Ridge

#include <Skigen/LinearModel>

template <typename Scalar = double>
class Skigen::Ridge(alpha=1, fit_intercept=true)

Linear least squares with L2 regularization.

Minimizes the objective function:

$$\|y - Xw\|_2^2 + \alpha \|w\|_2^2$$

This model solves a regression model where the loss function is the linear least squares function and regularization is given by the L2-norm. Also known as Ridge Regression or Tikhonov regularization.

Mirrors sklearn.linear_model.Ridge.

Read more in the User Guide.

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Parameters:

• alpha : Scalar, default=1 Constant that multiplies the L2 term (Scalar, default 1). Controls regularization strength. alpha = 0 is equivalent to ordinary least squares (use LinearRegression instead for numerical stability).

• fit_intercept : bool, default=true Whether the intercept should be estimated (bool, default true). If false, the data is assumed to be already centered.

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Attributes:

• alpha : Scalar Regularization strength.

• fit_intercept : bool Whether an intercept is fitted.

• coef : RowVectorType Parameter vector $w$ (1 × n_features).

• intercept : Scalar Independent term in the decision function.

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Methods

fit(X, y)

Fit the Ridge model via Cholesky decomposition.

Centers the data when fit_intercept is true, then solves the regularized normal equation via Cholesky factorization.

Parameters:

• X : MatrixType Design matrix of shape (n_samples, n_features).

• y : VectorType Target vector of shape (n_samples,). Will be cast to Scalar if necessary.

Returns:

• result : Ridge Reference to the fitted estimator (*this).

note

sklearn parity gap: sample_weight parameter is not yet supported.

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predict(X)

Predict using the linear model.

Computes $\hat{y} = X w + b$ where $w$ and $b$ are the fitted coefficients and intercept.

Parameters:

• X : MatrixType Sample matrix of shape (n_samples, n_features).

Returns:

• result : VectorType Predicted values of shape (n_samples,).

Throws:

• std::runtime_error — if the model has not been fitted.

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score(X, y)

Return the $R^2$ coefficient of determination on test data.

$R^2 = 1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2}$. Best possible score is 1.0; it can be negative if the model is arbitrarily worse than predicting the mean.

Parameters:

• X : MatrixType Test samples of shape (n_samples, n_features).

• y : VectorType True values of shape (n_samples,).

Returns:

• result : ScalarType $R^2$ score.

Throws:

• std::runtime_error — if the model has not been fitted.

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Example

// Compare different alpha values
std::cout << "=== Ridge: alpha sweep ===\n";
for (double alpha : {0.01, 0.1, 1.0, 10.0, 100.0}) {
    Skigen::Ridge<double> model(alpha);
    model.fit(X_tr, split.y_train);
    std::cout << "  alpha=" << std::setw(6) << alpha
              << "  R²=" << model.score(X_te, split.y_test)
              << "  coef=" << model.coef() << "\n";
}

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