Paper Info
Title
An EM and a Stochastic Version of the EM Algorithm for Nonparametric Hidden Semi-Markov Models
Abstract
The Hidden semi-Markov models (HSMMs) were 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 were proposed that model the sojourn times by a parametric or a nonparametric family of distributions. In this article, we concentrate our interest on the nonparametric case where the duration distributions are attached to transitions and not to states as in most of the published papers in HSMMs. Therefore, it is worth noticing that here we treat the underlying hidden semi-Markov chain in its general probabilistic structure. In that case, Barbu and Limnios (2008) proposed an Expectation-Maximization (EM) algorithm in order to estimate the semi-Markov kernel and the emission probabilities that characterize the dynamics of the model. In this article, we consider an improved version of Barbu and Limnios' EM algorithm which is faster than the original one. Moreover, we propose a stochastic version of the EM algorithm that achieves comparable estimates with the EM algorithm in less execution time. Some numerical examples are provided which illustrate the efficient performance of the proposed algorithms.
Year
DOI
Venue
2010
10.1080/03610910903411185
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Keywords
Field
DocType
EM algorithm,Hidden semi-Markov models,Maximum likelihood estimation,Stochastic EM algorithm
Econometrics,Expectation–maximization algorithm,Parametric family,Markov model,Markov chain,Nonparametric statistics,Probability distribution,Statistics,Hidden Markov model,Mathematics,Hidden semi-Markov model
Journal
Volume
Issue
ISSN
39
2
0361-0918
Citations 
PageRank 
References 
2
0.37
5
Authors
3
Name
Order
Citations
PageRank
Sonia Malefaki1314.89
Samis Trevezas241.09
Nikolaos Limnios3836.93