Exponential curvature of Markov models

Junnichi Takeuchi; Tsutomu Kawabata

doi:10.1109/ISIT.2007.4557657

Exponential curvature of Markov models

Junnichi Takeuchi, Tsutomu Kawabata

Mathematical Informatics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

7 Citations (Scopus)

Abstract

We prove that the non FSMX tree model is not an exponential family. It is noted in [Weinberger et al., 95] that the tree source is classified into two classes; a FSMX source or not, depending on shape of the context tree. The FSMX source is a tree source and a finite state machine. It is known that the FSMX model is an exponential family. In this situation our concern is whether the non FSMX tree model is an exponential family or not. This paper's contribution is to show that the non FSMX tree model is not an exponential family. Hence, for the tree model, to be an FSMX model is a necessary and sufficient condition for to be an exponential family.

Original language	English
Title of host publication	Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007
Pages	2891-2895
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2007.4557657
Publication status	Published - Dec 1 2007
Event	2007 IEEE International Symposium on Information Theory, ISIT 2007 - Nice, France Duration: Jun 24 2007 → Jun 29 2007

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8101

Other

Other	2007 IEEE International Symposium on Information Theory, ISIT 2007
Country/Territory	France
City	Nice
Period	6/24/07 → 6/29/07

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2007.4557657

Cite this

Takeuchi, J & Kawabata, T 2007, Exponential curvature of Markov models. in Proceedings - 2007 IEEE International Symposium on Information Theory, ISIT 2007., 4557657, IEEE International Symposium on Information Theory - Proceedings, pp. 2891-2895, 2007 IEEE International Symposium on Information Theory, ISIT 2007, Nice, France, 6/24/07. https://doi.org/10.1109/ISIT.2007.4557657

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abstract = "We prove that the non FSMX tree model is not an exponential family. It is noted in [Weinberger et al., 95] that the tree source is classified into two classes; a FSMX source or not, depending on shape of the context tree. The FSMX source is a tree source and a finite state machine. It is known that the FSMX model is an exponential family. In this situation our concern is whether the non FSMX tree model is an exponential family or not. This paper's contribution is to show that the non FSMX tree model is not an exponential family. Hence, for the tree model, to be an FSMX model is a necessary and sufficient condition for to be an exponential family.",

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AU - Takeuchi, Junnichi

AU - Kawabata, Tsutomu

PY - 2007/12/1

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N2 - We prove that the non FSMX tree model is not an exponential family. It is noted in [Weinberger et al., 95] that the tree source is classified into two classes; a FSMX source or not, depending on shape of the context tree. The FSMX source is a tree source and a finite state machine. It is known that the FSMX model is an exponential family. In this situation our concern is whether the non FSMX tree model is an exponential family or not. This paper's contribution is to show that the non FSMX tree model is not an exponential family. Hence, for the tree model, to be an FSMX model is a necessary and sufficient condition for to be an exponential family.

AB - We prove that the non FSMX tree model is not an exponential family. It is noted in [Weinberger et al., 95] that the tree source is classified into two classes; a FSMX source or not, depending on shape of the context tree. The FSMX source is a tree source and a finite state machine. It is known that the FSMX model is an exponential family. In this situation our concern is whether the non FSMX tree model is an exponential family or not. This paper's contribution is to show that the non FSMX tree model is not an exponential family. Hence, for the tree model, to be an FSMX model is a necessary and sufficient condition for to be an exponential family.

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Exponential curvature of Markov models

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