Linear regression

A Gaussian linear model estimates a real-valued conditional mean. With a complete penalty $R$, its objective is

Choose L1 for sparsity, ridge for quadratic shrinkage, or another compatible penalty. The response must contain one finite real value per observation.

Fit an elastic net

use faer::{Col, Mat};
use shrinkage::{ElasticNet, Gaussian, Problem, ProximalGradient, Termination};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let x = Mat::from_fn(6, 2, |i, j| if j == 0 { i as f64 } else { (i % 2) as f64 });
    let y = [1.0, 3.0, 4.0, 7.0, 8.0, 11.0];
    let fit = Problem::new(&x, Gaussian::new(&y), ElasticNet::new(0.1, 0.2))
        .fit_with(&ProximalGradient::<Col<f64>>::new())?;
    assert_eq!(fit.termination(), Termination::Converged);
    println!("Original-scale coefficients: {:?}", fit.coefficients());
    println!("Response means: {:?}", fit.predict(&x)?);
    Ok(())
}

The default fits an unpenalized intercept and standardizes features using training statistics. See normalization to change these modeling choices.

For Gaussian L1 problems, coordinate descent and the Lasso builder provide a specialized implementation. IRLS also supports separable penalties; the hybrid solver handles supported fusion and SLOPE models. The compatibility table lists the available combinations.