Forward algorithm

The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.init t = 0 {displaystyle t=0} , transition probabilities p ( x t | x t − 1 ) {displaystyle p(x_{t}|x_{t-1})} , emission probabilities, p ( y j | x i ) {displaystyle p(y_{j}|x_{i})} , observed sequence, y ( 1 : t ) {displaystyle y(1:t)} The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.