/**
 * Forward Algorithm for Hidden Markov Models
 *
 * Computes forward probabilities α(t,i) = P(o₁...oₜ, qₜ=i | λ)
 * Uses scaling for numerical stability
 */
import { ForwardResult } from '../../schemas/ForwardResultSchema';
import { EmissionParams } from '../../schemas/EmissionParamsSchema';
/**
 * Forward Algorithm with scaling
 *
 * @param observations - T x D matrix of observations
 * @param transitionMatrix - N x N transition probability matrix
 * @param emissionParams - Emission parameters for each state
 * @param initialProbs - Initial state probabilities
 * @returns Forward probabilities and scaling factors
 *
 * @example
 * ```typescript
 * const result = forward(observations, transitionMatrix, emissionParams, initialProbs);
 * console.log(result.logLikelihood); // Log-likelihood of observations
 * ```
 */
export declare function forward(observations: number[][], transitionMatrix: number[][], emissionParams: EmissionParams[], initialProbs: number[]): ForwardResult;