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The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions ::=, …,, i.e. it computes, for all hidden state variables {, …,}, the distribution ( | :).
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch ...
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 .
This is done especially in the context of Markov information sources and hidden Markov models (HMM). The algorithm has found universal application in decoding the convolutional codes used in both CDMA and GSM digital cellular, dial-up modems, satellite, deep-space communications, and 802.11 wireless LANs.
Baum–Welch algorithm: computes maximum likelihood estimates and posterior mode estimates for the parameters of a hidden Markov model; Forward-backward algorithm: a dynamic programming algorithm for computing the probability of a particular observation sequence; Viterbi algorithm: find the most likely sequence of hidden states in a hidden ...
Island algorithm; L. Layered hidden Markov model This page was last edited on 30 March 2013, at 04:46 (UTC). Text is available under the Creative Commons ...
Hidden Markov models (8 P) M. Markov networks (8 P) Pages in category "Markov models" ... Forward–backward algorithm; G. Gene prediction;