A POSTERIORI PROBABILITY DISTANCES BETWEEN FINITE-ALPHABET HIDDEN MARKOV MODELS

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

doi:10.1016/s1474-6670(17)30540-2

A POSTERIORI PROBABILITY DISTANCES BETWEEN FINITE-ALPHABET HIDDEN MARKOV MODELS

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

Research output: Contribution to journal › Conference article › peer-review

Abstract

In this paper, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of regular conditional relative entropy between regular conditional probability measures is introduced as an a posteriori probability distance when a realized observation sequence is observed. Using a measure change and a relation between the Radon-Nikodym derivatives of probability measures and regular conditional probability measures, we derive a representation for regular conditional relative entropy. With this representation, we can calculate this distance using an information state approach. The regular conditional relative entropy rate is also considered.

Original language	English
Pages (from-to)	627-632
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	37
Issue number	21
DOIs	https://doi.org/10.1016/s1474-6670(17)30540-2
Publication status	Published - 2004
Externally published	Yes
Event	2nd IFAC Symposium on System Structure and Control 2004 - Oaxaca, Mexico Duration: 8 Dec 2004 → 10 Dec 2004

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10.1016/s1474-6670(17)30540-2

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title = "A POSTERIORI PROBABILITY DISTANCES BETWEEN FINITE-ALPHABET HIDDEN MARKOV MODELS",

abstract = "In this paper, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of regular conditional relative entropy between regular conditional probability measures is introduced as an a posteriori probability distance when a realized observation sequence is observed. Using a measure change and a relation between the Radon-Nikodym derivatives of probability measures and regular conditional probability measures, we derive a representation for regular conditional relative entropy. With this representation, we can calculate this distance using an information state approach. The regular conditional relative entropy rate is also considered.",

keywords = "a posteriori probability distances, finite-alphabet hidden Markov models, regular conditional relative entropy",

author = "Li Xie and Ugrinovskii, \{Valery A.\} and Petersen, \{Ian R.\}",

note = "Publisher Copyright: Copyright {\textcopyright} IFAC 2004.; 2nd IFAC Symposium on System Structure and Control 2004 ; Conference date: 08-12-2004 Through 10-12-2004",

year = "2004",

doi = "10.1016/s1474-6670(17)30540-2",

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T1 - A POSTERIORI PROBABILITY DISTANCES BETWEEN FINITE-ALPHABET HIDDEN MARKOV MODELS

AU - Xie, Li

AU - Ugrinovskii, Valery A.

AU - Petersen, Ian R.

PY - 2004

Y1 - 2004

N2 - In this paper, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of regular conditional relative entropy between regular conditional probability measures is introduced as an a posteriori probability distance when a realized observation sequence is observed. Using a measure change and a relation between the Radon-Nikodym derivatives of probability measures and regular conditional probability measures, we derive a representation for regular conditional relative entropy. With this representation, we can calculate this distance using an information state approach. The regular conditional relative entropy rate is also considered.

AB - In this paper, we consider a probability distance problem for a class of hidden Markov models (HMMs). The notion of regular conditional relative entropy between regular conditional probability measures is introduced as an a posteriori probability distance when a realized observation sequence is observed. Using a measure change and a relation between the Radon-Nikodym derivatives of probability measures and regular conditional probability measures, we derive a representation for regular conditional relative entropy. With this representation, we can calculate this distance using an information state approach. The regular conditional relative entropy rate is also considered.

KW - a posteriori probability distances

KW - finite-alphabet hidden Markov models

KW - regular conditional relative entropy

UR - https://www.scopus.com/pages/publications/85178326046

U2 - 10.1016/s1474-6670(17)30540-2

DO - 10.1016/s1474-6670(17)30540-2

M3 - Conference article

AN - SCOPUS:85178326046

SN - 2405-8971

VL - 37

SP - 627

EP - 632

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 21

T2 - 2nd IFAC Symposium on System Structure and Control 2004

Y2 - 8 December 2004 through 10 December 2004

ER -

A POSTERIORI PROBABILITY DISTANCES BETWEEN FINITE-ALPHABET HIDDEN MARKOV MODELS

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