Implement Core Batch Correction Algorithms

[ianfd]

Description

Develop mathematical foundations for batch correction algorithms to address technical variation in single-cell data.

Objectives

• Create efficient implementations of established batch correction methods
• Optimize for performance with parallel processing
• Support both dense and sparse matrix operations

Key Components to Implement

Linear Regression Batch Correction

• Implement linear regression framework for batch effect modeling
• Add robust fitting methods for outlier resistance
• Support for covariates in the regression model

ComBat Implementation

• Implement empirical Bayes framework for parameter estimation
• Add mean and variance adjustment capabilities
• Support for both parametric and non-parametric adjustments

Mutual Nearest Neighbors (MNN)

• Implement efficient nearest neighbor search algorithms
• Develop batch vector calculation methods
• Add correction vector application functionality

Advanced Methods (Lower Priority)

• Harmony algorithm core components
• Scanorama stitching mechanism
• Framework for integration with deep learning approaches (similar to scVI)

Utility Functions

• Batch effect quantification metrics
• Covariate-aware matrix operations
• Specialized distance calculations for batch integration

Integration Points

• Must work with existing matrix representations
• Should leverage Rayon for parallelization
• Support for both f32 and f64 precision

Technical Notes

• Prioritize implementation order: Linear regression → ComBat → MNN → others
• Consider GPU acceleration for matrix operations where applicable
• Implement progress tracking for long-running operations