Module path 

Lambda path generation for regularized regression.

This module provides utilities for generating a sequence of lambda values for regularization paths, matching the R glmnet implementation’s output/approach.

Lambda Path Construction

The lambda path follows this geometric decay pattern (following the glmnet R implementation):

lambda[0] = infinity            // effectively infinite (all coefficients zero)
lambda[1] = lambda_decay_factor * lambda_max           // First "real" lambda
lambda[k] = lambda[k-1] * lambda_decay_factor    // Geometric decay

Where (mapping implementation variables to the Friedman et al. paper):

• LAMBDA_EFFECTIVE_INFINITY = infinity: Sentinel value (effectively infinite lambda)
• lambda_max: Theoretical maximum lambda (paper: $\lambda_{max}$)
• lambda_decay_factor: Geometric decay factor (paper: $(\epsilon)^{1/(K-1)}$)
• lambda_min_ratio: Minimum lambda ratio (paper: $\epsilon$)
• eps = 1.0e-6: Implementation constant for stability

Note on LAMBDA_EFFECTIVE_INFINITY

The first lambda value is set to infinity, which produces all-zero coefficients. This matches glmnet’s behavior and provides a complete view of the regularization path, showing the exact point where each coefficient enters the model as lambda decreases. Users who don’t need this can simply ignore the first element.

Structs

LambdaPathOptions

Options for generating a lambda path.

Functions

compute_lambda_max

Computes lambda_max: the smallest lambda for which all penalized coefficients are zero.

extract_lambdas

Extracts a specific set of lambdas from a path.

make_lambda_path

Generates a lambda path.