DRAFT ! c 1996

نویسنده

Christopher Manning

چکیده

Hidden Markov Models (HMMs) have been the mainstay of the language mod-eling used in modern speech recognition systems. Despite their limitations, variants on HMMs are still the most widely used technique in that domain, and are generally regarded as the most successful. In this chapter we will develop the basic theory of HMMs and touch on their applications. In the next chapter is found some more detailed information on extending the basic HMM model and engineering practical implementations. Further information on the application of HMMs to Statistical NLP can be found in Chapters x and y. The theory behind Hidden Markov Models was developed by Baum and his colleagues in the late sixties and early seventies, and advocated for use in speech recognition in lectures by Jack Ferguson from the Institute for Defense Analyses. It was applied to speech processing in the 1970s by Baker at CMU and by Jelinek and colleagues at IBM, and then later found its way at IBM and elsewhere into use for other kinds of language modeling, such as part of speech tagging. An HMM is nothing more than a probabilistic function of a Markov process. Markov processes/chains/models were rst developed by Andrei A. Markov (a student of Chebyshev). Their rst use was actually for a linguistic purpose { modeling the letter sequences in works of Russian literature (Markov 1913) { but Markov models were then developed as a general statistical tool. We will refer to vanilla Markov models as Visible Markov Models (VMMs) when we want to be careful to distinguish them from HMMs. 5.1 Markov models Often we want to consider a sequence (perhaps through time) of random variables that aren't independent, but depend rather on previous elements in the sequence. For many such systems, it seems reasonable to assume that we can predict the future based just on the present (and don't need the past). That is, future elements of the sequence are conditionally independent of past elements,

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