ARDRegression

#include <Skigen/LinearModel>

template <typename Scalar = double>
class Skigen::ARDRegression(max_iter=300, tol=1e-3, alpha_1=1e-6, alpha_2=1e-6, lambda_1=1e-6, lambda_2=1e-6, compute_score=false, threshold_lambda=1e4, fit_intercept=true, copy_X=true, verbose=false)

Bayesian Automatic Relevance Determination (ARD) regression.

Maintains a per-feature precision $\lambda_j$ and prunes features whose precision exceeds threshold_lambda during the evidence-maximisation iteration. Mirrors sklearn.linear_model.ARDRegression.

The posterior covariance over the surviving features is

$$\Sigma = \bigl(\operatorname{diag}(\lambda_{\text{keep}}) + \alpha\, X_{\text{keep}}^\top X_{\text{keep}}\bigr)^{-1}$$

and the posterior mean is $w_{\text{keep}} = \alpha\, \Sigma\, X_{\text{keep}}^\top y$.

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Attributes:

• max_iter : int

• tol : Scalar

• alpha_1 : Scalar

• alpha_2 : Scalar

• lambda_1 : Scalar

• lambda_2 : Scalar

• compute_score : bool

• threshold_lambda : Scalar

• fit_intercept : bool

• verbose : bool

• coef : RowVectorType

• intercept : Scalar

• alpha : Scalar

• lambda_ : RowVectorType Per-feature weight precisions, shape (n_features,).

• sigma : MatrixType

• scores : VectorType

• n_iter : int

• X_offset : RowVectorType

• X_scale : RowVectorType

• y_offset : Scalar

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Methods

SKIGEN_PARAMS()

Fit the ARD model via evidence maximisation with feature pruning.

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fit(X, y)

Fit from a sparse design matrix (densifies internally).

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predict(X)

Predictive mean.

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score(X, y)

$R^2$ score.

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predict(X)

Predictive mean and standard deviation (tag-dispatch overload).

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predict(X)

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Example

Skigen::ARDRegression<double> ard(
    /*max_iter=*/300, /*tol=*/1e-3,
    /*alpha_1=*/1e-6, /*alpha_2=*/1e-6,
    /*lambda_1=*/1e-6, /*lambda_2=*/1e-6,
    /*compute_score=*/false,
    /*threshold_lambda=*/1e4);
ard.fit(X, y);

std::cout << "=== ARDRegression ===\n";
std::cout << "  alpha    = " << ard.alpha() << "\n";
std::cout << "  lambda_  = " << ard.lambda_() << "\n";
std::cout << "  coef     = " << ard.coef() << "\n";
std::cout << "  n_iter   = " << ard.n_iter() << "\n";
std::cout << "  R^2 (train) = " << ard.score(X, y) << "\n";

// Predictions with confidence intervals on first 5 samples.
Eigen::MatrixXd X_test = X.topRows(5);
auto [y_mean, y_std] = ard.predict(X_test, Skigen::with_std);
std::cout << "\nPredictions with 95% CI (first 5 rows):\n";
for (Eigen::Index i = 0; i < y_mean.size(); ++i) {
    std::cout << "  y_pred = " << std::setw(7) << y_mean(i)
              << "  +/- " << std::setw(6) << 1.96 * y_std(i)
              << "  (true=" << y(i) << ")\n";
}

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