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A generalization of the Viterbi algorithm, termed the max-sum algorithm (or max-product algorithm) can be used to find the most likely assignment of all or some subset of latent variables in a large number of graphical models, e.g. Bayesian networks, Markov random fields and conditional random fields.
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. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.
A hidden Markov model is a Markov chain for which the state is only partially observable or noisily observable. In other words, observations are related to the state of the system, but they are typically insufficient to precisely determine the state. Several well-known algorithms for hidden Markov models exist.
Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o 1, ..., o n} having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an internal step. The scaled ...
Hidden Markov models (8 P) M. Markov networks (8 P) Pages in category "Markov models" ... Variable-order Markov model; Viterbi algorithm; W. Word n-gram language model
The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch.The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. [2]
Another related approach are hidden Markov models (HMM) and it has been shown that the Viterbi algorithm used to search for the most likely path through the HMM is equivalent to stochastic DTW. [24] [25] [26] DTW and related warping methods are typically used as pre- or post-processing steps in data analyses.