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 7

Various Observation Distributions

Abstract

Different applications are usually characterized by different observation distributions. There are many observation distributions defined for HSMMs in the literature. A mixture of distributions is often used to describe complexly distributed observations or a compounded observation distribution. A multispace probability distribution is applied to express a composition of different dimensional observation spaces, or a mixture of continuous and discrete ones. A segmental model is used to describe parametric trajectories that change over time. An event sequence model is used to model and analyze event-based random processes. This chapter presents all these typical observation distributions.