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January 31

HMM: Efficiently calculating a probability of a subsequence given the next hidden state

The forward-backward algorithm offers an efficient way to calculate the joint probability of a subsequence of observed states y1...yt and a hidden state xt = i (via alpha values).

However, I am interested in calculating the probability of a subsequence given the value of the next hidden variable: P(y1..yt|x_t+1 = i). Is there an efficient way to calculate this quantity using the forward-backward algorithm or a variation of it?

Thanks — Preceding unsigned comment added by 87.70.147.230 (talk) 07:53, 31 January 2019 (UTC)[reply]

The Forward–backward algorithm (see article) can be used to find the most likely state for any point in time. It cannot, however, be used to find the most likely sequence of states (see Viterbi algorithm). DroneB (talk) 12:13, 31 January 2019 (UTC)[reply]