book

Hidden Semi-Markov Models

by Shun-Zheng Yu

October 2015

Beginner to intermediate

208 pages

6h 3m

English

Elsevier

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Abstract1.1 Markov Renewal Process and Semi-Markov Process
1.3 Dynamic Bayesian Networks1.4 Conditional Random Fields1.5 Hidden Semi-Markov Models1.6 History of Hidden Semi-Markov Models
Abstract2.1 A General Definition of HSMM2.2 Forward–Backward Algorithm for HSMM
2.4 Forward-Only Algorithm for HSMM2.5 Viterbi Algorithm for HSMM2.6 Constrained-Path Algorithm for HSMM

Abstract3.1 EM Algorithm and Maximum-Likelihood Estimation3.2 Re-estimation Algorithms of Model Parameters
3.4 Online Update of Model Parameters
Abstract4.1 Heuristic Scaling4.2 Posterior Notation4.3 Logarithmic Form4.4 Practical Issues in Implementation
Abstract5.1 Explicit Duration HSMM5.2 Variable Transition HSMM5.3 Variable-Transition and Explicit-Duration Combined HSMM5.4 Residual Time HSMM
Abstract6.1 Exponential Family Distribution of Duration6.2 Discrete Coxian Distribution of Duration6.3 Duration Distributions for Viterbi HSMM Algorithms
Abstract7.1 Typical Parametric Distributions of Observations7.2 A Mixture of Distributions of Observations7.3 Multispace Probability Distributions7.4 Segmental Model7.5 Event Sequence Model
Abstract8.1 Switching HSMM8.2 Adaptive Factor HSMM8.3 Context-Dependent HSMM
8.5 Signal Model of HSMM8.6 Infinite HSMM and HDP-HSMM8.7 HSMM Versus HMM
Abstract9.1 Speech Synthesis9.2 Human Activity Recognition9.3 Network Traffic Characterization and Anomaly Detection9.4 fMRI/EEG/ECG Signal Analysis

Content preview from Hidden Semi-Markov Models

Chapter 6

Various Duration Distributions

Abstract

A nonparametric distribution of state duration can express probabilities of every state duration that may occur. The number of model parameters for the state duration distributions is thus determined by the maximum duration of a state. In some applications, however, parametric distributions of state duration are preferred so that only a few parameters that specify the selected distribution functions are needed. More importantly, a parametric distribution with a few parameters can express infinite length of state duration. This implies that a training sequence of observations can be shorter than the maximum duration of states. This chapter presents the most popular parametric distributions of state ...