Struct BayesianLinearRegression 

pub struct BayesianLinearRegression {
    pub alpha_prior: f64,
    pub beta_noise: f64,
    pub posterior_mean: Vec<f64>,
    pub posterior_cov: Vec<Vec<f64>>,
}

Bayesian linear regression with conjugate Gaussian prior on weights.

Model: y = X w + ε, ε ~ N(0, σ² I). Prior: w ~ N(w₀, α⁻¹ I).

Fields

alpha_prior: f64

Prior precision α (= 1/σ_prior²).

beta_noise: f64

Noise precision β (= 1/σ_noise²).

posterior_mean: Vec<f64>

Posterior mean weights (set after fitting).

posterior_cov: Vec<Vec<f64>>

Posterior covariance matrix (row-major, set after fitting).

Implementations

impl BayesianLinearRegression

pub fn new(alpha_prior: f64, beta_noise: f64) -> Self

Creates a new Bayesian linear regression model.

Arguments

• alpha_prior - Prior precision (inverse variance) on weights.
• beta_noise - Noise precision.

pub fn fit(&mut self, x_mat: &[Vec<f64>], y: &[f64])

Fits the model to design matrix x_mat (n × d) and targets y (n).

Computes the posterior mean and covariance analytically.

pub fn predict_mean(&self, x_new: &[f64]) -> f64

Returns the predictive mean for a new input vector x_new.

pub fn predict_variance(&self, x_new: &[f64]) -> f64

Returns the predictive variance for a new input x_new.

σ²_pred = 1/β + x^T S_N x.

pub fn log_evidence(&self, x_mat: &[Vec<f64>], y: &[f64]) -> f64

Returns the log marginal likelihood (model evidence) log p(y | X, α, β).

log p(y) = (d/2) ln α + (n/2) ln β - (1/2)(β ||y - X m_N||² + α ||m_N||²) - (1/2) ln|S_N^{-1}| - (n/2) ln(2π)

Trait Implementations

impl Clone for BayesianLinearRegression

fn clone(&self) -> BayesianLinearRegression

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for BayesianLinearRegression

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

Formats the value using the given formatter.