Forward-Backward Algorithm
The Forward-Backward Algorithm is a dynamic programming algorithm used to compute the posterior marginals of hidden states in a Hidden Markov Model (HMM). It is a two-pass algorithm that first computes the forward probabilities, which are the probabilities of being in a particular state at a particular time given all the observations up to that time, and then computes the backward probabilities, which are the probabilities of observing the remaining observations from a particular state at a particular time. The product of the forward and backward probabilities gives the posterior marginal probabilities of being in a particular state at a particular time given all the observations. The Forward-Backward Algorithm is used in a variety of applications, including speech recognition, natural language processing, and bioinformatics.
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