Struct ElasticNetFit 

pub struct ElasticNetFit { /* private fields */ }

A fitted elastic-net regression model and its diagnostics.

Elastic net minimizes

(1/2n)‖y − Xβ‖² + λ[ α‖β_pen‖₁ + ½(1 − α)‖β_pen‖² ],

blending the lasso (α = 1) and ridge (α → 0) penalties. The α mixing parameter controls sparsity-versus-grouping: pure lasso arbitrarily picks one of a set of correlated predictors, while a little ridge (α < 1) shares the coefficient across the group. Fit by cyclic coordinate descent with soft-thresholding (glmnet-style).

Intercept and scaling

Identical conventions to LassoFit: a detected constant column is an unpenalized intercept, predictors are standardized internally, and λ is on the standardized (1/2n)-objective scale.

Effective degrees of freedom

Unlike lasso, where the degrees of freedom are just the active-set size, the ridge part shrinks the surviving coefficients, so the elastic net spends fewer than |active set| degrees of freedom. This type reports the shrinkage-aware trace

df = tr[ Z_A (Z_Aᵀ Z_A + n·λ(1 − α) I)⁻¹ Z_Aᵀ ] (+1 for the intercept),

over the standardized active columns Z_A. It reduces to |active set| at α = 1 (recovering the lasso count) and to the full ridge effective df when nothing is zeroed. The information criteria use it.

Implementations

impl ElasticNetFit

pub fn new( x: Array2<f64>, y: Array1<f64>, lambda: f64, alpha: f64, ) -> Result<Self>

Fit elastic-net regression of y on X with penalty lambda ≥ 0 and mixing alpha ∈ [0, 1] (default tolerance 1e-7, up to 10_000 sweeps).

alpha = 1 is pure lasso (equivalent to LassoFit); alpha = 0 is pure ridge on the standardized scale.

Errors

• RegressionError::EmptyInput / RegressionError::ShapeMismatch.
• RegressionError::InvalidParameter if lambda < 0 or alpha ∉ [0, 1].
• RegressionError::NotConverged if coordinate descent does not converge within the iteration budget.

pub fn with_options( x: Array2<f64>, y: Array1<f64>, lambda: f64, alpha: f64, tol: f64, max_iter: usize, ) -> Result<Self>

Like ElasticNetFit::new with an explicit tolerance and sweep cap.

pub fn lambda(&self) -> f64

The penalty λ this model was fit with.

pub fn alpha(&self) -> f64

The mixing parameter α (1 = lasso, 0 = ridge).

pub fn n_observations(&self) -> usize

Number of observations.

pub fn n_parameters(&self) -> usize

Number of coefficients (design columns, intercept included).

pub fn has_intercept(&self) -> bool

Whether an unpenalized intercept is present.

pub fn iterations(&self) -> usize

Coordinate-descent sweeps taken to converge.

pub fn design_matrix(&self) -> ArrayView2<'_, f64>

The design matrix as fitted.

pub fn coefficients(&self) -> ArrayView1<'_, f64>

Elastic-net coefficients, aligned to the design columns. Coefficients shrunk out are exactly 0.0.

pub fn fitted_values(&self) -> ArrayView1<'_, f64>

Fitted values ŷ = Xβ.

pub fn residuals(&self) -> ArrayView1<'_, f64>

Residuals y − ŷ.

pub fn residual_sum_of_squares(&self) -> f64

Residual sum of squares.

pub fn response(&self) -> ArrayView1<'_, f64>

Response vector.

pub fn active_set(&self) -> Vec<usize>

Indices of the design columns with non-zero coefficients — the active set (excludes the intercept).

pub fn n_nonzero(&self) -> usize

Number of non-zero penalized coefficients (active-set size).

pub fn effective_df(&self) -> f64

Shrinkage-aware effective degrees of freedom (see the type docs): the active-set trace under the ridge part, plus one for the intercept.

pub fn log_likelihood(&self) -> f64

Gaussian log-likelihood at the fitted residual variance.

pub fn aic(&self) -> f64

AIC using the effective degrees of freedom as the parameter count.

pub fn bic(&self) -> f64

BIC using the effective degrees of freedom.

Trait Implementations

impl Clone for ElasticNetFit

fn clone(&self) -> ElasticNetFit

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ElasticNetFit

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.