Module regularized 

Ridge and Lasso regression (glmnet-compatible implementations).

This module provides regularized regression methods that are compatible with R’s glmnet package. The implementations follow the same objective functions, standardization conventions, and scaling approaches as glmnet.

Objective Function

The elastic net objective (which includes ridge and lasso as special cases) is:

minimize over (β₀, β):

    (1/(2n)) * Σᵢ (yᵢ - β₀ - xᵢᵀβ)²
    + λ * [(1 - α) * ||β||₂² / 2 + α * ||β||₁]

Where:

• α = 0: Ridge regression (L2 penalty)
• α = 1: Lasso regression (L1 penalty)
• β₀ (intercept) is never penalized
• λ controls the overall penalty strength

Standardization

By default, predictors are standardized before fitting (matching glmnet’s standardize=TRUE default):

• Each column of X is centered to mean 0 (if intercept is used)
• Each column is scaled to unit variance
• Coefficients are returned on the original scale

Compatibility with glmnet

These implementations match R’s glmnet behavior:

• Same objective function form
• Same standardization defaults
• Intercept is never penalized
• Coefficients are returned on original data scale

Modules

• preprocess - Data standardization utilities
• ridge - Ridge regression (L2 penalty)
• lasso - Lasso regression (L1 penalty)
• path - Lambda path generation for regularization paths

Re-exports

pub use lasso::lasso_fit;

pub use lasso::LassoFit;

pub use lasso::LassoFitOptions;

pub use path::make_lambda_path;

pub use path::LambdaPathOptions;

pub use preprocess::standardize_xy;

pub use preprocess::unstandardize_coefficients;

pub use preprocess::StandardizationInfo;

pub use ridge::ridge_fit;

pub use ridge::RidgeFit;

pub use ridge::RidgeFitOptions;

Modules

lasso

Lasso regression (L1-regularized linear regression).

path

Lambda path generation for regularized regression.

preprocess

Data preprocessing for regularized regression.

ridge

Ridge regression (L2-regularized linear regression).