solvr 0.2.0-beta.2

Advanced computing library for real-world problem solving - optimization, differential equations, interpolation, statistics, and more
Documentation 
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//! Gaussian Mixture Model trait.
use crate::DType;

use numr::error::Result;
use numr::runtime::Runtime;
use numr::tensor::Tensor;

/// Covariance parameterization.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
pub enum CovarianceType {
    /// Each component has its own full covariance `[k, d, d]`.
    #[default]
    Full,
    /// All components share one covariance `[d, d]`.
    Tied,
    /// Diagonal covariance `[k, d]`.
    Diagonal,
    /// Scalar variance per component `[k]`.
    Spherical,
}

/// Initialization method for GMM.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
pub enum GmmInit {
    /// Initialize via K-Means.
    #[default]
    KMeans,
    /// Random initialization.
    Random,
}

/// Options for Gaussian Mixture Model.
#[derive(Debug, Clone)]
pub struct GmmOptions {
    /// Number of mixture components.
    pub n_components: usize,
    /// Covariance type.
    pub covariance_type: CovarianceType,
    /// Maximum EM iterations.
    pub max_iter: usize,
    /// Convergence tolerance on log-likelihood.
    pub tol: f64,
    /// Number of random restarts.
    pub n_init: usize,
    /// Initialization method.
    pub init: GmmInit,
    /// Regularization added to covariance diagonal.
    pub reg_covar: f64,
}

impl Default for GmmOptions {
    fn default() -> Self {
        Self {
            n_components: 1,
            covariance_type: CovarianceType::Full,
            max_iter: 100,
            tol: 1e-3,
            n_init: 1,
            init: GmmInit::KMeans,
            reg_covar: 1e-6,
        }
    }
}

/// Fitted Gaussian Mixture Model.
#[derive(Debug, Clone)]
pub struct GmmModel<R: Runtime<DType = DType>> {
    /// Mixture weights `[k]` (sum = 1).
    pub weights: Tensor<R>,
    /// Component means `[k, d]`.
    pub means: Tensor<R>,
    /// Covariances (shape depends on covariance_type).
    pub covariances: Tensor<R>,
    /// Precomputed Cholesky of precision matrices.
    pub precisions_cholesky: Tensor<R>,
    /// Whether EM converged.
    pub converged: bool,
    /// Number of iterations run.
    pub n_iter: usize,
    /// Final log-likelihood lower bound.
    pub lower_bound: f64,
}

/// Gaussian Mixture Model algorithms.
pub trait GmmAlgorithms<R: Runtime<DType = DType>> {
    /// Fit GMM to data `[n, d]`.
    fn gmm_fit(&self, data: &Tensor<R>, options: &GmmOptions) -> Result<GmmModel<R>>;

    /// Predict most likely component for each point.
    fn gmm_predict(&self, model: &GmmModel<R>, data: &Tensor<R>) -> Result<Tensor<R>>;

    /// Predict component probabilities `[n, k]`.
    fn gmm_predict_proba(&self, model: &GmmModel<R>, data: &Tensor<R>) -> Result<Tensor<R>>;

    /// Compute per-sample log-likelihood.
    fn gmm_score(&self, model: &GmmModel<R>, data: &Tensor<R>) -> Result<Tensor<R>>;

    /// Bayesian Information Criterion: n_params * ln(n) - 2 * log_likelihood.
    fn gmm_bic(&self, model: &GmmModel<R>, data: &Tensor<R>) -> Result<Tensor<R>>;

    /// Akaike Information Criterion: 2 * n_params - 2 * log_likelihood.
    fn gmm_aic(&self, model: &GmmModel<R>, data: &Tensor<R>) -> Result<Tensor<R>>;
}