export type CovarianceType = 'full' | 'tied' | 'diag' | 'spherical';
/**
 * Covariance container per covariance type:
 *  - 'full':      k × d × d  (number[][][])
 *  - 'tied':      d × d      (number[][])
 *  - 'diag':      k × d      (number[][])
 *  - 'spherical': k          (number[])
 */
export type Covariances = number[][][] | number[][] | number[];
export interface GaussianSufficientStats {
    /** effective number of samples per component (Σᵢ respᵢₖ + 10·eps) */
    nk: number[];
    /** k × d weighted means */
    means: number[][];
    /** per-type covariance container (regCovar already added to diagonals) */
    covariances: Covariances;
}
/**
 * Weighted Gaussian parameter estimates from responsibilities — the M-step of
 * EM (and the sufficient statistics of variational Bayes).
 */
export declare function estimateGaussianParameters(X: number[][], resp: number[][], regCovar: number, covarianceType: CovarianceType): GaussianSufficientStats;
/**
 * n × k matrix of log N(xᵢ | μₖ, Σₖ). 'full'/'tied' go through a Cholesky
 * factor (log-det from the diagonal, quadratic form by triangular solve);
 * 'diag'/'spherical' use closed forms.
 */
export declare function estimateLogGaussianProb(X: number[][], means: number[][], covariances: Covariances, covarianceType: CovarianceType): number[][];
/**
 * Per-component log-determinant of the precision Cholesky factor,
 * i.e. −½·log det Σₖ (sklearn's `_compute_log_det_cholesky`). 'tied' is
 * replicated across the k components.
 */
export declare function computeLogDetCholesky(covariances: Covariances, covarianceType: CovarianceType, nComponents: number, nFeatures: number): number[];
/**
 * Initial responsibilities: one-hot k-means labels or normalized uniform
 * random rows. The k-means run is seeded from the fit-local RNG so nInit
 * restarts differ but a seeded fit stays fully deterministic.
 */
export declare function initializeResponsibilities(X: number[][], nComponents: number, initParams: 'kmeans' | 'random', rng: () => number): number[][];