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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 .
The general algorithm involves message passing and is substantially similar to the belief propagation algorithm (which is the generalization of the forward-backward algorithm). With an algorithm called iterative Viterbi decoding , one can find the subsequence of an observation that matches best (on average) to a given hidden Markov model.
Hidden Markov models (8 P) M. Markov networks (8 P) Pages in category "Markov models" ... Forward–backward algorithm; G. Gene prediction;
Graphical model. Bayesian network; D-separation; Markov random field; Tree decomposition (Junction tree) and treewidth; Graph triangulation (see also Chordal graph) Perfect order; Hidden Markov model. Baum–Welch algorithm; Viterbi algorithm; Incidence matrix; Independent set problem; Knowledge representation. Conceptual graph; Mind map; Level ...
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 ...