HMMs - Summary

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Frequently, patterns do not appear in isolation but as part of a series in time - this progression can sometimes be used to assist in their recognition. Assumptions are usually made about the time based process - a common assumption is that the process's state is dependent only on the preceding N states - then we have an order N Markov model. The simplest case is N=1.

Various examples exists where the process states (patterns) are not directly observable, but are indirectly, and probabalistically, observable as another set of patterns - we can then define a hidden Markov model - these models have proved to be of great value in many current areas of research, notably speech recognition.

Such models of real processes pose three problems that are amenable to immediate attack; these are :

  • Evaluation : with what probability does a given model generate a given sequence of observations. The forward algorithm solves this problem efficiently.