Unified Treatment of Hidden Markov Switching Models

Several problems encountered in application areas such as finance, biology, speech analysis, control engineering, robotics, etc. require the modeling of time-series containing switching among different dynamics regimes (see Ephraim (2002) for a review). For example, system fault diagnosis deals with detecting behavioural deviations from normality originated by failures in the system. Such a modeling is often achieved by employing probabilistic approaches in which regime switching is described by a set of discrete hidden random variables, related by a first-order Markovian dependence. All such models, that we call hidden Markov switching models (HMSMs), can be viewed as extensions of the popular hidden Markov model Rabiner (1989). The wide interdisciplinary attention to this research area has produced many different HMSMs as well as different approaches and implementations of HMSMs of fundamentally similar structure, resulting in a dense literature from which extracting differences and commonalities among models is often challenging. In this paper we provide a simple unified treatment of existing HMSMs, highlighting properties and connections that were not observed in previous review papers Ephraim (2002); Gales and Young (1993); Murphy (2002); Ostendorf et al. (1996); Rabiner (1989); Yu (2010), and introduce novel extensions. Our exposition enables a deep understanding of the fundamental structure and relations of different approaches. This is achieved by using the framework of graphical models, which allows to easily define complex models by using a graphical representation and to derive efficient inference routines by visual inspection of the graph, avoiding complex algebraic manipulations.