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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| Format: | Article |
| Language: | English |
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MDPI AG
2014-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/4/2223 |
| _version_ | 1798003981373407232 |
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| author | Badong Chen Guangmin Wang Nanning Zheng Jose C. Principe |
| author_facet | Badong Chen Guangmin Wang Nanning Zheng Jose C. Principe |
| author_sort | Badong Chen |
| collection | DOAJ |
| 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). |
| first_indexed | 2024-04-11T12:16:14Z |
| format | Article |
| id | doaj.art-80c3024a337d474cb5233c6f3fd93eb2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:16:14Z |
| publishDate | 2014-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-80c3024a337d474cb5233c6f3fd93eb22022-12-22T04:24:19ZengMDPI 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 |
| 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 |
| title | 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_short | 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 |
| topic | estimation minimum error entropy Renyi entropy information potential |
| url | http://www.mdpi.com/1099-4300/16/4/2223 |
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