دانلود کتاب راهنمای جامع HSMM

Hidden Markov models (HMMs) were introduced in the 1960s by Baum and Petrie (1966), first in the case of discrete observations. They have become classical tools to analyze time series whose dynamics can be explained by those of a hidden process. The model is composed of two sets of random variables that are two linked dynamical stochastic processes: one hidden and one observed. This family of models was originally popularized by applications in speech recognition (Baker 1975) and later in other domains like genomics (Churchill 1989). In parallel, developments were achieved in computational statistics to make statistical estimation possible. At the beginning of the 1980s, it was observed that the Markovian assumption on hidden state dynamics was not satisfied in the context of speech recognition. Thus, different relaxations of this assumption were proposed, leading to explicit duration HMMs (Ferguson 1980, ED-HMMs), reformulated shortly after in their modern, more parsimonious form by Russell and Moore (1985). More general semi-Markov models were introduced by Murphy (2002), as an extension of so-called segment HMMs, which are themselves generalizations of ED-HMMs. Concomitantly with those generalizations of HMMs leading progressively to HSMMs, focusing on refinements on how state and sojourn durations at the current jump depend on the same quantities as the previous jump, HMMs underwent developments on modeling dependencies between several interacting chains, which is the subject of Chapter 3 in this book. These developments were once again motivated by applications in speech or video processing and oriented toward two directions: representing coupling of (shared) hidden states through observations (Ghahramani and Jordan 1997) or directly coupling through states, keeping observations conditionally independent given their unique associated hidden state (Brand et al. 1997).