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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]
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 .
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 ...
It detects homology by comparing a profile-HMM (a Hidden Markov model constructed explicitly for a particular search) to either a single sequence or a database of sequences. Sequences that score significantly better to the profile-HMM compared to a null model are considered to be homologous to the sequences that were used to construct the ...
Some current major algorithms for part-of-speech tagging include the Viterbi algorithm, Brill tagger, Constraint Grammar, and the Baum-Welch algorithm (also known as the forward-backward algorithm). Hidden Markov model and visible Markov model taggers can both be implemented using the Viterbi algorithm. The rule-based Brill tagger is unusual in ...
PCFGs models extend context-free grammars the same way as hidden Markov models extend regular grammars. The Inside-Outside algorithm is an analogue of the Forward-Backward algorithm. It computes the total probability of all derivations that are consistent with a given sequence, based on some PCFG.
Download QR code; Print/export ... Pages in category "Hidden Markov models" ... Island algorithm; L. Layered hidden Markov model