Measuring the Influence of Observations in HMMs Through the Kullback–Leibler Distance

Author

Perduca, V. ; Nuel, G.

Author_Institution

Lab. MAP5, Univ. Paris Descartes, Paris, France

Volume

20

Issue

2

fYear

2013

fDate

Feb. 2013

Firstpage

145

Lastpage

148

Abstract

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states´ chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting meaningful observations} in HMM data series.

Keywords

hidden Markov models; statistical distributions; HMM data series; Kullback-Leibler distance; conditional distribution; hidden Markov model; hidden states; linear complexity algorithm; Complexity theory; Entropy; Hidden Markov models; Markov processes; Signal processing algorithms; Standards; Temperature measurement; Forward-backward algorithm; Hidden Markov Models; local outlier factor; outlier detection; relative entropy;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2012.2235830

Filename

6389710