A Posteriori Probability Distances Between Finite-Alphabet Hidden Markov Models

Author

Xie, Li ; Ugrinovskii, Valery A. ; Petersen, Ian R.

Author_Institution

Sch. of Inf. Technol. & Electr. Eng., Univ. of New South Wales at the Australian Defence Force Acad., Canberra, ACT

Volume

53

Issue

2

fYear

2007

Firstpage

783

Lastpage

793

Abstract

In this correspondence, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of conditional relative entropy between conditional probability measures is introduced as an a posteriori probability distance which can be used to measure the discrepancy between hidden Markov models when a realized observation sequence is observed. Using a measure change technique, we derive a representation for conditional relative entropy in terms of the parameters of the HMMs and conditional expectations given measurements. With this representation, we show that this distance can be calculated using an information state approach

Keywords

entropy; hidden Markov models; probability; aposteriori probability distances; conditional relative entropy; finite-alphabet HMM; hidden Markov models; information state method; measure change technique; Automatic control; Control systems; Entropy; Hidden Markov models; Interchannel interference; Multiaccess communication; Power control; Routing; Spread spectrum communication; Symmetric matrices; A posteriori probability distances; conditional relative entropy; finite-alphabet hidden Markov models; information state; measure change;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.887076

Filename

4069166