Struct LassoFit 

pub struct LassoFit { /* private fields */ }

A fitted lasso-regression model and its diagnostics.

Lasso solves min (1/2n)‖y − Xβ‖² + λ‖β_pen‖₁. Unlike ridge there is no closed form, so this fits by cyclic coordinate descent with soft-thresholding — the standard, well-conditioned algorithm (glmnet-style).

Intercept and scaling

A detected constant column is an unpenalized intercept. Predictors are standardized internally (centered and scaled to unit variance) before the penalty is applied, then coefficients are transformed back to the original scale; the intercept is recovered from the means. Because standardization is internal, λ is on the standardized (1/2n)-objective scale — not comparable to ridge’s λ.

The natural diagnostic: the active set

Lasso’s defining behavior is that it drives coefficients exactly to zero. The size of the surviving active_set is an unbiased estimate of the model’s degrees of freedom (Zou, Hastie & Tibshirani, 2007), which is what the information criteria here use as the parameter count.

Implementations

impl LassoFit

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

Fit lasso regression of y on X with penalty lambda ≥ 0 using coordinate descent (default tolerance 1e-7, up to 10_000 sweeps).

Errors

• RegressionError::EmptyInput / RegressionError::ShapeMismatch.
• RegressionError::InvalidParameter if lambda < 0.
• RegressionError::NotConverged if coordinate descent does not converge within the iteration budget.

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

Like LassoFit::new but with an explicit convergence tolerance and maximum number of coordinate-descent sweeps.

pub fn lambda(&self) -> f64

The penalty λ this model was fit with.

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>

Lasso coefficients, aligned to the design columns. Penalized coefficients that were 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 (surviving) coefficients — the active set. Excludes the intercept.

pub fn n_nonzero(&self) -> usize

Number of non-zero penalized coefficients — the active-set size, which is lasso’s degrees-of-freedom estimate (Zou–Hastie–Tibshirani).

pub fn effective_df(&self) -> f64

Effective degrees of freedom: the active-set size plus one for the intercept if present.

pub fn log_likelihood(&self) -> f64

Gaussian log-likelihood at the fitted residual variance.

pub fn aic(&self) -> f64

AIC using the active-set-based degrees of freedom as the parameter count.

pub fn bic(&self) -> f64

BIC using the active-set-based degrees of freedom.

Trait Implementations

impl Clone for LassoFit

fn clone(&self) -> LassoFit

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for LassoFit

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

Formats the value using the given formatter.