Bayesian decision theory on three layered neural networks

Yoshifusa Ito; Cidambi Srinivasan

Bayesian decision theory on three layered neural networks

Yoshifusa Ito
, Cidambi Srinivasan

Dr. Bing Zhang Department of Statistics

Research output: Contribution to conference › Paper › peer-review

6 Scopus citations

Abstract

We treat the Bayesian decision problem, mainly the two-category case. A three layered neural network, having a logistic output unit and a small number of hidden layer units, can approximate the a posteriori probability in L²-norm, without knowing the type of the probability distribution before learning, if the log ratio of the a posteriori probabilities is a polynomial of low degree as in the case of most familiar probability distributions. This is because the log ratio itself can be well approximated by a linear sum of outputs of the hidden layer units in L²-norm.

Original language	English
Pages	377-382
Number of pages	6
State	Published - 2001
Event	9th European Symposium on Artificial Neural Networks, ESANN 2001 - Bruges, Belgium Duration: Apr 25 2001 → Apr 27 2001

Conference

Conference	9th European Symposium on Artificial Neural Networks, ESANN 2001
Country/Territory	Belgium
City	Bruges
Period	4/25/01 → 4/27/01

Bibliographical note

Publisher Copyright:
© 2001 ESANN. All Rights Reserved.

ASJC Scopus subject areas

Artificial Intelligence
Information Systems

Cite this

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abstract = "We treat the Bayesian decision problem, mainly the two-category case. A three layered neural network, having a logistic output unit and a small number of hidden layer units, can approximate the a posteriori probability in L2-norm, without knowing the type of the probability distribution before learning, if the log ratio of the a posteriori probabilities is a polynomial of low degree as in the case of most familiar probability distributions. This is because the log ratio itself can be well approximated by a linear sum of outputs of the hidden layer units in L2-norm.",

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AB - We treat the Bayesian decision problem, mainly the two-category case. A three layered neural network, having a logistic output unit and a small number of hidden layer units, can approximate the a posteriori probability in L2-norm, without knowing the type of the probability distribution before learning, if the log ratio of the a posteriori probabilities is a polynomial of low degree as in the case of most familiar probability distributions. This is because the log ratio itself can be well approximated by a linear sum of outputs of the hidden layer units in L2-norm.

UR - https://www.scopus.com/pages/publications/105035387669

UR - https://www.scopus.com/pages/publications/105035387669#tab=citedBy

M3 - Paper

AN - SCOPUS:105035387669

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T2 - 9th European Symposium on Artificial Neural Networks, ESANN 2001

Y2 - 25 April 2001 through 27 April 2001

ER -

Bayesian decision theory on three layered neural networks

Abstract

Conference

Bibliographical note

ASJC Scopus subject areas

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Cite this