An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion

An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are...

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Main Authors: Badong Chen, Guangmin Wang, Nanning Zheng, Jose C. Principe
Format: Article
Language:English
Published: MDPI AG 2014-04-01
Series:Entropy
Subjects:
estimation
minimum error entropy
Renyi entropy
information potential
Online Access:http://www.mdpi.com/1099-4300/16/4/2223
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spelling doaj-80c3024a337d474cb5233c6f3fd93eb22020-11-25T00:29:08ZengMDPI AGEntropy1099-43002014-04-011642223223310.3390/e16042223e16042223An Extended Result on the Optimal Estimation Under the Minimum Error Entropy CriterionBadong Chen0Guangmin Wang1Nanning Zheng2Jose C. Principe3Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, ChinaInstitute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, ChinaInstitute of Artificial Intelligence and Robotics, Xi'an Jiaotong University, Xi'an 710049, ChinaDepartment of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USAThe minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the α-order information potential (IP).http://www.mdpi.com/1099-4300/16/4/2223estimationminimum error entropyRenyi entropyinformation potential
collection DOAJ
language English
format Article
sources DOAJ
author Badong Chen
Guangmin Wang
Nanning Zheng
Jose C. Principe
spellingShingle Badong Chen
Guangmin Wang
Nanning Zheng
Jose C. Principe
An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
Entropy
estimation
minimum error entropy
Renyi entropy
information potential
author_facet Badong Chen
Guangmin Wang
Nanning Zheng
Jose C. Principe
author_sort Badong Chen
title An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
title_short An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
title_full An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
title_fullStr An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
title_full_unstemmed An Extended Result on the Optimal Estimation Under the Minimum Error Entropy Criterion
title_sort extended result on the optimal estimation under the minimum error entropy criterion
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2014-04-01
description The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the α-order information potential (IP).
topic estimation
minimum error entropy
Renyi entropy
information potential
url http://www.mdpi.com/1099-4300/16/4/2223
work_keys_str_mv AT badongchen anextendedresultontheoptimalestimationundertheminimumerrorentropycriterion
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AT josecprincipe anextendedresultontheoptimalestimationundertheminimumerrorentropycriterion
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AT guangminwang extendedresultontheoptimalestimationundertheminimumerrorentropycriterion
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