The Hidden semi-Markov models (HSMMs) have been introduced to overcome the constraint of a geometric sojourn time distribution for the different hidden states in the classical hidden Markov models. Several variations of HSMMs have been proposed that model the sojourn times by a parametric or a nonparametric family of distributions. In this article, we concentrate our interest on the nonparametr...

A semi-Markov HMM (more properly called a hidden semi-Markov model, or HSMM) is like an HMM except each state can emit a sequence of observations. Let Y (Gt) be the subsequence emitted by “generalized state” Gt. The “generalized state” usually contains both the automaton state, Qt, and the length (duration) of the segment, Lt. We will define Y (Gt) to be the subsequence yt−l+1:t. After emitting...

This paper introduces the hhsmm R package, which involves functions for initializing, fitting, and predication of hidden hybrid Markov/semi-Markov models. These models are flexible with both Markovian semi-Markovian states, applied to situations where model absorbing or macro-states. The left-to-right series/parallel networks states two states. also includes switching regression as well auto-re...

We formulate the problem of change-point detection in a segmental semi-Markov model framework where a change-point corresponds to state switching. The semi-Markov part of the model allows us to incorporate prior knowledge about the time of change in a Bayesian manner. The segmental part of the model allows exible modeling of the data within individual segments, e.g., as linear, quadratic, or ot...

This report introduces a new model for event-driven temporal sequence processing: Generalized Hidden Semi-Markov Models (GHSMMs). GHSMMs are an extension of hidden Markov models to continuous time that builds on turning the stochastic process of hidden state traversals into a semi-Markov process. A large variety of probability distributions can be used to specify transition durations. It is sho...

The duration high-order hidden Markov model (DHO-HMM) can capture the dynamic evolution of a physical system more precisely than can the first-order hidden Markov model (HMM). The relations among the DHO-HMM, high-order HMM (HOHMM), hidden semi-Markov model (HSMM), and HMM are presented and discussed. Recursive forward and backward probability functions for the partial observation sequence were...