Module: aprender::linear_model

Public module of the aprender-core crate.

Source

crates/aprender-core/src/linear_model.rs or directory.

Example

use aprender::linear_model;
// See `cargo doc -p aprender-core --open` for full API reference.

Module summary

aprender::linear_model provides ordinary least squares regression plus the three regularized linear models that cover the vast majority of tabular regression problems: ridge (L2), lasso (L1), and elastic net (L1 + L2). The solvers are deterministic, single-threaded, and ship with closed-form solutions where possible (Cholesky for OLS/Ridge, coordinate descent for Lasso). Reach for this module when you need an interpretable linear baseline, a fast pre-NN sanity check, or a feature-selection-friendly model via lasso sparsity.

Key types

TypeDescription
LinearRegressionOLS regression via normal equations + Cholesky. Fits in O(p³).
RidgeOLS with L2 penalty on coefficients. Closed-form solution with a regularization parameter alpha.
LassoOLS with L1 penalty, solved via coordinate descent. Produces sparse coefficient vectors.
ElasticNetCombined L1 + L2 penalty. Tunable mixing ratio l1_ratio between 0 and 1.

All four implement the Estimator trait, so they share the same fit / predict / score surface.

Usage patterns

Pattern 1: OLS regression with R² scoring

use aprender::prelude::*;

let x = Matrix::from_vec(4, 1, vec![1.0, 2.0, 3.0, 4.0])
    .expect("valid 4x1 matrix");
let y = Vector::from_slice(&[3.0, 5.0, 7.0, 9.0]);

let mut model = LinearRegression::new();
model.fit(&x, &y).expect("fit succeeds on well-conditioned data");

let preds = model.predict(&x);
let r2 = model.score(&x, &y);
assert!(r2 > 0.99, "perfectly linear data must score near 1.0");
println!("predictions: {:?}", preds.as_slice());

Pattern 2: Lasso for feature selection

use aprender::prelude::*;

// 6 samples, 3 features — only the first feature is informative
let x = Matrix::from_vec(6, 3, vec![
    1.0, 0.5, 0.2,
    2.0, 0.6, 0.1,
    3.0, 0.7, 0.3,
    4.0, 0.5, 0.2,
    5.0, 0.6, 0.4,
    6.0, 0.5, 0.1,
]).expect("valid 6x3 matrix");
let y = Vector::from_slice(&[2.0, 4.0, 6.0, 8.0, 10.0, 12.0]);

let mut lasso = Lasso::new(0.1);
lasso.fit(&x, &y).expect("lasso fit");

// Lasso zeroes out coefficients of uninformative features.
let coefs = lasso.coefficients();
println!("non-zero coefficients: {}",
    coefs.as_slice().iter().filter(|&&c| c.abs() > 1e-3).count());

See also

  • optim — solvers (Cholesky, coordinate descent, FISTA) used internally
  • loss — MSE/MAE losses that drive the underlying optimization
  • metrics — r_squared, mse, rmse used by score()
  • regularization — broader regularization techniques beyond linear models
  • model_selection — grid_search_alpha for tuning the regularization strength

Full API

Run cargo doc -p aprender-core --open for the rendered rustdoc, or browse docs.rs/aprender for the published version.