Struct Ridge 

pub struct Ridge { /* private fields */ }

Ridge regression with L2 regularization.

Fits a linear model with L2 penalty on coefficient magnitudes. The optimization objective is:

minimize ||y - Xβ||² + α||β||²

where α (alpha) controls the regularization strength.

Solver

Uses regularized normal equations: β = (X^T X + αI)^-1 X^T y

When to use Ridge

• When you have many correlated features (multicollinearity)
• To prevent overfitting with limited samples
• When all features are expected to contribute

Examples

use aprender::prelude::*;
use aprender::linear_model::Ridge;

// Data with some noise
let x = Matrix::from_vec(5, 2, vec![
    1.0, 2.0,
    2.0, 3.0,
    3.0, 4.0,
    4.0, 5.0,
    5.0, 6.0,
]).expect("Valid matrix dimensions");
let y = Vector::from_slice(&[5.0, 8.0, 11.0, 14.0, 17.0]);

let mut model = Ridge::new(1.0);  // alpha = 1.0
model.fit(&x, &y).expect("Fit should succeed with valid data");

let predictions = model.predict(&x);
let r2 = model.score(&x, &y);
assert!(r2 > 0.9);

Implementations

impl Ridge

pub fn new(alpha: f32) -> Ridge

Creates a new Ridge regression with the given regularization strength.

Arguments

• alpha - Regularization strength. Larger values = more regularization. Must be non-negative. Use 0.0 for no regularization (equivalent to OLS).

pub fn with_intercept(self, fit_intercept: bool) -> Ridge

Sets whether to fit an intercept term.

pub fn alpha(&self) -> f32

Returns the regularization strength (alpha).

pub fn coefficients(&self) -> &Vector<f32>

Returns the coefficients (excluding intercept).

Panics

Panics if model is not fitted.

pub fn intercept(&self) -> f32

Returns the intercept term.

pub fn is_fitted(&self) -> bool

Returns true if the model has been fitted.

pub fn save<P>(&self, path: P) -> Result<(), String>

where P: AsRef<Path>,

Saves the model to a binary file using bincode.

Errors

Returns an error if serialization or file writing fails.

pub fn load<P>(path: P) -> Result<Ridge, String>

where P: AsRef<Path>,

Loads a model from a binary file.

Errors

Returns an error if file reading or deserialization fails.

pub fn save_safetensors<P>(&self, path: P) -> Result<(), String>

where P: AsRef<Path>,

Saves the model to SafeTensors format.

SafeTensors format is compatible with:

• HuggingFace ecosystem
• Ollama (can convert to GGUF)
• PyTorch, TensorFlow
• realizar inference engine

Errors

Returns an error if:

• Model is not fitted
• Serialization fails
• File writing fails

pub fn load_safetensors<P>(path: P) -> Result<Ridge, String>

where P: AsRef<Path>,

Loads a model from SafeTensors format.

Errors

Returns an error if:

• File reading fails
• SafeTensors format is invalid
• Required tensors are missing

Trait Implementations

impl Clone for Ridge

fn clone(&self) -> Ridge

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Ridge

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for Ridge

fn deserialize<__D>( __deserializer: __D, ) -> Result<Ridge, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Estimator for Ridge

fn fit(&mut self, x: &Matrix<f32>, y: &Vector<f32>) -> Result<(), AprenderError>

Fits the Ridge regression model using regularized normal equations.

Solves: β = (X^T X + αI)^-1 X^T y

Errors

Returns an error if input dimensions don’t match or matrix is singular.

fn predict(&self, x: &Matrix<f32>) -> Vector<f32>

Predicts target values for input data.

Panics

Panics if model is not fitted.

fn score(&self, x: &Matrix<f32>, y: &Vector<f32>) -> f32

Computes the R² score.

impl Serialize for Ridge

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.