best_ll = log_likelihood(initial_params)
    
    # Simple optimization loop
    for iter in 1:100
        # Random perturbation
        candidate = best_params + 0.01 * randn(T, length(best_params))
        
        # Check stability constraints for AR parameters
        ar_candidate = candidate[1:model.p]
        if model.p > 0
            # Simple stability check: |ar_params| < 1
            if any(abs.(ar_candidate) .>= 0.99)
                continue
            end
        end
        
        ll = log_likelihood(candidate)
        if ll < best_ll
            best_ll = ll
            best_params = candidate
        end
    end
    
    # Store fitted parameters
    model.ar_params = best_params[1:model.p]
    model.ma_params = best_params[model.p+1:model.p+model.q]
    model.intercept = best_params[end]
    
    # Calculate final residuals and fitted values
    residuals = zeros(T, n_diff)
    fitted_vals = zeros(T, n_diff)
    
    for t in max(model.p, model.q)+1:n_diff
        ar_term = sum(model.ar_params[i] * y_diff[t-i] for i in 1:model.p)
        ma_term = sum(model.ma_params[i] * residuals[t-i] for i in 1:model.q)
        fitted_vals[t] = model.intercept + ar_term + ma_term
        residuals[t] = y_diff[t] - fitted_vals[t]
    end
    
    model.fitted_values = fitted_vals
    model.residuals = residuals
    model.sigma2 = var(residuals[max(model.p, model.q)+1:end])
    
    # Calculate information criteria
    k = model.p + model.q + 1  # Number of parameters
    n_eff = n_diff - max(model.p, model.q)
    model.aic = 2 * k + 2 * best_ll
    model.bic = k * log(n_eff) + 2 * best_ll
    
    model.fitted = true
    return model
end

"""
Forecast using fitted ARIMA model.
"""
function forecast(model::ARIMA{T}, n_ahead::Int; confidence_level::T=T(0.95)) where T<:Real
    @assert model.fitted "Model must be fitted before forecasting"
    
    forecasts = zeros(T, n_ahead)
    forecast_var = zeros(T, n_ahead)
    
    # Use last values for initialization
    last_values = model.fitted_values[end-max(model.p-1, 0):end]
    last_residuals = model.residuals[end-max(model.q-1, 0):end]
    
    for h in 1:n_ahead
        # AR component
        ar_term = T(0)
        for i in 1:min(model.p, length(last_values))
            if h <= i
                ar_term += model.ar_params[i] * forecasts[h-i]
            else
                ar_term += model.ar_params[i] * last_values[end-(i-h)]
            end
        end
        
        # MA component (only for h=1, as future errors are unknown)
        ma_term = T(0)
        if h == 1
            for i in 1:min(model.q, length(last_residuals))
                ma_term += model.ma_params[i] * last_residuals[end-(i-1)]
            end
        end
        
        forecasts[h] = model.intercept + ar_term + ma_term
        
        # Forecast variance (simplified)
        if h == 1
            forecast_var[h] = model.sigma2
        else
            forecast_var[h] = model.sigma2 * h  # Simplified variance calculation
        end
    end
    
    # Calculate confidence intervals
    z_alpha = quantile(Normal(), 1 - (1 - confidence_level) / 2)
    forecast_se = sqrt.(forecast_var)
    
    lower_ci = forecasts .- z_alpha .* forecast_se
    upper_ci = forecasts .+ z_alpha .* forecast_se
    
    return (forecast=forecasts, lower_ci=lower_ci, upper_ci=upper_ci, se=forecast_se)
end

"""
Exponential smoothing models (Simple, Holt, Holt-Winters).
"""
mutable struct ExponentialSmoothing{T<:Real}
    model_type::Symbol  # :simple, :holt, :holt_winters
    alpha::T  # Level smoothing parameter
    beta::T   # Trend smoothing parameter
    gamma::T  # Seasonal smoothing parameter
    level::T
    trend::T
    seasonal::Vector{T}
    period::Int
    fitted_values::Vector{T}
    fitted::Bool
    
    function ExponentialSmoothing{T}(model_type::Symbol; period::Int=12) where T<:Real
        new{T}(model_type, T(0.3), T(0.1), T(0.1), zero(T), zero(T), 
               T[], period, T[], false)
    end
end

ExponentialSmoothing(model_type::Symbol; kwargs...) = ExponentialSmoothing{Float64}(model_type; kwargs...)

function fit!(model::ExponentialSmoothing{T}, y::Vector{T}) where T<:Real
    n = length(y)
    
    # Initialize level
    model.level = y[1]
    
    # Initialize trend (for Holt and Holt-Winters)
    if model.model_type in [:holt, :holt_winters]
        model.trend = y[2] - y[1]
    end
    
    # Initialize seasonal components (for Holt-Winters)
    if model.model_type == :holt_winters
        # Simple seasonal initialization
        model.seasonal = zeros(T, model.period)
        for i in 1:model.period
            if i <= n
                model.seasonal[i] = y[i] / model.level - 1
            end
        end
    end
    
    model.fitted_values = zeros(T, n)
    
    # Fit the model
    for t in 1:n
        if model.model_type == :simple
            # Simple exponential smoothing
            if t == 1
                model.fitted_values[t] = model.level
            else
                prev_level = model.level
                model.level = model.alpha * y[t] + (1 - model.alpha) * prev_level
                model.fitted_values[t] = prev_level
            end
            
        elseif model.model_type == :holt
            # Holt's linear trend method
            if t == 1
                model.fitted_values[t] = model.level
            else
                prev_level = model.level
                prev_trend = model.trend
                
                model.level = model.alpha * y[t] + (1 - model.alpha) * (prev_level + prev_trend)
                model.trend = model.beta * (model.level - prev_level) + (1 - model.beta) * prev_trend
                
                model.fitted_values[t] = prev_level + prev_trend
            end
            
        elseif model.model_type == :holt_winters
            # Holt-Winters seasonal method
            seasonal_idx = ((t - 1) % model.period) + 1
            
            if t <= model.period
                model.fitted_values[t] = model.level * (1 + model.seasonal[seasonal_idx])
            else
                prev_level = model.level
                prev_trend = model.trend
                prev_seasonal = model.seasonal[seasonal_idx]
                
                model.level = model.alpha * y[t] / (1 + prev_seasonal) + 
                             (1 - model.alpha) * (prev_level + prev_trend)
                model.trend = model.beta * (model.level - prev_level) + 
                             (1 - model.beta) * prev_trend
                model.seasonal[seasonal_idx] = model.gamma * (y[t] / model.level - 1) + 
                                              (1 - model.gamma) * prev_seasonal
                
                model.fitted_values[t] = (prev_level + prev_trend) * (1 + prev_seasonal)
            end
        end
    end
    
    model.fitted = true
    return model
end

"""
Forecast using exponential smoothing model.
"""
function forecast(model::ExponentialSmoothing{T}, n_ahead::Int) where T<:Real
    @assert model.fitted "Model must be fitted before forecasting"
    
    forecasts = zeros(T, n_ahead)
    
    for h in 1:n_ahead
        if model.model_type == :simple
            forecasts[h] = model.level
            
        elseif model.model_type == :holt
            forecasts[h] = model.level + h * model.trend
            
        elseif model.model_type == :holt_winters
            seasonal_idx = ((h - 1) % model.period) + 1
            forecasts[h] = (model.level + h * model.trend) * (1 + model.seasonal[seasonal_idx])
        end
    end
    
    return forecasts
end

"""
Change point detection using PELT (Pruned Exact Linear Time) algorithm.
"""
function detect_changepoints(y::Vector{T}; penalty::T=T(2.0), min_size::Int=5) where T<:Real
    n = length(y)
    
    # Cost function (sum of squared errors)
    function segment_cost(start::Int, end::Int)
        if end <= start
            return T(Inf)
        end
        
        segment = y[start:end]
        μ = mean(segment)
        return sum((segment .- μ) .^ 2)
    end
    
    # Dynamic programming arrays
    F = fill(T(Inf), n + 1)  # Optimal cost up to time t
    F[1] = T(0)
    changepoints = Vector{Int}[]
    
    # PELT algorithm (simplified)
    for t in 2:(n + 1)
        candidates = Int[]
        costs = T[]
        
        for s in 1:(t - min_size)
            if F[s] < Inf
                cost = F[s] + segment_cost(s, t - 1) + penalty
                push!(candidates, s)
                push!(costs, cost)
            end
        end
        
        if !isempty(costs)
            min_idx = argmin(costs)
            F[t] = costs[min_idx]
            
            if min_idx > 1  # Found a changepoint
                push!(changepoints, candidates[min_idx])
            end
        end
    end
    
    # Extract final changepoints
    final_changepoints = unique(sort([cp for cp in changepoints if cp > 1 && cp < n]))
    
    return final_changepoints
end

"""
Calculate forecast accuracy metrics.
"""
function forecast_accuracy(actual::Vector{T}, predicted::Vector{T}) where T<:Real
    @assert length(actual) == length(predicted) "Vectors must have same length"
    
    n = length(actual)
    errors = actual .- predicted
    
    metrics = Dict{String, T}()
    
    # Mean Error
    metrics["ME"] = mean(errors)
    
    # Mean Absolute Error
    metrics["MAE"] = mean(abs.(errors))
    
    # Mean Squared Error
    metrics["MSE"] = mean(errors .^ 2)
    
    # Root Mean Squared Error
    metrics["RMSE"] = sqrt(metrics["MSE"])
    
    # Mean Absolute Percentage Error
    non_zero_actual = actual[actual .!= 0]
    non_zero_predicted = predicted[actual .!= 0]
    if !isempty(non_zero_actual)
        metrics["MAPE"] = mean(abs.((non_zero_actual .- non_zero_predicted) ./ non_zero_actual)) * 100
    else
        metrics["MAPE"] = T(Inf)
    end
    
    # Mean Absolute Scaled Error (MASE)
    if n > 1
        naive_errors = abs.(actual[2:end] .- actual[1:end-1])
        mae_naive = mean(naive_errors)
        metrics["MASE"] = metrics["MAE"] / mae_naive
    else
        metrics["MASE"] = T(Inf)
    end
    
    return metrics
end

end # module TimeSeriesAnalysis

# ═══════════════════════════════════════════════════════════════════════════════
#                           8. OPTIMIZATION AND NUMERICAL METHODS
# ═══════════════════════════════════════════════════════════════════════════════

"""
Advanced optimization algorithms for ML parameter estimation.
"""
module OptimizationMethods

using LinearAlgebra, Random
using Optim, ForwardDiff
using Statistics

export GradientDescent, AdaptiveGradient, LBFGS, PSO, GeneticAlgorithm
export optimize_function, constrained_optimization

"""
Advanced gradient descent with adaptive learning rates.
"""
mutable struct AdaptiveGradient{T<:Real}
    learning_rate::T
    decay_rate::T
    epsilon::T
    accumulated_gradients::Vector{T}
    iteration::Int
    
    function AdaptiveGradient{T}(learning_rate::T=T(0.01), decay_rate::T=T(0.9), 
                               epsilon::T=T(1e-8)) where T<:Real
        new{T}(learning_rate, decay_rate, epsilon, T[], 0)
    end
end

AdaptiveGradient(; kwargs...) = AdaptiveGradient{Float64}(; kwargs...)

function update!(optimizer::AdaptiveGradient{T}, parameters::Vector{T}, 
                gradients::Vector{T}) where T<:Real
    
    optimizer.iteration += 1
    
    if isempty(optimizer.accumulated_gradients)
        optimizer.accumulated_gradients = zeros(T, length(parameters))
    end
    
    # AdaGrad update
    optimizer.accumulated_gradients .+= gradients .^ 2
    
    # Adaptive learning rate
    adaptive_lr = optimizer.learning_rate ./ 
                 (sqrt.(optimizer.accumulated_gradients) .+ optimizer.epsilon)
    
    # Update parameters
    parameters .-= adaptive_lr .* gradients
    
    return parameters
end

"""
Particle Swarm Optimization for global optimization.
"""
mutable struct PSO{T<:Real}
    n_particles::Int
    n_dimensions::Int
    bounds::Tuple{Vector{T}, Vector{T}}
    inertia_weight::T
    cognitive_coeff::T
    social_coeff::T
    particles::Matrix{T}
    velocities::Matrix{T}
    personal_best::Matrix{T}
    personal_best_fitness::Vector{T}
    global_best::Vector{T}
    global_best_fitness::T
    iteration::Int
    max_iterations::Int
    
    function PSO{T}(n_particles::Int, bounds::Tuple{Vector{T}, Vector{T}};
                   inertia_weight::T=T(0.7), cognitive_coeff::T=T(1.5),
                   social_coeff::T=T(1.5), max_iterations::Int=1000) where T<:Real
        
        n_dimensions = length(bounds[1])
        
        # Initialize particles randomly within bounds
        particles = zeros(T, n_particles, n_dimensions)
        for i in 1:n_particles
            for j in 1:n_dimensions
                particles[i, j] = bounds[1][j] + rand(T) * (bounds[2][j] - bounds[1][j])
            end
        end
        
        # Initialize velocities
        velocities = zeros(T, n_particles, n_dimensions)
        
        # Initialize personal bests
        personal_best = copy(particles)
        personal_best_fitness = fill(T(Inf), n_particles)
        
        # Initialize global best
        global_best = zeros(T, n_dimensions)
        global_best_fitness = T(Inf)
        
        new{T}(n_particles, n_dimensions, bounds, inertia_weight, cognitive_coeff,
               social_coeff, particles, velocities, personal_best, personal_best_fitness,
               global_best, global_best_fitness, 0, max_iterations)
    end
end

PSO(n_particles::Int, bounds; kwargs...) = PSO{Float64}(n_particles, bounds; kwargs...)

function optimize!(pso::PSO{T}, objective_function) where T<:Real
    
    for iteration in 1:pso.max_iterations
        pso.iteration = iteration
        
        # Evaluate fitness for each particle
        for i in 1:pso.n_particles
            position = pso.particles[i, :]
            fitness = objective_function(position)
            
            # Update personal best
            if fitness < pso.personal_best_fitness[i]
                pso.personal_best_fitness[i] = fitness
                pso.personal_best[i, :] = position
                
                # Update global best
                if fitness < pso.global_best_fitness
                    pso.global_best_fitness = fitness
                    pso.global_best = copy(position)
                end
            end
        end
        
        # Update velocities and positions
        for i in 1:pso.n_particles
            for j in 1:pso.n_dimensions
                r1, r2 = rand(T), rand(T)
                
                # Velocity update
                pso.velocities[i, j] = pso.inertia_weight * pso.velocities[i, j] +
                                      pso.cognitive_coeff * r1 * (pso.personal_best[i, j] - pso.particles[i, j]) +
                                      pso.social_coeff * r2 * (pso.global_best[j] - pso.particles[i, j])
                
                # Position update
                pso.particles[i, j] += pso.velocities[i, j]
                
                # Enforce bounds
                pso.particles[i, j] = clamp(pso.particles[i, j], pso.bounds[1][j], pso.bounds[2][j])
            end
        end
        
        # Print progress
        if iteration % 100 == 0
            println("Iteration $iteration: Best fitness = $(pso.global_best_fitness)")
        end
    end
    
    return (best_solution=pso.global_best, best_fitness=pso.global_best_fitness)
end

"""
Genetic Algorithm for evolutionary optimization.
"""
mutable struct GeneticAlgorithm{T<:Real}
    population_size::Int
    n_genes::Int
    bounds::Tuple{Vector{T}, Vector{T}}
    mutation_rate::T
    crossover_rate::T
    elitism_rate::T
    population::Matrix{T}
    fitness::Vector{T}
    generation::Int
    max_generations::Int
    
    function GeneticAlgorithm{T}(population_size::Int, bounds::Tuple{Vector{T}, Vector{T}};
                                mutation_rate::T=T(0.1), crossover_rate::T=T(0.8),
                                elitism_rate::T=T(0.1), max_generations::Int=1000) where T<:Real
        
        n_genes = length(bounds[1])
        
        # Initialize population randomly
        population = zeros(T, population_size, n_genes)
        for i in 1:population_size
            for j in 1:n_genes
                population[i, j] = bounds[1][j] + rand(T) * (bounds[2][j] - bounds[1][j])
            end
        end
        
        fitness = fill(T(Inf), population_size)
        
        new{T}(population_size, n_genes, bounds, mutation_rate, crossover_rate,
               elitism_rate, population, fitness, 0, max_generations)
    end
end

GeneticAlgorithm(population_size::Int, bounds; kwargs...) = 
    GeneticAlgorithm{Float64}(population_size, bounds; kwargs...)

function tournament_selection(ga::GeneticAlgorithm{T}, tournament_size::Int=3) where T<:Real
    # Select random individuals for tournament
    tournament_indices = rand(1:ga.population_size, tournament_size)
    tournament_fitness = ga.fitness[tournament_indices]
    
    # Return index of best individual in tournament
    best_idx = argmin(tournament_fitness)
    return tournament_indices[best_idx]
end

function crossover(parent1::Vector{T}, parent2::Vector{T}) where T<:Real
    n = length(parent1)
    crossover_point = rand(1:n-1)
    
    child1 = [parent1[1:crossover_point]; parent2[crossover_point+1:end]]
    child2 = [parent2[1:crossover_point]; parent1[crossover_point+1:end]]
    
    return child1, child2
end

function mutate!(individual::Vector{T}, bounds::Tuple{Vector{T}, Vector{T}}, 
                mutation_rate::T) where T<:Real
    
    for i in 1:length(individual)
        if rand(T) < mutation_rate
            # Gaussian mutation
            mutation_strength = T(0.1) * (bounds[2][i] - bounds[1][i])
            individual[i] += randn(T) * mutation_strength
            
            # Enforce bounds
            individual[i] = clamp(individual[i], bounds[1][i], bounds[2][i])
        end
    end
    
    return individual
end

function evolve!(ga::GeneticAlgorithm{T}, objective_function) where T<:Real
    
    # Evaluate initial population
    for i in 1:ga.population_size
        ga.fitness[i] = objective_function(ga.population[i, :])
    end
    
    for generation in 1:ga.max_generations
        ga.generation = generation
        
        # Create new population
        new_population = zeros(T, ga.population_size, ga.n_genes)
        new_fitness = zeros(T, ga.population_size)
        
        # Elitism: keep best individuals
        n_elite = round(Int, ga.elitism_rate * ga.population_size)
        elite_indices = sortperm(ga.fitness)[1:n_elite]
        
        for i in 1:n_elite
            new_population[i, :] = ga.population[elite_indices[i], :]
            new_fitness[i] = ga.fitness[elite_indices[i]]
        end
        
        # Generate offspring
        offspring_count = n_elite
        while offspring_count < ga.population_size
            # Selection
            parent1_idx = tournament_selection(ga)
            parent2_idx = tournament_selection(ga)
            
            parent1 = ga.population[parent1_idx, :]
            parent2 = ga.population[parent2_idx, :]
            
            # Crossover
            if rand(T) < ga.crossover_rate
                child1, child2 = crossover(parent1, parent2)
            else
                child1, child2 = copy(parent1), copy(parent2)
            end
            
            # Mutation
            mutate!(child1, ga.bounds, ga.mutation_rate)
            mutate!(child2, ga.bounds, ga.mutation_rate)
            
            # Add to new population
            if offspring_count + 1 <= ga.population_size
                new_population[offspring_count + 1, :] = child1
                new_fitness[offspring_count + 1] = objective_function(child1)
                offspring_count += 1
            end
            
            if offspring_count + 1 <= ga.population_size
                new_population[offspring_count + 1, :] = child2
                new_fitness[offspring_count + 1] = objective_function(child2)
                offspring_count += 1
            end
        end
        
        # Replace population
        ga.population = new_population
        ga.fitness = new_fitness
        
        # Print progress
        if generation % 100 == 0
            best_fitness = minimum(ga.fitness)
            println("Generation $generation: Best fitness = $best_fitness")
        end
    end
    
    best_idx = argmin(ga.fitness)
    return (best_solution=ga.population[best_idx, :], best_fitness=ga.fitness[best_idx])
end

"""
General optimization interface supporting multiple algorithms.
"""
function optimize_function(objective_function, initial_guess::Vector{T};
                         method::Symbol=:lbfgs, bounds=nothing,
                         max_iterations::Int=1000) where T<:Real
    
    if method == :lbfgs
        result = optimize(objective_function, initial_guess, LBFGS(),
                         Optim.Options(iterations=max_iterations))
        return (solution=Optim.minimizer(result), 
                objective=Optim.minimum(result),
                converged=Optim.converged(result))
        
    elseif method == :pso && bounds !== nothing
        pso = PSO(50, bounds, max_iterations=max_iterations)
        result = optimize!(pso, objective_function)
        return (solution=result.best_solution, 
                objective=result.best_fitness,
                converged=true)
        
    elseif method == :genetic && bounds !== nothing
        ga = GeneticAlgorithm(100, bounds, max_generations=max_iterations)
        result = evolve!(ga, objective_function)
        return (solution=result.best_solution,
                objective=result.best_fitness,
                converged=true)
        
    else
        throw(ArgumentError("Unsupported optimization method: $method"))
    end
end

end # module OptimizationMethods


# ═══════════════════════════════════════════════════════════════════════════════
#                           9. MODEL DEPLOYMENT AND PRODUCTION
# ═══════════════════════════════════════════════════════════════════════════════

"""
Production deployment utilities for Julia ML models with enterprise-grade features.
"""
module ModelDeployment

using HTTP, JSON3
using BSON, JLD2
using Dates
using Statistics
using Distributed
using Base.Threads

export ModelServer, save_model, load_model, create_prediction_api
export batch_predict, model_monitoring, ModelRegistry, PerformanceMonitor

"""
Enterprise-grade model server for high-throughput predictions.
"""
mutable struct ModelServer{T}
    models::Dict{String, Any}
    preprocessing_functions::Dict{String, Function}
    postprocessing_functions::Dict{String, Function}
    request_count::Atomic{Int}
    prediction_times::Vector{Float64}
    error_count::Atomic{Int}
    start_time::DateTime
    max_batch_size::Int
    request_queue::Channel{Any}
    worker_pool::Vector{Task}
    
    function ModelServer{T}(; max_batch_size::Int=1000, num_workers::Int=4) where T
        server = new{T}(
            Dict{String, Any}(), 
            Dict{String, Function}(), 
            Dict{String, Function}(), 
            Atomic{Int}(0), 
            Float64[], 
            Atomic{Int}(0), 
            now(),
            max_batch_size,
            Channel{Any}(100),
            Task[]
        )
        
        # Start worker threads
        for i in 1:num_workers
            worker = @async process_requests(server)
            push!(server.worker_pool, worker)
        end
        
        return server
    end
end

ModelServer(; kwargs...) = ModelServer{Float64}(; kwargs...)

"""
Process prediction requests asynchronously.
"""
function process_requests(server::ModelServer)
    while true
        try
            request = take!(server.request_queue)
            if request === nothing  # Shutdown signal
                break
            end
            
            # Process the request
            result = execute_prediction(server, request)
            
            # Store result in request object for retrieval
            request.result = result
            request.completed = true
            
        catch e
            @error "Worker error: $e"
        end
    end
end

"""
Enhanced model registration with versioning and metadata.
"""
function register_model!(server::ModelServer, model_name::String, model;
                        version::String="1.0.0",
                        preprocessor=nothing, 
                        postprocessor=nothing,
                        metadata::Dict=Dict())
    
    model_info = Dict(
        "model" => model,
        "version" => version,
        "registered_at" => now(),
        "metadata" => metadata
    )
    
    server.models[model_name] = model_info
    
    if preprocessor !== nothing
        server.preprocessing_functions[model_name] = preprocessor
    end
    
    if postprocessor !== nothing
        server.postprocessing_functions[model_name] = postprocessor
    end
    
    println("Model '$model_name' v$version registered successfully")
    return model_info
end

"""
Execute prediction with comprehensive monitoring.
"""
function execute_prediction(server::ModelServer, request)
    start_time = time()
    
    try
        atomic_add!(server.request_count, 1)
        
        model_name = request.model_name
        input_data = request.input_data
        
        # Validate model exists
        if !haskey(server.models, model_name)
            throw(ArgumentError("Model '$model_name' not found"))
        end
        
        model_info = server.models[model_name]
        model = model_info["model"]
        processed_input = input_data
        
        # Apply preprocessing
        if haskey(server.preprocessing_functions, model_name)
            processed_input = server.preprocessing_functions[model_name](input_data)
        end
        
        # Make prediction
        prediction = if hasmethod(predict, (typeof(model), typeof(processed_input)))
            predict(model, processed_input)
        else
            model(processed_input)
        end
        
        # Apply postprocessing
        if haskey(server.postprocessing_functions, model_name)
            prediction = server.postprocessing_functions[model_name](prediction)
        end
        
        # Record timing
        prediction_time = (time() - start_time) * 1000
        push!(server.prediction_times, prediction_time)
        
        return Dict(
            "success" => true,
            "prediction" => prediction,
            "model_version" => model_info["version"],
            "processing_time_ms" => prediction_time,
            "timestamp" => now()
        )
        
    catch e
        atomic_add!(server.error_count, 1)
        error_time = (time() - start_time) * 1000
        
        return Dict(
            "success" => false,
            "error" => string(e),
            "processing_time_ms" => error_time,
            "timestamp" => now()
        )
    end
end

"""
High-performance REST API with advanced features.
"""
function create_prediction_api(server::ModelServer; 
                              port::Int=8080, 
                              host::String="127.0.0.1",
                              enable_cors::Bool=true,
                              rate_limit::Int=1000)
    
    # Middleware for CORS
    function cors_middleware(handler)
        return function(req::HTTP.Request)
            if enable_cors
                headers = [
                    "Access-Control-Allow-Origin" => "*",
                    "Access-Control-Allow-Methods" => "GET, POST, OPTIONS",
                    "Access-Control-Allow-Headers" => "Content-Type, Authorization"
                ]
                
                if req.method == "OPTIONS"
                    return HTTP.Response(200, headers)
                end
                
                response = handler(req)
                for (key, value) in headers
                    HTTP.setheader(response, key => value)
                end
                return response
            else
                return handler(req)
            end
        end
    end
    
    # Rate limiting middleware
    request_counts = Dict{String, Tuple{Int, DateTime}}()
    
    function rate_limit_middleware(handler)
        return function(req::HTTP.Request)
            client_ip = get(HTTP.header(req, "X-Real-IP"), "127.0.0.1")
            current_time = now()
            
            if haskey(request_counts, client_ip)
                count, last_reset = request_counts[client_ip]
                if current_time - last_reset > Minute(1)
                    request_counts[client_ip] = (1, current_time)
                elseif count >= rate_limit
                    return HTTP.Response(429, JSON3.write(Dict("error" => "Rate limit exceeded")))
                else
                    request_counts[client_ip] = (count + 1, last_reset)
                end
            else
                request_counts[client_ip] = (1, current_time)
            end
            
            return handler(req)
        end
    end
    
    # Health check endpoint with detailed metrics
    function health_handler(req::HTTP.Request)
        uptime = now() - server.start_time
        
        # Calculate performance metrics
        avg_response_time = isempty(server.prediction_times) ? 0.0 : mean(server.prediction_times)
        p95_response_time = isempty(server.prediction_times) ? 0.0 : 
                           quantile(server.prediction_times, 0.95)
        
        stats = Dict(
            "status" => "healthy",
            "uptime_seconds" => uptime.value / 1000,
            "total_requests" => server.request_count[],
            "error_count" => server.error_count[],
            "error_rate" => server.request_count[] > 0 ? 
                          server.error_count[] / server.request_count[] : 0.0,
            "average_response_time_ms" => avg_response_time,
            "p95_response_time_ms" => p95_response_time,
            "available_models" => collect(keys(server.models)),
            "active_workers" => length(server.worker_pool),
            "queue_size" => length(server.request_queue.data),
            "memory_usage_mb" => Base.gc_live_bytes() / 1024 / 1024
        )
        
        return HTTP.Response(200, JSON3.write(stats))
    end
    
    # Single prediction endpoint
    function predict_handler(req::HTTP.Request)
        try
            body = JSON3.read(String(req.body))
            model_name = get(body, "model", "")
            input_data = get(body, "data", nothing)
            
            if isempty(model_name) || input_data === nothing
                return HTTP.Response(400, JSON3.write(Dict(
                    "error" => "Both 'model' and 'data' fields are required"
                )))
            end
            
            # Convert input data to appropriate format
            processed_input = if isa(input_data, Vector)
                reshape(Float64.(input_data), 1, :)
            elseif isa(input_data, Vector{Vector})
                reduce(hcat, input_data)'
            else
                input_data
            end
            
            # Create request object
            request_obj = (
                model_name=model_name,
                input_data=processed_input,
                result=nothing,
                completed=false
            )
            
            # Submit to queue
            put!(server.request_queue, request_obj)
            
            # Wait for completion (with timeout)
            timeout_ms = 5000
            start_wait = time()
            while !request_obj.completed && (time() - start_wait) * 1000 < timeout_ms
                sleep(0.001)
            end
            
            if !request_obj.completed
                return HTTP.Response(408, JSON3.write(Dict("error" => "Request timeout")))
            end
            
            result = request_obj.result
            
            if result["success"]
                return HTTP.Response(200, JSON3.write(result))
            else
                return HTTP.Response(500, JSON3.write(result))
            end
            
        catch e
            return HTTP.Response(500, JSON3.write(Dict("error" => string(e))))
        end
    end
    
    # Batch prediction endpoint
    function batch_predict_handler(req::HTTP.Request)
        try
            body = JSON3.read(String(req.body))
            model_name = get(body, "model", "")
            batch_data = get(body, "batch_data", nothing)
            
            if isempty(model_name) || batch_data === nothing
                return HTTP.Response(400, JSON3.write(Dict(
                    "error" => "Both 'model' and 'batch_data' fields are required"
                )))
            end
            
            if length(batch_data) > server.max_batch_size
                return HTTP.Response(413, JSON3.write(Dict(
                    "error" => "Batch size exceeds maximum allowed ($(server.max_batch_size))"
                )))
            end
            
            # Process batch in parallel
            batch_results = batch_predict(server.models[model_name]["model"], batch_data,
                                        batch_size=min(100, length(batch_data)),
                                        parallel=true)
            
            response = Dict(
                "predictions" => batch_results,
                "model" => model_name,
                "batch_size" => length(batch_data),
                "timestamp" => now()
            )
            
            return HTTP.Response(200, JSON3.write(response))
            
        catch e
            return HTTP.Response(500, JSON3.write(Dict("error" => string(e))))
        end
    end
    
    # Model info endpoint
    function model_info_handler(req::HTTP.Request)
        try
            model_name = HTTP.URIs.splitpath(req.target)[3]  # /models/{model_name}
            
            if !haskey(server.models, model_name)
                return HTTP.Response(404, JSON3.write(Dict("error" => "Model not found")))
            end
            
            model_info = server.models[model_name]
            info = Dict(
                "name" => model_name,
                "version" => model_info["version"],
                "registered_at" => model_info["registered_at"],
                "metadata" => model_info["metadata"],
                "has_preprocessor" => haskey(server.preprocessing_functions, model_name),
                "has_postprocessor" => haskey(server.postprocessing_functions, model_name)
            )
            
            return HTTP.Response(200, JSON3.write(info))
            
        catch e
            return HTTP.Response(500, JSON3.write(Dict("error" => string(e))))
        end
    end
    
    # Create router with middleware
    router = HTTP.Router()
    
    # Apply middleware
    cors_handler = cors_middleware
    rate_limit_handler = rate_limit_middleware
    
    # Register routes
    HTTP.register!(router, "GET", "/health", cors_handler(health_handler))
    HTTP.register!(router, "POST", "/predict", cors_handler(rate_limit_handler(predict_handler)))
    HTTP.register!(router, "POST", "/batch_predict", cors_handler(rate_limit_handler(batch_predict_handler)))
    HTTP.register!(router, "GET", "/models/*", cors_handler(model_info_handler))
    
    println("Starting enhanced model server on $host:$port")
    println("Features enabled:")
    println("  - CORS: $enable_cors")
    println("  - Rate limiting: $rate_limit requests/minute")
    println("  - Worker threads: $(length(server.worker_pool))")
    println("  - Max batch size: $(server.max_batch_size)")
    println("\nEndpoints:")
    println("  GET  /health - Health check and metrics")
    println("  POST /predict - Single prediction")
    println("  POST /batch_predict - Batch predictions")
    println("  GET  /models/{name} - Model information")
    
    HTTP.serve(router, host, port; verbose=false)
end

"""
Model registry for version management and metadata storage.
"""
mutable struct ModelRegistry
    models::Dict{String, Dict{String, Any}}
    storage_path::String
    
    function ModelRegistry(storage_path::String="./model_registry")
        if !isdir(storage_path)
            mkpath(storage_path)
        end
        
        registry = new(Dict{String, Dict{String, Any}}(), storage_path)
        load_registry!(registry)
        return registry
    end
end

"""
Save model with comprehensive metadata and versioning.
"""
function save_model(registry::ModelRegistry, model, model_name::String;
                   version::String="1.0.0", 
                   description::String="",
                   tags::Vector{String}=String[],
                   metadata::Dict=Dict())
    
    model_id = "$(model_name)_v$(version)"
    model_path = joinpath(registry.storage_path, "$(model_id).jld2")
    
    # Comprehensive metadata
    full_metadata = merge(metadata, Dict(
        "name" => model_name,
        "version" => version,
        "description" => description,
        "tags" => tags,
        "saved_at" => now(),
        "julia_version" => string(VERSION),
        "model_type" => string(typeof(model)),
        "model_size_bytes" => 0,  # Will be calculated after saving
        "checksum" => ""  # Will be calculated after saving
    ))
    
    # Save model
    model_data = Dict(
        "model" => model,
        "metadata" => full_metadata
    )
    
    JLD2.save(model_path, model_data)
    
    # Calculate file size and checksum
    file_size = filesize(model_path)
    checksum = bytes2hex(open(sha256, model_path))
    
    full_metadata["model_size_bytes"] = file_size
    full_metadata["checksum"] = checksum
    full_metadata["file_path"] = model_path
    
    # Update registry
    if !haskey(registry.models, model_name)
        registry.models[model_name] = Dict{String, Any}()
    end
    
    registry.models[model_name][version] = full_metadata
    
    # Save registry
    save_registry(registry)
    
    println("Model saved: $model_name v$version")
    println("Size: $(round(file_size / 1024 / 1024, digits=2)) MB")
    println("Path: $model_path")
    
    return model_path
end

"""
Load model with validation and version management.
"""
function load_model(registry::ModelRegistry, model_name::String; 
                   version::String="latest")
    
    if !haskey(registry.models, model_name)
        throw(ArgumentError("Model '$model_name' not found in registry"))
    end
    
    model_versions = registry.models[model_name]
    
    # Determine version to load
    if version == "latest"
        version_keys = collect(keys(model_versions))
        version = maximum(version_keys)  # Simple string comparison, could be improved
    end
    
    if !haskey(model_versions, version)
        available_versions = collect(keys(model_versions))
        throw(ArgumentError("Version '$version' not found. Available: $available_versions"))
    end
    
    metadata = model_versions[version]
    model_path = metadata["file_path"]
    
    # Validate file exists and checksum
    if !isfile(model_path)
        throw(ArgumentError("Model file not found: $model_path"))
    end
    
    current_checksum = bytes2hex(open(sha256, model_path))
    if current_checksum != metadata["checksum"]
        @warn "Checksum mismatch for model file: $model_path"
    end
    
    # Load model
    model_data = JLD2.load(model_path)
    
    println("Model loaded: $model_name v$version")
    println("Saved: $(metadata["saved_at"])")
    println("Type: $(metadata["model_type"])")
    
    return (model=model_data["model"], metadata=model_data["metadata"])
end

"""
Performance monitor for production deployments.
"""
mutable struct PerformanceMonitor
    metrics_history::Vector{Dict{String, Any}}
    alert_thresholds::Dict{String, Float64}
    monitoring_interval::Int  # seconds
    monitoring_task::Union{Task, Nothing}
    
    function PerformanceMonitor(; 
                               response_time_threshold::Float64=1000.0,  # ms
                               error_rate_threshold::Float64=0.05,      # 5%
                               memory_threshold::Float64=8000.0,        # MB
                               monitoring_interval::Int=60)            # seconds
        
        thresholds = Dict(
            "response_time_ms" => response_time_threshold,
            "error_rate" => error_rate_threshold,
            "memory_usage_mb" => memory_threshold
        )
        
        new(Dict{String, Any}[], thresholds, monitoring_interval, nothing)
    end
end

"""
Start monitoring with alerting.
"""
function start_monitoring!(monitor::PerformanceMonitor, server::ModelServer)
    monitor.monitoring_task = @async begin
        while true
            try
                # Collect metrics
                current_metrics = collect_metrics(server)
                push!(monitor.metrics_history, current_metrics)
                
                # Check thresholds and alert
                check_alerts(monitor, current_metrics)
                
                # Keep only recent history (last 24 hours)
                max_history = 24 * 60 * 60 ÷ monitor.monitoring_interval
                if length(monitor.metrics_history) > max_history
                    monitor.metrics_history = monitor.metrics_history[end-max_history+1:end]
                end
                
                sleep(monitor.monitoring_interval)
                
            catch e
                @error "Monitoring error: $e"
                sleep(monitor.monitoring_interval)
            end
        end
    end
    
    println("Performance monitoring started (interval: $(monitor.monitoring_interval)s)")
end

"""
Collect comprehensive performance metrics.
"""
function collect_metrics(server::ModelServer)
    current_time = now()
    
    # Calculate recent performance metrics (last 5 minutes)
    recent_cutoff = current_time - Minute(5)
    recent_times = filter(t -> t > (time() - 300), server.prediction_times)
    
    metrics = Dict{String, Any}(
        "timestamp" => current_time,
        "total_requests" => server.request_count[],
        "error_count" => server.error_count[],
        "error_rate" => server.request_count[] > 0 ? 
                       server.error_count[] / server.request_count[] : 0.0,
        "avg_response_time_ms" => isempty(recent_times) ? 0.0 : mean(recent_times),
        "p95_response_time_ms" => isempty(recent_times) ? 0.0 : quantile(recent_times, 0.95),
        "p99_response_time_ms" => isempty(recent_times) ? 0.0 : quantile(recent_times, 0.99),
        "requests_per_second" => length(recent_times) / 300,  # last 5 minutes
        "memory_usage_mb" => Base.gc_live_bytes() / 1024 / 1024,
        "queue_length" => length(server.request_queue.data),
        "active_workers" => count(t -> !istaskdone(t), server.worker_pool)
    )
    
    return metrics
end

"""
Check alert thresholds and trigger notifications.
"""
function check_alerts(monitor::PerformanceMonitor, metrics::Dict{String, Any})
    alerts = String[]
    
    for (metric_name, threshold) in monitor.alert_thresholds
        if haskey(metrics, metric_name)
            value = metrics[metric_name]
            
            if metric_name == "error_rate" && value > threshold
                push!(alerts, "High error rate: $(round(value * 100, digits=2))% > $(round(threshold * 100, digits=2))%")
            elseif metric_name == "response_time_ms" && value > threshold
                push!(alerts, "High response time: $(round(value, digits=1))ms > $(threshold)ms")
            elseif metric_name == "memory_usage_mb" && value > threshold
                push!(alerts, "High memory usage: $(round(value, digits=1))MB > $(threshold)MB")
            end
        end
    end
    
    if !isempty(alerts)
        @warn "Performance alerts triggered:" alerts
        
        # Here you could integrate with external alerting systems
        # send_slack_alert(alerts)
        # send_email_alert(alerts)
        # trigger_pagerduty(alerts)
    end
end

"""
High-performance batch prediction with intelligent batching.
"""
function batch_predict(model, data_batch::Vector; 
                      batch_size::Int=1000, 
                      parallel::Bool=true,
                      show_progress::Bool=true)
    
    n_samples = length(data_batch)
    n_batches = ceil(Int, n_samples / batch_size)
    
    if show_progress
        println("Processing $n_samples samples in $n_batches batches (batch_size=$batch_size)")
    end
    
    if parallel && nprocs() > 1
        # Distributed processing
        @everywhere model_batch = $model
        
        results = @distributed (vcat) for batch_idx in 1:n_batches
            start_idx = (batch_idx - 1) * batch_size + 1
            end_idx = min(batch_idx * batch_size, n_samples)
            
            batch_data = data_batch[start_idx:end_idx]
            process_batch(model_batch, batch_data)
        end
        
    elseif parallel && Threads.nthreads() > 1
        # Multi-threaded processing
        results = Vector{Any}(undef, n_samples)
        
        Threads.@threads for batch_idx in 1:n_batches
            start_idx = (batch_idx - 1) * batch_size + 1
            end_idx = min(batch_idx * batch_size, n_samples)
            
            batch_data = data_batch[start_idx:end_idx]
            batch_results = process_batch(model, batch_data)
            
            results[start_idx:end_idx] = batch_results
        end
        
    else
        # Sequential processing
        results = []
        
        for batch_idx in 1:n_batches
            start_idx = (batch_idx - 1) * batch_size + 1
            end_idx = min(batch_idx * batch_size, n_samples)
            
            batch_data = data_batch[start_idx:end_idx]
            batch_results = process_batch(model, batch_data)
            
            append!(results, batch_results)
            
            if show_progress && batch_idx % 10 == 0
                println("Processed $(min(end_idx, n_samples))/$n_samples samples")
            end
        end
    end
    
    return results
end

"""
Process a single batch of data.
"""
function process_batch(model, batch_data)
    batch_results = []
    
    for data_point in batch_data
        processed_input = if isa(data_point, Vector)
            reshape(Float64.(data_point), 1, :)
        else
            data_point
        end
        
        prediction = if hasmethod(predict, (typeof(model), typeof(processed_input)))
            predict(model, processed_input)
        else
            model(processed_input)
        end
        
        push!(batch_results, prediction)
    end
    
    return batch_results
end

"""
Graceful shutdown of model server.
"""
function shutdown_server!(server::ModelServer)
    println("Shutting down model server...")
    
    # Send shutdown signal to workers
    for _ in 1:length(server.worker_pool)
        put!(server.request_queue, nothing)
    end
    
    # Wait for workers to finish
    for worker in server.worker_pool
        wait(worker)
    end
    
    println("Model server shutdown complete")
end

end # module ModelDeployment

# ═══════════════════════════════════════════════════════════════════════════════
#                           10. COMPREHENSIVE EXAMPLES AND WORKFLOWS
# ═══════════════════════════════════════════════════════════════════════════════

"""
Complete machine learning workflows demonstrating Julia's capabilities.
"""
module MLWorkflows

using ..DataPreprocessing, ..MachineLearning, ..DeepLearning
using ..ParallelComputing, ..TimeSeriesAnalysis, ..OptimizationMethods
using ..ModelDeployment
using DataFrames, CSV, Statistics, Random
using Plots

export complete_ml_pipeline, time_series_pipeline, hyperparameter_optimization_pipeline
export ensemble_modeling_pipeline, deep_learning_pipeline, production_deployment_pipeline

"""
Complete end-to-end machine learning pipeline with deployment.
"""
function complete_ml_pipeline(data_file::String, target_column::String;
                             test_size::Float64=0.2, 
                             random_state::Int=42,
                             deploy::Bool=false)
    
    println("=== COMPLETE MACHINE LEARNING PIPELINE ===")
    println("Loading data from: $data_file")
    
    # 1. Load and validate data
    data = CSV.read(data_file, DataFrame)
    println("Data loaded: $(nrow(data)) rows, $(ncol(data)) columns")
    
    # Data quality check
    missing_percentage = sum(ismissing.(data)) / (nrow(data) * ncol(data)) * 100
    println("Missing values: $(round(missing_percentage, digits=2))%")
    
    # 2. Advanced data preprocessing
    println("\n1. Data Preprocessing...")
    processor = preprocess_pipeline(data, target_column,
                                  create_polynomials=true,
                                  create_interactions=true)
    
    processed_data = processor.data
    
    # 3. Intelligent feature selection
    println("\n2. Feature Selection...")
    numerical_cols = processor.numerical_columns
    target_col = processed_data[:, target_column]
    
    if length(numerical_cols) > 0
        # Multiple feature selection methods
        correlations = [abs(cor(processed_data[:, col], target_col)) for col in numerical_cols]
        top_features = numerical_cols[sortperm(correlations, rev=true)[1:min(15, length(correlations))]]
        
        X = Matrix(processed_data[:, top_features])
        y = Vector(target_col)
        
        println("Selected $(length(top_features)) features using correlation analysis")
    else
        X = Matrix(processed_data[:, setdiff(names(processed_data), [target_column])])
        y = Vector(target_col)
    end
    
    # 4. Advanced train-test split with stratification
    println("\n3. Data Splitting...")
    X_train, X_val, X_test, y_train, y_val, y_test = split_data(X, y, 
                                                               train_ratio=0.7,
                                                               val_ratio=0.15,
                                                               stratify=false,
                                                               random_state=random_state)
    
    # 5. Comprehensive model training
    println("\n4. Model Training and Evaluation...")
    models = Dict()
    results = Dict()
    
    # Linear Regression with regularization
    println("Training Regularized Linear Regression...")
    lr = LinearRegression{Float64}()
    fit!(lr, X_train, y_train)
    lr_pred = predict(lr, X_test)
    lr_mse = mean((lr_pred .- y_test) .^ 2)
    lr_r2 = 1 - sum((y_test .- lr_pred) .^ 2) / sum((y_test .- mean(y_test)) .^ 2)
    
    models["Linear Regression"] = lr
    results["Linear Regression"] = Dict("MSE" => lr_mse, "R²" => lr_r2, "predictions" => lr_pred)
    
    # K-Means clustering analysis
    println("Training K-Means for data insights...")
    kmeans = KMeans{Float64}(min(5, size(X_train, 1) ÷ 100))
    fit!(kmeans, X_train)
    cluster_labels = predict(kmeans, X_test)
    
    models["K-Means"] = kmeans
    results["K-Means"] = Dict("labels" => cluster_labels, "centroids" => kmeans.centroids)
    
    # PCA for dimensionality reduction
    println("Training PCA...")
    pca = PCA{Float64}(min(10, size(X_train, 2)))
    X_train_pca = fit_transform!(pca, X_train)
    """
Production deployment utilities for Julia ML models.
"""
module ModelDeployment

using HTTP, JSON3
using BSON, JLD2
using Dates
using Statistics

export ModelServer, save_model, load_model, create_prediction_api
export batch_predict, model_monitoring

"""
High-performance model server for real-time predictions.
"""
mutable struct ModelServer{T}
    models::Dict{String, Any}
    preprocessing_functions::Dict{String, Function}
    postprocessing_functions::Dict{String, Function}
    request_count::Int
    prediction_times::Vector{Float64}
    error_count::Int
    start_time::DateTime
    
    function ModelServer{T}() where T
        new{T}(Dict{String, Any}(), Dict{String, Function}(), 
               Dict{String, Function}(), 0, Float64[], 0, now())
    end
end

ModelServer() = ModelServer{Float64}()

"""
Register a model with the server.
"""
function register_model!(server::ModelServer, model_name::String, model;
                        preprocessor=nothing, postprocessor=nothing)
    server.models[model_name] = model
    
    if preprocessor !== nothing
        server.preprocessing_functions[model_name] = preprocessor
    end
    
    if postprocessor !== nothing
        server.postprocessing_functions[model_name] = postprocessor
    end
    
    println("Model '$model_name' registered successfully")
end

"""
Make prediction with error handling and monitoring.
"""
function predict_with_monitoring(server::ModelServer, model_name::String, input_data)
    start_time = time()
    
    try
        server.request_count += 1
        
        # Check if model exists
        if !haskey(server.models, model_name)
            throw(ArgumentError("Model '$model_name' not found"))
        end
        
        model = server.models[model_name]
        processed_input = input_data
        
        # Apply preprocessing if available
        if haskey(server.preprocessing_functions, model_name)
            processed_input = server.preprocessing_functions[model_name](input_data)
        end
        
        # Make prediction
        if hasmethod(predict, (typeof(model), typeof(processed_input)))
            prediction = predict(model, processed_input)
        else
            prediction = model(processed_input)  # For neural networks
        end
        
        # Apply postprocessing if available
        if haskey(server.postprocessing_functions, model_name)
            prediction = server.postprocessing_functions[model_name](prediction)
        end
        
        # Record timing
        prediction_time = (time() - start_time) * 1000  # Convert to milliseconds
        push!(server.prediction_times, prediction_time)
        
        return (success=true, prediction=prediction, time_ms=prediction_time)
        
    catch e
        server.error_count += 1
        error_time = (time() - start_time) * 1000
        
        return (success=false, error=string(e), time_ms=error_time)
    end
end

"""
Create REST API for model serving using HTTP.jl.
"""
function create_prediction_api(server::ModelServer; port::Int=8080, host::String="127.0.0.1")
    
    # Health check endpoint
    function health_handler(req::HTTP.Request)
        uptime = now() - server.start_time
        
        stats = Dict(
            "status" => "healthy",
            "uptime_seconds" => uptime.value / 1000,
            "total_requests" => server.request_count,
            "error_count" => server.error_count,
            "average_response_time_ms" => isempty(server.prediction_times) ? 0.0 : mean(server.prediction_times),
            "available_models" => collect(keys(server.models))
        )
        
        return HTTP.Response(200, JSON3.write(stats))
    end
    
    # Prediction endpoint
    function predict_handler(req::HTTP.Request)
        try
            # Parse request body
            body = JSON3.read(String(req.body))
            model_name = get(body, "model", "")
            input_data = get(body, "data", nothing)
            
            if isempty(model_name)
                return HTTP.Response(400, JSON3.write(Dict("error" => "Model name is required")))
            end
            
            if input_data === nothing
                return HTTP.Response(400, JSON3.write(Dict("error" => "Input data is required")))
            end
            
            # Convert input data to appropriate format
            if isa(input_data, Vector)
                # Convert to matrix if needed
                input_matrix = reshape(Float64.(input_data), 1, :)
            elseif isa(input_data, Vector{Vector})
                input_matrix = hcat(input_data...)'
            else
                input_matrix = input_data
            end
            
            # Make prediction
            result = predict_with_monitoring(server, model_name, input_matrix)
            
            if result.success
                response = Dict(
                    "prediction" => result.prediction,
                    "model" => model_name,
                    "processing_time_ms" => result.time_ms,
                    "timestamp" => now()
                )
                return HTTP.Response(200, JSON3.write(response))
            else
                return HTTP.Response(500, JSON3.write(Dict("error" => result.error)))
            end
            
        catch e
            return HTTP.Response(500, JSON3.write(Dict("error" => string(e))))
        end
    end
    
    # Batch prediction endpoint
    function batch_predict_handler(req::HTTP.Request)
        try
            body = JSON3.read(String(req.body))
            model_name = get(body, "model", "")
            batch_data = get(body, "batch_data", nothing)
            
            if isempty(model_name) || batch_data === nothing
                return HTTP.Response(400, JSON3.write(Dict("error" => "Model name and batch_data are required")))
            end
            
            # Process batch
            predictions = []
            total_time = 0.0
            
            for data_point in batch_data
                if isa(data_point, Vector)
                    input_matrix = reshape(Float64.(data_point), 1, :)
                else
                    input_matrix = data_point
                end
                
                result = predict_with_monitoring(server, model_name, input_matrix)
                
                if result.success
                    push!(predictions, result.prediction)
                    total_time += result.time_ms
                else
                    push!(predictions, Dict("error" => result.error))
                end
            end
            
            response = Dict(
                "predictions" => predictions,
                "model" => model_name,
                "batch_size" => length(batch_data),
                "total_processing_time_ms" => total_time,
                "average_time_per_prediction_ms" => total_time / length(batch_data),
                "timestamp" => now()
            )
            
            return HTTP.Response(200, JSON3.write(response))
            
        catch e
            return HTTP.Response(500, JSON3.write(Dict("error" => string(e))))
        end
    end
    
    # Create router
    router = HTTP.Router()
    HTTP.register!(router, "GET", "/health", health_handler)
    HTTP.register!(router, "POST", "/predict", predict_handler)
    HTTP.register!(router, "POST", "/batch_predict", batch_predict_handler)
    
    # Start server
    println("Starting model server on $host:$port")
    println("Endpoints:")
    println("  GET  /health - Health check and statistics")
    println("  POST /predict - Single prediction")
    println("  POST /batch_predict - Batch predictions")
    
    HTTP.serve(router, host, port; verbose=false)
end

"""
Save model with metadata for production deployment.
"""
function save_model(model, filepath::String; metadata::Dict=Dict())
    model_data = Dict(
        "model" => model,
        "metadata" => merge(metadata, Dict(
            "saved_at" => now(),
            "julia_version" => VERSION,
            "model_type" => string(typeof(model))
        ))
    )
    
    if endswith(filepath, ".jld2")
        JLD2.save(filepath, model_data)
    elseif endswith(filepath, ".bson")
        BSON.save(filepath, model_data)
    else
        throw(ArgumentError("Unsupported file format. Use .jld2 or .bson"))
    end
    
    println("Model saved to: $filepath")
    return filepath
end

"""
Load model with metadata validation.
"""
function load_model(filepath::String)
    if !isfile(filepath)
        throw(ArgumentError("File not found: $filepath"))
    end
    
    if endswith(filepath, ".jld2")
        model_data = JLD2.load(filepath)
    elseif endswith(filepath, ".bson")
        model_data = BSON.load(filepath)
    else
        throw(ArgumentError("Unsupported file format. Use .jld2 or .bson"))
    end
    
    model = model_data["model"]
    metadata = get(model_data, "metadata", Dict())
    
    println("Model loaded from: $filepath")
    if haskey(metadata, "saved_at")
        println("Saved at: $(metadata["saved_at"])")
    end
    if haskey(metadata, "model_type")
        println("Model type: $(metadata["model_type"])")
    end
    
    return (model=model, metadata=metadata)
end

"""
Batch prediction with parallel processing.
"""
function batch_predict(model, data_batch::Vector; 
                      batch_size::Int=1000, parallel::Bool=true)
    
    n_samples = length(data_batch)
    n_batches = ceil(Int, n_samples / batch_size)
    
    println("Processing $n_samples samples in $n_batches batches")
    
    if parallel && nprocs() > 1
        # Distributed processing
        @everywhere model_distributed = $model
        
        results = @distributed (vcat) for batch_idx in 1:n_batches
            start_idx = (batch_idx - 1) * batch_size + 1
            end_idx = min(batch_idx * batch_size, n_samples)
            
            batch_data = data_batch[start_idx:end_idx]
            batch_predictions = []
            
            for data_point in batch_data
                if isa(data_point, Vector)
                    input_matrix = reshape(Float64.(data_point), 1, :)
                else
                    input_matrix = data_point
                end
                
                if hasmethod(predict, (typeof(model_distributed), typeof(input_matrix)))
                    pred = predict(model_distributed, input_matrix)
                else
                    pred = model_distributed(input_matrix)
                end
                
                push!(batch_predictions, pred)
            end
            
            batch_predictions
        end
    else
        # Sequential processing
        results = []
        
        @showprogress "Batch prediction..." for batch_idx in 1:n_batches
            start_idx = (batch_idx - 1) * batch_size + 1
            end_idx = min(batch_idx * batch_size, n_samples)
            
            for i in start_idx:end_idx
                data_point = data_batch[i]
                
                if isa(data_point, Vector)
                    input_matrix = reshape(Float64.(data_point), 1, :)
                else
                    input_matrix = data_point
                end
                
                if hasmethod(predict, (typeof(model), typeof(input_matrix)))
                    pred = predict(model, input_matrix)
                else
                    pred = model(input_matrix)
                end
                
                push!(results, pred)
            end
        end
    end
    
    return results
end

"""
Model monitoring and drift detection.
"""
mutable struct ModelMonitor{T<:Real}
    reference_data::Matrix{T}
    reference_predictions::Vector{T}
    drift_threshold::T
    performance_threshold::T
    monitoring_history::Vector{Dict}
    
    function ModelMonitor{T}(reference_data::Matrix{T}, reference_predictions::Vector{T};
                           drift_threshold::T=T(0.1), performance_threshold::T=T(0.05)) where T<:Real
        new{T}(reference_data, reference_predictions, drift_threshold, performance_threshold, Dict[])
    end
end

ModelMonitor(reference_data, reference_predictions; kwargs...) = 
    ModelMonitor{Float64}(reference_data, reference_predictions; kwargs...)

"""
Detect data drift using statistical tests.
"""
function detect_drift(monitor::ModelMonitor{T}, new_data::Matrix{T}) where T<:Real
    n_features = size(monitor.reference_data, 2)
    drift_detected = false
    feature_drifts = Dict{Int, T}()
    
    for feature_idx in 1:n_features
        ref_feature = monitor.reference_data[:, feature_idx]
        new_feature = new_data[:, feature_idx]
        
        # Kolmogorov-Smirnov test (simplified)
        ref_sorted = sort(ref_feature)
        new_sorted = sort(new_feature)
        
        # Empirical CDF comparison
        n_ref = length(ref_sorted)
        n_new = length(new_sorted)
        
        # Calculate maximum difference between CDFs
        max_diff = T(0)
        for val in [ref_sorted; new_sorted]
            cdf_ref = sum(ref_sorted .<= val) / n_ref
            cdf_new = sum(new_sorted .<= val) / n_new
            max_diff = max(max_diff, abs(cdf_ref - cdf_new))
        end
        
        feature_drifts[feature_idx] = max_diff
        
        if max_diff > monitor.drift_threshold
            drift_detected = true
        end
    end
    
    return (drift_detected=drift_detected, feature_drifts=feature_drifts)
end

"""
Monitor model performance over time.
"""
function monitor_performance(monitor::ModelMonitor{T}, model, new_data::Matrix{T}, 
                           new_targets::Vector{T}) where T<:Real
    
    # Make predictions on new data
    if hasmethod(predict, (typeof(model), typeof(new_data)))
        new_predictions = predict(model, new_data)
    else
        new_predictions = model(new_data)
    end
    
    # Calculate performance metrics
    if length(unique(new_targets)) <= 10  # Classification
        accuracy = mean(new_predictions .== new_targets)
        ref_accuracy = mean(monitor.reference_predictions .== 
                           monitor.reference_predictions)  # Placeholder
        
        performance_drop = ref_accuracy - accuracy
        performance_degraded = performance_drop > monitor.performance_threshold
        
        metrics = Dict(
            "accuracy" => accuracy,
            "performance_drop" => performance_drop,
            "performance_degraded" => performance_degraded
        )
    else  # Regression
        mse = mean((new_predictions .- new_targets) .^ 2)
        ref_mse = mean((monitor.reference_predictions .- new_targets[1:length(monitor.reference_predictions)]) .^ 2)
        
        performance_increase = mse - ref_mse
        performance_degraded = performance_increase > monitor.performance_threshold
        
        metrics = Dict(
            "mse" => mse,
            "performance_increase" => performance_increase,
            "performance_degraded" => performance_degraded
        )
    end
    
    # Detect drift
    drift_results = detect_drift(monitor, new_data)
    
    # Store monitoring results
    monitoring_result = Dict(
        "timestamp" => now(),
        "performance_metrics" => metrics,
        "drift_results" => drift_results,
        "n_samples" => size(new_data, 1)
    )
    
    push!(monitor.monitoring_history, monitoring_result)
    
    # Print alerts
    if drift_results.drift_detected
        println("⚠️  Data drift detected!")
        println("Features with drift: $(collect(keys(filter(p -> p.second > monitor.drift_threshold, drift_results.feature_drifts))))")
    end
    
    if metrics["performance_degraded"]
        println("⚠️  Model performance degradation detected!")
    end
    
    return monitoring_result
end

end # module ModelDeployment

# ═══════════════════════════════════════════════════════════════════════════════
#                           10. COMPREHENSIVE EXAMPLES AND WORKFLOWS
# ═══════════════════════════════════════════════════════════════════════════════

"""
Complete machine learning workflows demonstrating Julia's capabilities.
"""
module MLWorkflows

using ..DataPreprocessing, ..MachineLearning, ..DeepLearning
using ..ParallelComputing, ..TimeSeriesAnalysis, ..OptimizationMethods
using DataFrames, CSV, Statistics, Random
using Plots

export complete_ml_pipeline, time_series_pipeline, hyperparameter_optimization_pipeline
export ensemble_modeling_pipeline, deep_learning_pipeline

"""
Complete end-to-end machine learning pipeline.
"""
function complete_ml_pipeline(data_file::String, target_column::String;
                             test_size::Float64=0.2, random_state::Int=42)
    
    println("=== COMPLETE MACHINE LEARNING PIPELINE ===")
    println("Loading data from: $data_file")
    
    # 1. Load data
    data = CSV.read(data_file, DataFrame)
    println("Data loaded: $(nrow(data)) rows, $(ncol(data)) columns")
    
    # 2. Data preprocessing
    println("\n1. Data Preprocessing...")
    processor = preprocess_pipeline(data, target_column,
                                  create_polynomials=true,
                                  create_interactions=true)
    
    processed_data = processor.data
    
    # 3. Feature selection using correlation
    println("\n2. Feature Selection...")
    numerical_cols = processor.numerical_columns
    target_col = processed_data[:, target_column]
    
    if length(numerical_cols) > 0
        correlations = [abs(cor(processed_data[:, col], target_col)) for col in numerical_cols]
        top_features = numerical_cols[sortperm(correlations, rev=true)[1:min(10, length(correlations))]]
        
        # Create feature matrix
        X = Matrix(processed_data[:, top_features])
        y = Vector(target_col)
        
        println("Selected $(length(top_features)) top features")
    else
        X = Matrix(processed_data[:, setdiff(names(processed_data), [target_column])])
        y = Vector(target_col)
    end
    
    # 4. Train-test split
    println("\n3. Data Splitting...")
    X_train, X_val, X_test, y_train, y_val, y_test = split_data(X, y, 
                                                               train_ratio=0.7,
                                                               val_ratio=0.15,
                                                               stratify=false,
                                                               random_state=random_state)
    
    # 5. Model training
    println("\n4. Model Training...")
    models = Dict()
    
    # Linear Regression
    println("Training Linear Regression...")
    lr = LinearRegression{Float64}()
    fit!(lr, X_train, y_train)
    models["Linear Regression"] = lr
    
    # K-Means (for demonstration)
    println("Training K-Means...")
    kmeans = KMeans{Float64}(3)
    fit!(kmeans, X_train)
    models["K-Means"] = kmeans
    
    # PCA
    println("Training PCA...")
    pca = PCA{Float64}(min(5, size(X_train, 2)))
    X_train_pca = fit_transform!(pca, X_train)
    models["PCA"] = pca
    
    # 6. Model evaluation
    println("\n5. Model Evaluation...")
    results = Dict()
    
    # Evaluate Linear Regression
    lr_pred = predict(lr, X_test)
    lr_mse = mean((lr_pred .- y_test) .^ 2)
    lr_r2 = 1 - sum((y_test .- lr_pred) .^ 2) / sum((y_test .- mean(y_test)) .^ 2)
    
    results["Linear Regression"] = Dict("MSE" => lr_mse, "R²" => lr_r2)
    
    println("Linear Regression - MSE: $(round(lr_mse, digits=4)), R²: $(round(lr_r2, digits=4))")
    
    # 7. Cross-validation
    println("\n6. Cross-Validation...")
    cv_results = cross_validate(() -> LinearRegression{Float64}(), X, y, 5, 
                               metrics=[:mse, :r2])
    
    # 8. Visualization
    println("\n7. Creating Visualizations...")
    
    # Actual vs Predicted plot
    p1 = scatter(y_test, lr_pred, xlabel="Actual", ylabel="Predicted", 
                title="Linear Regression: Actual vs Predicted", alpha=0.6)
    plot!(p1, [minimum(y_test), maximum(y_test)], [minimum(y_test), maximum(y_test)], 
          color=:red, linestyle=:dash, label="Perfect Prediction")
    
    # PCA visualization (first 2 components)
    if size(X_train_pca, 2) >= 2
        p2 = scatter(X_train_pca[:, 1], X_train_pca[:, 2], 
                    title="PCA Visualization (First 2 Components)",
                    xlabel="PC1", ylabel="PC2", alpha=0.6)
    else
        p2 = plot(title="PCA: Insufficient Components")
    end
    
    # Combine plots
    final_plot = plot(p1, p2, layout=(1, 2), size=(1000, 400))
    
    println("\n=== PIPELINE COMPLETED ===")
    println("Models trained: $(length(models))")
    println("Best R² score: $(maximum([r["R²"] for r in values(results) if haskey(r, "R²")]))")
    
    return (
        models=models,
        results=results,
        cv_results=cv_results,
        test_predictions=lr_pred,
        plots=final_plot,
        processor=processor
    )
end

"""
Time series analysis and forecasting pipeline.
"""
function time_series_pipeline(ts_data::Vector{T}, period::Int=12; 
                             forecast_horizon::Int=12) where T<:Real
    
    println("=== TIME SERIES ANALYSIS PIPELINE ===")
    println("Time series length: $(length(ts_data))")
    println("Seasonal period: $period")
    
    # 1. Seasonal decomposition
    println("\n1. Seasonal Decomposition...")
    decomposition = seasonal_decompose(ts_data, period)
    
    # 2. ARIMA modeling
    println("\n2. ARIMA Modeling...")
    arima = ARIMA{T}(1, 1, 1)  # ARIMA(1,1,1)
    fit!(arima, ts_data)
    
    # 3. Exponential smoothing
    println("\n3. Exponential Smoothing...")
    ets = ExponentialSmoothing{T}(:holt_winters, period=period)
    fit!(ets, ts_data)
    
    # 4. Forecasting
    println("\n4. Generating Forecasts...")
    arima_forecast = forecast(arima, forecast_horizon)
    ets_forecast = forecast(ets, forecast_horizon)
    
    # 5. Change point detection
    println("\n5. Change Point Detection...")
    changepoints = detect_changepoints(ts_data)
    
    # 6. Visualization
    println("\n6. Creating Visualizations...")
    
    # Original time series with decomposition
    p1 = plot(ts_data, title="Original Time Series", label="Data", linewidth=2)
    if !isempty(changepoints)
        for cp in changepoints
            vline!(p1, [cp], color=:red, linestyle=:dash, alpha=0.7, label="")
        end
    end
    
    # Decomposition plot
    p2 = plot(decomposition.trend, title="Trend Component", label="Trend", color=:blue)
    p3 = plot(decomposition.seasonal, title="Seasonal Component", label="Seasonal", color=:green)
    p4 = plot(decomposition.remainder, title="Remainder", label="Remainder", color=:orange)
    
    # Forecasts
    n = length(ts_data)
    future_indices = (n+1):(n+forecast_horizon)
    
    p5 = plot(ts_data, title="Forecasts", label="Historical", linewidth=2, color=:black)
    plot!(p5, future_indices, arima_forecast.forecast, label="ARIMA", linewidth=2, color=:red)
    plot!(p5, future_indices, ets_forecast, label="Exp. Smoothing", linewidth=2, color=:blue)
    
    # Add confidence intervals for ARIMA
    plot!(p5, future_indices, arima_forecast.lower_ci, fillrange=arima_forecast.upper_ci, 
          alpha=0.3, color=:red, label="")
    
    final_plot = plot(p1, p2, p3, p4, p5, layout=(3, 2), size=(1200, 800))
    
    # 7. Accuracy metrics (on in-sample fit)
    println("\n7. Model Evaluation...")
    
    # Use fitted values for evaluation (simplified)
    if length(arima.fitted_values) > 0
        arima_residuals = ts_data[length(ts_data)-length(arima.fitted_values)+1:end] .- arima.fitted_values
        arima_mae = mean(abs.(arima_residuals))
        println("ARIMA MAE: $(round(arima_mae, digits=4))")
    end
    
    if length(ets.fitted_values) > 0
        ets_residuals = ts_data .- ets.fitted_values
        ets_mae = mean(abs.(ets_residuals))
        println("Exponential Smoothing MAE: $(round(ets_mae, digits=4))")
    end
    
    println("\n=== TIME SERIES PIPELINE COMPLETED ===")
    println("Change points detected: $(length(changepoints))")
    println("Forecast horizon: $forecast_horizon periods")
    
    return (
        decomposition=decomposition,
        arima_model=arima,
        ets_model=ets,
        arima_forecast=arima_forecast,
        ets_forecast=ets_forecast,
        changepoints=changepoints,
        plots=final_plot
    )
end

"""
Hyperparameter optimization pipeline using multiple algorithms.
"""
function hyperparameter_optimization_pipeline(X::Matrix{T}, y::Vector{T};
                                             optimization_method::Symbol=:pso) where T<:Real
    
    println("=== HYPERPARAMETER OPTIMIZATION PIPELINE ===")
    println("Optimization method: $optimization_method")
    println("Dataset size: $(size(X))")
    
    # Define objective function for Linear Regression with regularization
    function objective_function(params)
        alpha = params[1]  # L2 regularization parameter
        
        # Simple cross-validation
        n_folds = 3
        fold_size = size(X, 1) ÷ n_folds
        total_error = T(0)
        
        for fold in 1:n_folds
            # Create train/test split for this fold
            test_start = (fold - 1) * fold_size + 1
            test_end = fold == n_folds ? size(X, 1) : fold * fold_size
            
            test_indices = test_start:test_end
            train_indices = setdiff(1:size(X, 1), test_indices)
            
            X_train_fold = X[train_indices, :]
            y_train_fold = y[train_indices]
            X_test_fold = X[test_indices, :]
            y_test_fold = y[test_indices]
            
            # Add L2 regularization to normal equations
            λ = alpha
            I_reg = λ * I(size(X_train_fold, 2))
            X_with_intercept = hcat(ones(T, size(X_train_fold, 1)), X_train_fold)
            
            # Regularized solution
            reg_matrix = X_with_intercept' * X_with_intercept + [0 zeros(T, 1, size(X_train_fold, 2)); zeros(T, size(X_train_fold, 2), 1) I_reg]
            θ = reg_matrix \ (X_with_intercept' * y_train_fold)
            
            # Make predictions
            X_test_with_intercept = hcat(ones(T, size(X_test_fold, 1)), X_test_fold)
            y_pred = X_test_with_intercept * θ
            
            # Calculate MSE
            fold_error = mean((y_pred .- y_test_fold) .^ 2)
            total_error += fold_error
        end
        
        return total_error / n_folds
    end
    
    # Bounds for regularization parameter
    bounds = ([T(0.001)], [T(10.0)])
    
    println("\n1. Starting hyperparameter optimization...")
    
    if optimization_method == :pso
        # Particle Swarm Optimization
        result = optimize_function(objective_function, [T(1.0)], 
                                 method=:pso, bounds=bounds, max_iterations=50)
        
    elseif optimization_method == :genetic
        # Genetic Algorithm
        result = optimize_function(objective_function, [T(1.0)],
                                 method=:genetic, bounds=bounds, max_iterations=50)
    else
        # L-BFGS (requires initial guess)
        result = optimize_function(objective_function, [T(1.0)], method=:lbfgs)
    end
    
    println("\n2. Optimization Results:")
    println("Best regularization parameter: $(result.solution[1])")
    println("Best cross-validation MSE: $(round(result.objective, digits=6))")
    println("Converged: $(result.converged)")
    
    # Train final model with best parameters
    println("\n3. Training final model with optimized parameters...")
    
    best_alpha = result.solution[1]
    λ = best_alpha
    I_reg = λ * I(size(X, 2))
    X_with_intercept = hcat(ones(T, size(X, 1)), X)
    
    reg_matrix = X_with_intercept' * X_with_intercept + [0 zeros(T, 1, size(X, 2)); zeros(T, size(X, 2), 1) I_reg]
    final_θ = reg_matrix \ (X_with_intercept' * y)
    
    # Make final predictions
    final_predictions = X_with_intercept * final_θ
    final_mse = mean((final_predictions .- y) .^ 2)
    final_r2 = 1 - sum((y .- final_predictions) .^ 2) / sum((y .- mean(y)) .^ 2)
    
    println("Final model performance:")
    println("MSE: $(round(final_mse, digits=6))")
    println("R²: $(round(final_r2, digits=4))")
    
    # Visualization
    p1 = scatter(y, final_predictions, xlabel="Actual", ylabel="Predicted",
                title="Optimized Model: Actual vs Predicted", alpha=0.6)
    plot!(p1, [minimum(y), maximum(y)], [minimum(y), maximum(y)], 
          color=:red, linestyle=:dash, label="Perfect Prediction")
    
    println("\n=== HYPERPARAMETER OPTIMIZATION COMPLETED ===")
    
    return (
        best_params=result.solution,
        best_score=result.objective,
        final_model_coefficients=final_θ,
        final_predictions=final_predictions,
        final_metrics=Dict("MSE" => final_mse, "R²" => final_r2),
        optimization_plot=p1
    )
end

"""
Ensemble modeling pipeline combining multiple algorithms.
"""
function ensemble_modeling_pipeline(X::Matrix{T}, y::Vector{T}; 
                                   ensemble_size::Int=5) where T<:Real
    
    println("=== ENSEMBLE MODELING PIPELINE ===")
    println("Creating ensemble with $ensemble_size base models")
    println("Dataset size: $(size(X))")
    
    # Split data
    X_train, X_val, X_test, y_train, y_val, y_test = split_data(X, y, 
                                                               train_ratio=0.6,
                                                               val_ratio=0.2,
                                                               random_state=42)
    
    # Train base models with different configurations
    base_models = []
    model_predictions_val = []
    model_predictions_test = []
    model_names = String[]
    
    println("\n1. Training base models...")
    
    for i in 1:ensemble_size
        println("Training base model $i/$ensemble_size...")
        
        # Use different random subsets and parameters for diversity
        Random.seed!(i * 42)
        
        # Random feature subset
        n_features = size(X_train, 2)
        feature_subset = sample(1:n_features, max(1, n_features ÷ 2), replace=false)
        
        X_train_subset = X_train[:, feature_subset]
        X_val_subset = X_val[:, feature_subset]
        X_test_subset = X_test[:, feature_subset]
        
        # Add noise to create diversity
        noise_level = T(0.01)
        X_train_noisy = X_train_subset + noise_level * randn(T, size(X_train_subset))
        
        # Train linear regression
        model = LinearRegression{T}()
        fit!(model, X_train_noisy, y_train)
        
        # Make predictions
        val_pred = predict(model, X_val_subset)
        test_pred = predict(model, X_test_subset)
        
        push!(base_models, (model=model, features=feature_subset))
        push!(model_predictions_val, val_pred)
        push!(model_predictions_test, test_pred)
        push!(model_names, "Model_$i")
    end
    
    # Create ensemble predictions using different strategies
    println("\n2. Creating ensemble predictions...")
    
    # Simple averaging
    ensemble_pred_val_avg = mean(hcat(model_predictions_val...), dims=2)[:]
    ensemble_pred_test_avg = mean(hcat(model_predictions_test...), dims=2)[:]
    
    # Weighted averaging based on validation performance
    val_mses = [mean((pred .- y_val) .^ 2) for pred in model_predictions_val]
    weights = 1 ./ (val_mses .+ eps(T))  # Inverse MSE weighting
    weights = weights ./ sum(weights)  # Normalize
    
    ensemble_pred_val_weighted = sum(hcat(model_predictions_val...) .* weights', dims=2)[:]
    ensemble_pred_test_weighted = sum(hcat(model_predictions_test...) .* weights', dims=2)[:]
    
    # Evaluate ensemble performance
    println("\n3. Evaluating ensemble performance...")
    
    # Individual model performance
    individual_r2s = []
    for i in 1:ensemble_size
        r2 = 1 - sum((y_test .- model_predictions_test[i]) .^ 2) / sum((y_test .- mean(y_test)) .^ 2)
        push!(individual_r2s, r2)
        println("Model $i R²: $(round(r2, digits=4))")
    end
    
    # Ensemble performance
    r2_avg = 1 - sum((y_test .- ensemble_pred_test_avg) .^ 2) / sum((y_test .- mean(y_test)) .^ 2)
    r2_weighted = 1 - sum((y_test .- ensemble_pred_test_weighted) .^ 2) / sum((y_test .- mean(y_test)) .^ 2)
    
    println("\nEnsemble Results:")
    println("Average R²: $(round(r2_avg, digits=4))")
    println("Weighted R²: $(round(r2_weighted, digits=4))")
    println("Best individual R²: $(round(maximum(individual_r2s), digits=4))")
    println("Improvement over best individual: $(round(max(r2_avg, r2_weighted) - maximum(individual_r2s), digits=4))")
    
    # Visualization
    p1 = scatter(y_test, ensemble_pred_test_avg, xlabel="Actual", ylabel="Predicted",
                title="Ensemble (Average): Actual vs Predicted", alpha=0.6, color=:blue)
    plot!(p1, [minimum(y_test), maximum(y_test)], [minimum(y_test), maximum(y_test)], 
          color=:red, linestyle=:dash, label="Perfect")
    
    p2 = scatter(y_test, ensemble_pred_test_weighted, xlabel="Actual", ylabel="Predicted",
                title="Ensemble (Weighted): Actual vs Predicted", alpha=0.6, color=:green)
    plot!(p2, [minimum(y_test), maximum(y_test)], [minimum(y_test), maximum(y_test)], 
          color=:red, linestyle=:dash, label="Perfect")
    
    # Model weights visualization
    p3 = bar(1:ensemble_size, weights, xlabel="Model", ylabel="Weight", 
            title="Ensemble Model Weights", color=:orange)
    
    final_plot = plot(p1, p2, p3, layout=(2, 2), size=(1000, 800))
    
    println("\n=== ENSEMBLE MODELING COMPLETED ===")
    
    return (
        base_models=base_models,
        ensemble_predictions_avg=ensemble_pred_test_avg,
        ensemble_predictions_weighted=ensemble_pred_test_weighted,
        model_weights=weights,
        individual_r2s=individual_r2s,
        ensemble_r2_avg=r2_avg,
        ensemble_r2_weighted=r2_weighted,
        plots=final_plot
    )
end

"""
Deep learning pipeline with GPU acceleration.
"""
function deep_learning_pipeline(X::Matrix{T}, y::Vector{T}; 
                               architecture::Vector{Int}=[64, 32, 16],
                               epochs::Int=100) where T<:Real
    
    println("=== DEEP LEARNING PIPELINE ===")
    println("Architecture: Input -> $(join(architecture, " -> ")) -> Output")
    println("Training epochs: $epochs")
    println("Dataset size: $(size(X))")
    
    # Data preparation
    X_train, X_val, X_test, y_train, y_val, y_test = split_data(X, y,
                                                               train_ratio=0.7,
                                                               val_ratio=0.15,
                                                               random_state=42)
    
    # Reshape for MLUtils
    y_train_reshaped = reshape(y_train, 1, :)
    y_val_reshaped = reshape(y_val, 1, :)
    y_test_reshaped = reshape(y_test, 1, :)
    
    # Create data loaders
    train_data = [(X_train', y_train_reshaped)]
    val_data = [(X_val', y_val_reshaped)]
    test_data = [(X_test', y_test_reshaped)]
    
    println("\n1. Building neural network...")
    
    # Create neural network
    input_dim = size(X, 2)
    network = NeuralNetwork(input_dim, architecture, 1, 
                           activation=relu, output_activation=identity,
                           dropout_rate=0.1, use_batch_norm=true)
    
    # Set loss function for regression
    network.loss_function = Flux.mse
    network.optimizer = Adam(0.001)
    
    println("Network created with $(sum([prod(size(p)) for p in Flux.params(network.model)])) parameters")
    
    # Training
    println("\n2. Training neural network...")
    train_model!(network, train_data[1], val_data[1], 
                epochs=epochs, batch_size=32, verbose=true,
                early_stopping=true, patience=15)
    
    # Evaluation
    println("\n3. Evaluating model...")
    test_metrics = evaluate_model(network, test_data[1])
    
    println("Test Results:")
    for (metric, value) in test_metrics
        println("$metric: $(round(value, digits=4))")
    end
    
    # Make predictions for visualization
    test_predictions = network.model(X_test')'[:]
    
    # Visualization
    println("\n4. Creating visualizations...")
    
    # Training history
    p1 = plot_training_history(network)
    
    # Predictions plot
    p2 = scatter(y_test, test_predictions, xlabel="Actual", ylabel="Predicted",
                title="Deep Learning: Actual vs Predicted", alpha=0.6, color=:purple)
    plot!(p2, [minimum(y_test), maximum(y_test)], [minimum(y_test), maximum(y_test)], 
          color=:red, linestyle=:dash, label="Perfect")
    
    # Residuals plot
    residuals = y_test .- test_predictions
    p3 = scatter(test_predictions, residuals, xlabel="Predicted", ylabel="Residuals",
                title="Residuals Plot", alpha=0.6, color=:orange)
    hline!(p3, [0], color=:red, linestyle=:dash, label="Zero")
    
    final_plot = plot(p1, p2, p3, layout=(2, 2), size=(1200, 800))
    
    # Feature importance (using gradients)
    println("\n5. Computing feature importance...")
    
    # Simple gradient-based importance
    X_sample = X_test[1:min(100, size(X_test, 1)), :]'
    gradients = Flux.gradient(network.model, X_sample)[1]
    feature_importance = vec(mean(abs.(gradients), dims=2))
    
    p4 = bar(1:length(feature_importance), feature_importance, 
            xlabel="Feature", ylabel="Importance", 
            title="Feature Importance (Gradient-based)", color=:teal)
    
    println("\n=== DEEP LEARNING PIPELINE COMPLETED ===")
    println("Final test R²: $(round(test_metrics["r2"], digits=4))")
    
    return (
        network=network,
        test_metrics=test_metrics,
        test_predictions=test_predictions,
        feature_importance=feature_importance,
        training_plot=p1,
        results_plot=final_plot
    )
end

end # module MLWorkflows

# ═══════════════════════════════════════════════════════════════════════════════
#                     PERFORMANCE BENCHMARKING AND SYSTEM INFO
# ═══════════════════════════════════════════════════════════════════════════════

"""
Comprehensive system benchmarking for ML workloads.
"""
function benchmark_ml_performance()
    println("=== JULIA ML PERFORMANCE BENCHMARK ===")
    
    # System information
    println("\nSYSTEM INFORMATION:")
    println("Julia version: $(VERSION)")
    println("CPU threads: $(Threads.nthreads())")
    println("Available processes: $(nprocs())")
    
    if gpu_available
        println("GPU: Available")
    else
        println("GPU: Not available")
    end
    
    # Benchmark different operations
    println("\nPERFORMANCE BENCHMARKS:")
    
    # Matrix operations
    println("\n1. Linear Algebra Performance:")
    n = 2000
    A = randn(n, n)
    B = randn(n, n)
    
    # Matrix multiplication
    mat_mult_time = @belapsed $A * $B
    println("Matrix multiplication ($(n)×$(n)): $(round(mat_mult_time * 1000, digits=1)) ms")
    
    # Eigenvalue decomposition
    n_eigen = 1000
    A_sym = Symmetric(randn(n_eigen, n_eigen))
    eigen_time = @belapsed eigvals($A_sym)
    println("Eigenvalue decomposition ($(n_eigen)×$(n_eigen)): $(round(eigen_time * 1000, digits=1)) ms")
    
    # SVD
    svd_time = @belapsed svd($A_sym)
    println("SVD ($(n_eigen)×$(n_eigen)): $(round(svd_time * 1000, digits=1)) ms")
    
    # Machine learning operations
    println("\n2. ML Algorithm Performance:")
    
    # Generate test data
    n_samples, n_features = 10000, 100
    X = randn(n_samples, n_features)
    y = randn(n_samples)
    
    # Linear regression training
    lr_time = @belapsed begin
        lr = LinearRegression{Float64}()
        fit!(lr, $X, $y)
    end
    println("Linear regression training ($(n_samples)×$(n_features)): $(round(lr_time * 1000, digits=1)) ms")
    
    # K-means clustering
    kmeans_time = @belapsed begin
        kmeans = KMeans{Float64}(5)
        fit!(kmeans, $X)
    end
    println("K-means clustering ($(n_samples)×$(n_features), k=5): $(round(kmeans_time, digits=2)) s")
    
    # PCA
    pca_time = @belapsed begin
        pca = PCA{Float64}(10)
        fit_transform!(pca, $X)
    end
    println("PCA ($(n_samples)×$(n_features), 10 components): $(round(pca_time, digits=2)) s")
    
    # Memory and threading performance
    println("\n3. Parallel Performance:")
    
    # Threaded operations
    large_array = randn(10^7)
    sequential_time = @belapsed sum($large_array)
    threaded_time = @belapsed ThreadsX.sum($large_array)
    
    println("Sequential sum (10M elements): $(round(sequential_time * 1000, digits=1)) ms")
    println("Threaded sum (10M elements): $(round(threaded_time * 1000, digits=1)) ms")
    println("Threading speedup: $(round(sequential_time / threaded_time, digits=1))x")
    
    return (
        matrix_mult_time=mat_mult_time,
        eigen_time=eigen_time,
        svd_time=svd_time,
        lr_time=lr_time,
        kmeans_time=kmeans_time,
        pca_time=pca_time,
        sequential_time=sequential_time,
        threaded_time=threaded_time
    )
end

"""
Main function to demonstrate all capabilities.
"""
function demonstrate_julia_ml()
    println("=== JULIA AI/ML FRAMEWORK DEMONSTRATION ===")
    
    # Generate sample data
    Random.seed!(42)
    n_samples, n_features = 1000, 10
    
    # Create synthetic regression dataset
    X = randn(n_samples, n_features)
    true_coefficients = randn(n_features)
    noise = 0.1 * randn(n_samples)
    y = X * true_coefficients + noise
    
    println("Generated synthetic dataset:")
    println("Samples: $n_samples, Features: $n_features")
    println("True R²: 0.99 (low noise dataset)")
    
    # Demonstrate different modules
    println("\n" * "="^60)
    println("DEMONSTRATION RESULTS:")
    
    # 1. Basic ML pipeline
    println("\n1. Running complete ML pipeline...")
    try
        # Save data temporarily
        df = DataFrame(X, :auto)
        df.target = y
        CSV.write("temp_data.csv", df)
        
        ml_results = MLWorkflows.complete_ml_pipeline("temp_data.csv", "target")
        println("✓ ML pipeline completed successfully")
        
        # Clean up
        rm("temp_data.csv")
    catch e
        println("✗ ML pipeline failed: $e")
    end
    
    # 2. Time series analysis
    println("\n2. Running time series analysis...")
    try
        # Generate time series data
        t = 1:200
        trend = 0.1 * t
        seasonal = 5 * sin.(2π * t / 12)
        noise = randn(length(t))
        ts_data = trend + seasonal + noise
        
        ts_results = MLWorkflows.time_series_pipeline(ts_data, 12)
        println("✓ Time series analysis completed successfully")
    catch e
        println("✗ Time series analysis failed: $e")
    end
    
    # 3. Hyperparameter optimization
    println("\n3. Running hyperparameter optimization...")
    try
        opt_results = MLWorkflows.hyperparameter_optimization_pipeline(X, y, optimization_method=:pso)
        println("✓ Hyperparameter optimization completed successfully")
    catch e
        println("✗ Hyperparameter optimization failed: $e")
    end
    
    # 4. Performance benchmark
    println("\n4. Running performance benchmark...")
    try
        bench_results = benchmark_ml_performance()
        println("✓ Performance benchmark completed successfully")
    catch e
        println("✗ Performance benchmark failed: $e")
    end
    
    println("\n" * "="^60)
    println("JULIA AI/ML FRAMEWORK DEMONSTRATION COMPLETED")
    println("All major components have been tested and validated!")
    
    return true
end

# ═══════════════════════════════════════════════════════════════════════════════
#                     FRAMEWORK INITIALIZATION AND FINALIZATION
# ═══════════════════════════════════════════════════════════════════════════════

println("\n" * "="^80)
println("JULIA AI/ML FRAMEWORK LOADED SUCCESSFULLY")
println("="^80)

println("\nFRAMEWORK COMPONENTS:")
println("✓ Performance Optimization (Multi-threading, GPU support)")
println("✓ Data Preprocessing (Advanced pipeline with feature engineering)")
println("✓ Machine Learning (Linear models, clustering, dimensionality reduction)")
println("✓ Deep Learning (Neural networks with Flux.jl)")
println("✓ Parallel Computing (Distributed processing, threading)")
println("✓ Time Series Analysis (ARIMA, exponential smoothing, decomposition)")
println("✓ Optimization Methods (PSO, genetic algorithms, gradient descent)")
println("✓ Model Deployment (REST API, batch processing, monitoring)")
println("✓ Complete Workflows (End-to-end pipelines)")

println("\nPERFORMANCE FEATURES:")
println("✓ Multi-threading: $(Threads.nthreads()) threads available")
println("✓ Distributed computing: $(nprocs()) processes")
println("✓ GPU acceleration: $(gpu_available ? "Available" : "Not available")")
println("✓ BLAS optimization: $(BLAS.vendor()) with $(BLAS.get_num_threads()) threads")

println("\nQUICK START EXAMPLES:")
println("1. Complete ML Pipeline:")
println("   results = MLWorkflows.complete_ml_pipeline(\"data.csv\", \"target\")")
println("\n2. Time Series Analysis:")
println("   ts_results = MLWorkflows.time_series_pipeline(time_series_data, 12)")
println("\n3. Deep Learning:")
println("   dl_results = MLWorkflows.deep_learning_pipeline(X, y)")
println("\n4. Hyperparameter Optimization:")
println("   opt_results = MLWorkflows.hyperparameter_optimization_pipeline(X, y)")
println("\n5. Model Deployment:")
println("   server = ModelDeployment.ModelServer()")
println("   ModelDeployment.register_model!(server, \"my_model\", trained_model)")
println("\n6. Performance Benchmark:")
println("   benchmark_results = benchmark_ml_performance()")
println("\n7. Full Demonstration:")
println("   demonstrate_julia_ml()")

println("\nFOR OPTIMAL PERFORMANCE:")
println("- Set JULIA_NUM_THREADS environment variable before starting Julia")
println("- Use addprocs() for distributed computing")
println("- Install CUDA.jl for GPU acceleration")
println("- Use @time or @benchmark for performance profiling")

println("\nADVANCED FEATURES:")
println("- Automatic differentiation with Zygote.jl")
println("- High-performance linear algebra with native BLAS")
println("- Memory-efficient operations with view and broadcasting")
println("- Type stability for maximum performance")
println("- Zero-copy data sharing between processes")

println("\n" * "="^80)
println("READY FOR HIGH-PERFORMANCE ML AND AI WORKLOADS!")
println("="^80)    # Default parameters
    if trend_window === nothing
        trend_window = ceil(Int, 1.5 * period / (1 - 1.5/period))
    end
    if seasonal_window === nothing
        seasonal_window = 7  # Default seasonal smoothing
    end
    
    # Initialize components
    trend = zeros(T, n)
    seasonal = zeros(T, n)
    remainder = zeros(T, n)
    
    # Simple trend extraction using moving average
    half_window = trend_window ÷ 2
    for i in (half_window+1):(n-half_window)
        trend[i] = mean(y[(i-half_window):(i+half_window)])
    end
    
    # Extrapolate trend at boundaries
    trend[1:half_window] .= trend[half_window+1]
    trend[(n-half_window+1):n] .= trend[n-half_window]
    
    # Detrend the series
    detrended = y .- trend
    
    # Extract seasonal component
    seasonal_matrix = reshape(detrended[1:(period * (n ÷ period))], period, n ÷ period)
    seasonal_pattern = vec(mean(seasonal_matrix, dims=2))
    
    # Repeat seasonal pattern
    for i in 1:n
        seasonal[i] = seasonal_pattern[((i-1) % period) + 1]
    end
    
    # Calculate remainder
    remainder = y .- trend .- seasonal
    
    return (trend=trend, seasonal=seasonal, remainder=remainder, original=y)
end

"""
ARIMA model implementation with maximum likelihood estimation.
"""
mutable struct ARIMA{T<:Real}
    p::Int  # AR order
    d::Int  # Differencing order
    q::Int  # MA order
    ar_params::Vector{T}
    ma_params::Vector{T}
    intercept::T
    sigma2::T
    fitted_values::Vector{T}
    residuals::Vector{T}
    aic::T
    bic::T
    fitted::Bool
    
    function ARIMA{T}(p::Int, d::Int, q::Int) where T<:Real
        new{T}(p, d, q, T[], T[], zero(T), zero(T), T[], T[], 
               T(Inf), T(Inf), false)
    end
end

ARIMA(p::Int, d::Int, q::Int) = ARIMA{Float64}(p, d, q)

"""
Difference a time series to achieve stationarity.
"""
function difference_series(y::Vector{T}, d::Int) where T<:Real
    result = copy(y)
    for _ in 1:d
        result = diff(result)
    end
    return result
end

"""
Fit ARIMA model using conditional sum of squares.
"""
function fit!(model::ARIMA{T}, y::Vector{T}) where T<:Real
    n = length(y)
    
    # Apply differencing
    y_diff = difference_series(y, model.d)
    n_diff = length(y_diff)
    
    # Initialize parameters
    initial_params = [zeros(T, model.p); zeros(T, model.q); mean(y_diff)]
    
    # Define log-likelihood function
    function log_likelihood(params)
        ar_params = params[1:model.p]
        ma_params = params[model.p+1:model.p+model.q]
        intercept = params[end]
        
        # Initialize residuals and fitted values
        residuals = zeros(T, n_diff)
        fitted_vals = zeros(T, n_diff)
        
        # Calculate residuals using recursive approach
        for t in max(model.p, model.q)+1:n_diff
            # AR component
            ar_term = sum(ar_params[i] * y_diff[t-i] for i in 1:model.p)
            
            # MA component
            ma_term = sum(ma_params[i] * residuals[t-i] for i in 1:model.q)
            
            fitted_vals[t] = intercept + ar_term + ma_term
            residuals[t] = y_diff[t] - fitted_vals[t]
        end
        
        # Calculate log-likelihood
        sigma2 = var(residuals[max(model.p, model.q)+1:end])
        valid_residuals = residuals[max(model.p, model.q)+1:end]
        n_valid = length(valid_residuals)
        
        if sigma2 <= 0
            return T(Inf)
        end
        
        ll = -0.5 * n_valid * log(2π * sigma2) - 0.5 * sum(valid_residuals.^2) / sigma2
        return -ll  # Return negative for minimization
    end
    
    # Optimize parameters (simple grid search for demonstration)
    best_params = initial_params
    best_ll = log_likelihood(initial_params)
    
    # Simple optimization loop
    for iter in 1:100
        # Random perturbation
        candidate = best_params + 0.01 * randn(T, length(best_params))
        
        # Check stability constraints for AR parameters
        ar_candidate = candidate[1:model.p]
        if model.p > 0
            # Simple stability check: |ar_params| < 1
            if any(abs.(ar_candidate) .>= 0.99)
                continue
            end
        end
        
        ll = log_likelihood(candidate)
        if ll < best_ll
            best_ll = ll
            best_params = candidate
        end
    end
    
    # Store fitted parameters
    model.ar_params = best_params[1:model.p]
    model.ma_params = best_params[model.p+1:model.p+model.q]
    model.intercept = best_params[end]
    
    # Calculate final residuals and fitted values
    residuals = zeros(T, n_diff)
    fitted_vals = zeros(T, n_diff)
    
    for t in max(model.p, model.q)+1:n_diff
        ar_term = sum(model.ar_params[i] * y_diff[t-i] for i in 1:model.p)
        ma_term = sum(model.ma_params[i] * residuals[t-i] for i in 1:model.q)
        fitted_vals[t] = model.intercept + ar_term + ma_term
        residuals[t] = y_diff[t] - fitted_vals[t]
    end
    
    model.fitted_values = fitted_vals
    model.residuals = residuals
    model.sigma2 = var(residuals[max(model.p, model.q)+1:end])
    
    # Calculate information criteria
    k = model.p + model.q + 1  # Number of parameters
    n_eff = n_diff - max(model.p, model.q)
    model.aic = 2 * k + 2 * best_ll
    model.bic = k * log(n_eff) + 2 * best_ll
    
    model.fitted = true
    return model
end

"""
Forecast using fitted ARIMA model.
"""
function forecast(model::ARIMA{T}, n_ahead::Int; confidence_level::T=T(0.95)) where T<:Real
    @assert model.fitted "Model must be fitted before forecasting"
    
    forecasts = zeros(T, n_ahead)
    forecast_var = zeros(T, n_ahead)
    
    # Use last values for initialization
    last_values = model.fitted_values[end-max(model.p-1, 0):end]
    last_residuals = model.residuals[end-max(model.q-1, 0):end]
    
    for h in 1:n_ahead
        # AR component
        ar_term = T(0)
        for i in 1:min(model.p, length(last_values))
            if h <= i
                ar_term += model.ar_params[i] * forecasts[h-i]
            else
                ar_term += model.ar_params[i] * last_values[end-(i-h)]
            end
        end
        
        # MA component (only for h=1, as future errors are unknown)
        ma_term = T(0)
        if h == 1
            for i in 1:min(model.q, length(last_residuals))
                ma_term += model.ma_params[i] * last_residuals[end-(i-1)]
            end
        end
        
        forecasts[h] = model.intercept + ar_term + ma_term
        
        # Forecast variance (simplified)
        if h == 1
            forecast_var[h] = model.sigma2
        else
            forecast_var[h] = model.sigma2 * h  # Simplified variance calculation
        end
    end
    
    # Calculate confidence intervals
    z_alpha = quantile(Normal(), 1 - (1 - confidence_level) / 2)
    forecast_se = sqrt.(forecast_var)
    
    lower_ci = forecasts .- z_alpha .* forecast_se
    upper_ci = forecasts .+ z_alpha .* forecast_se
    
    return (forecast=forecasts, lower_ci=lower_ci, upper_ci=upper_ci, se=forecast_se)
end

"""
Exponential smoothing models (Simple, Holt, Holt-Winters).
"""
mutable struct ExponentialSmoothing{T<:Real}
    model_type::Symbol  # :simple, :holt, :holt_winters
    alpha::T  # Level smoothing parameter
    beta::T   # Trend smoothing parameter
    gamma::T  # Seasonal smoothing parameter
    level::T
    trend::T
    seasonal::Vector{T}
    period::Int
    fitted_values::Vector{T}
    fitted::Bool
    
    function ExponentialSmoothing{T}(model_type::Symbol; period::Int=12) where T<:Real
        new{T}(model_type, T(0.3), T(0.1), T(0.1), zero(T), zero(T), 
               T[], period, T[], false)
    end
end

ExponentialSmoothing(model_type::Symbol; kwargs...) = ExponentialSmoothing{Float64}(model_type; kwargs...)

function fit!(model::ExponentialSmoothing{T}, y::Vector{T}) where T<:Real
    n = length(y)
    
    # Initialize level
    model.level = y[1]
    
    # Initialize trend (for Holt and Holt-Winters)
    if model.model_type in [:holt, :holt_winters]
        model.trend = y[2] - y[1]
    end
    
    # Initialize seasonal components (for Holt-Winters)
    if model.model_type == :holt_winters
        # Simple seasonal initialization
        model.seasonal = zeros(T, model.period)
        for i in 1:model.period
            if i <= n
                model.seasonal[i] = y[i] / model.level - 1
            end
        end
    end
    
    model.fitted_values = zeros(T, n)
    
    # Fit the model
    for t in 1:n
        if model.model_type == :simple
            # Simple exponential smoothing
            if t == 1
                model.fitted_values[t] = model.level
            else
                prev_level = model.level
                model.level = model.alpha * y[t] + (1 - model.alpha) * prev_level
                model.fitted_values[t] = prev_level
            end
            
        elseif model.model_type == :holt
            # Holt's linear trend method
            if t == 1
                model.fitted_values[t] = model.level
            else
                prev_level = model.level
                prev_trend = model.trend
                
                model.level = model.alpha * y[t] + (1 - model.alpha) * (prev_level + prev_trend)
                model.trend = model.beta * (model.level - prev_level) + (1 - model.beta) * prev_trend
                
                model.fitted_values[t] = prev_level + prev_trend
            end
            
        elseif model.model_type == :holt_winters
            # Holt-Winters seasonal method
            seasonal_idx = ((t - 1) % model.period) + 1
            
            if t <= model.period
                model.fitted_values[t] = model.level * (1 + model.seasonal[seasonal_idx])
            else
                prev_level = model.level
                prev_trend = model.trend
                prev_seasonal = model.seasonal[seasonal_idx]
                
                model.level = model.alpha * y[t] / (1 + prev_seasonal) + 
                             (1 - model.alpha) * (prev_level + prev_trend)
                model.trend = model.beta * (model.level - prev_level) + 
                             (1 - model.beta) * prev_trend
                model.seasonal[seasonal_idx] = model.gamma * (y[t] / model.level - 1) + 
                                              (1 - model.gamma) * prev_seasonal
                
                model.fitted_values[t] = (prev_level + prev_trend) * (1 + prev_seasonal)
            end
        end
    end
    
    model.fitted = true
    return model
end

"""
Forecast using exponential smoothing model.
"""
function forecast(model::ExponentialSmoothing{T}, n_ahead::Int) where T<:Real
    @assert model.fitted "Model must be fitted before forecasting"
    
    forecasts = zeros(T, n_ahead)
    
    for h in 1:n_ahead
        if model.model_type == :simple
            forecasts[h] = model.level
            
        elseif model.model_type == :holt
            forecasts[h] = model.level + h * model.trend
            
        elseif model.model_type == :holt_winters
            seasonal_idx = ((h - 1) % model.period) + 1
            forecasts[h] = (model.level + h * model.trend) * (1 + model.seasonal[seasonal_idx])
        end
    end
    
    return forecasts
end

"""
Change point detection using PELT (Pruned Exact Linear Time) algorithm.
"""
function detect_changepoints(y::Vector{T}; penalty::T=T(2.0), min_size::Int=5) where T<:Real
    n = length(y)
    
    # Cost function (sum of squared errors)
    function segment_cost(start::Int, end::Int)
        if end <= start
            return T(Inf)
        end
        
        segment = y[start:end]
        μ = mean(segment)
        return sum((segment .- μ) .^ 2)
    end
    
    # Dynamic programming arrays
    F = fill(T(Inf), n + 1)  # Optimal cost up to time t
    F[1] = T(0)
    changepoints = Vector{Int}[]
    
    # PELT algorithm (simplified)
    for t in 2:(n + 1)
        candidates = Int[]
        costs = T[]
        
        for s in 1:(t - min_size)
            if F[s] < Inf
                cost = F[s] + segment_cost(s, t - 1) + penalty
                push!(candidates, s)
                push!(costs, cost)
            end
        end
        
        if !isempty(costs)
            min_idx = argmin(costs)
            F[t] = costs[min_idx]
            
            if min_idx > 1  # Found a changepoint
                push!(changepoints, candidates[min_idx])
            end
        end
    end
    
    # Extract final changepoints
    final_changepoints = unique(sort([cp for cp in changepoints if cp > 1 && cp < n]))
    
    return final_changepoints
end

"""
Calculate forecast accuracy metrics.
"""
function forecast_accuracy(actual::Vector{T}, predicted::Vector{T}) where T<:Real
    @assert length(actual) == length(predicted) "Vectors must have same length"
    
    n = length(actual)
    errors = actual .- predicted
    
    metrics = Dict{String, T}()
    
    # Mean Error
    metrics["ME"] = mean(errors)
    
    # Mean Absolute Error
    metrics["MAE"] = mean(abs.(errors))
    
    # Mean Squared Error
    metrics["MSE"] = mean(errors .^ 2)
    
    # Root Mean Squared Error
    metrics["RMSE"] = sqrt(metrics["MSE"])
    
    # Mean Absolute Percentage Error
    non_zero_actual = actual[actual .!= 0]
    non_zero_predicted = predicted[actual .!= 0]
    if !isempty(non_zero_actual)
        metrics["MAPE"] = mean(abs.((non_zero_actual .- non_zero_predicted) ./ non_zero_actual)) * 100
    else
        metrics["MAPE"] = T(Inf)
    end
    
    # Mean Absolute Scaled Error (MASE)
    if n > 1
        naive_errors = abs.(actual[2:end] .- actual[1:end-1])
        mae_naive = mean(naive_errors)
        metrics["MASE"] = metrics["MAE"] / mae_naive
    else
        metrics["MASE"] = T(Inf)
    end
    
    return metrics
end

end # module TimeSeriesAnalysis