Chapter 2

General Hidden Semi-Markov Model

Abstract

There are various definitions of hidden semi-Markov models (HSMMs) in the literature. This chapter provides a unified description of HSMMs and discusses the important issues related to inference in the general HSMM. When specific assumptions on the state transitions, duration distributions, and observation distributions are made, the general HSMM is reduced to the conventional HSMMs. Therefore, the algorithms and formulas derived for the general HSMM are applicable for any of the conventional HSMMs. To compute the filtered, predicted, smoothed probabilities, and the expected value or number of times that a random variable of HSMM occurs, the forward–backward algorithm, as well as its symmetric ...

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