Evaluations for Estimation of an Information Source Based on State Decomposition

Joe SUZUKI

Evaluations for Estimation of an Information Source Based on State Decomposition

Joe SUZUKI

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This paper's main objective is to analyze several procedures which select the model g among a set G of stochastic models to minimize the value of an information criterion in the form of L(g)H[g](zⁿ)+(k(g)/2)c(n), where zⁿ is the n observed data emitted by an information source θ which consists of the model g_θ∈G and k(g_θ) mutually independent stochastic parameters in the model g_θ∈G, H[g](zⁿ) is (-1) (the maximum log likelihood value of the data zⁿ with respect to a model g∈G), and c(n) is a predetermined function (penalty function) of n which controls the amount of penalty for increasing the model size. The result is focused on specific performances when the information criteria are applied to the framework of so-called state decomposition. Especially, upper bounds are derived of the following two performance measures for each penalty function c(n): the error probability of the model selection, and the average Kullback-Leibler information between the true information source and the estimated information source.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.7 pp.1240-1251

Publication Date: 1993/07/25

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Type of Manuscript: PAPER

Category: Information Theory and Coding Theory

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Joe SUZUKI, "Evaluations for Estimation of an Information Source Based on State Decomposition" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 7, pp. 1240-1251, July 1993, doi: .
Abstract: This paper's main objective is to analyze several procedures which select the model g among a set G of stochastic models to minimize the value of an information criterion in the form of L(g)H[g](zⁿ)+(k(g)/2)c(n), where zⁿ is the n observed data emitted by an information source θ which consists of the model g_θ∈G and k(g_θ) mutually independent stochastic parameters in the model g_θ∈G, H[g](zⁿ) is (-1) (the maximum log likelihood value of the data zⁿ with respect to a model g∈G), and c(n) is a predetermined function (penalty function) of n which controls the amount of penalty for increasing the model size. The result is focused on specific performances when the information criteria are applied to the framework of so-called state decomposition. Especially, upper bounds are derived of the following two performance measures for each penalty function c(n): the error probability of the model selection, and the average Kullback-Leibler information between the true information source and the estimated information source.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e76-a_7_1240/_p

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@ARTICLE{e76-a_7_1240,
author={Joe SUZUKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Evaluations for Estimation of an Information Source Based on State Decomposition},
year={1993},
volume={E76-A},
number={7},
pages={1240-1251},
abstract={This paper's main objective is to analyze several procedures which select the model g among a set G of stochastic models to minimize the value of an information criterion in the form of L(g)H[g](zⁿ)+(k(g)/2)c(n), where zⁿ is the n observed data emitted by an information source θ which consists of the model g_θ∈G and k(g_θ) mutually independent stochastic parameters in the model g_θ∈G, H[g](zⁿ) is (-1) (the maximum log likelihood value of the data zⁿ with respect to a model g∈G), and c(n) is a predetermined function (penalty function) of n which controls the amount of penalty for increasing the model size. The result is focused on specific performances when the information criteria are applied to the framework of so-called state decomposition. Especially, upper bounds are derived of the following two performance measures for each penalty function c(n): the error probability of the model selection, and the average Kullback-Leibler information between the true information source and the estimated information source.},
keywords={},
doi={},
ISSN={},
month={July},}

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TY - JOUR
TI - Evaluations for Estimation of an Information Source Based on State Decomposition
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1240
EP - 1251
AU - Joe SUZUKI
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 1993
AB - This paper's main objective is to analyze several procedures which select the model g among a set G of stochastic models to minimize the value of an information criterion in the form of L(g)H[g](zⁿ)+(k(g)/2)c(n), where zⁿ is the n observed data emitted by an information source θ which consists of the model g_θ∈G and k(g_θ) mutually independent stochastic parameters in the model g_θ∈G, H[g](zⁿ) is (-1) (the maximum log likelihood value of the data zⁿ with respect to a model g∈G), and c(n) is a predetermined function (penalty function) of n which controls the amount of penalty for increasing the model size. The result is focused on specific performances when the information criteria are applied to the framework of so-called state decomposition. Especially, upper bounds are derived of the following two performance measures for each penalty function c(n): the error probability of the model selection, and the average Kullback-Leibler information between the true information source and the estimated information source.
ER -