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

Entropy

Badong Chen¹  Guangmin Wang¹  Nanning Zheng¹ 

[1] Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an 710049, China; E-Mails:

关键词: estimation;    minimum error entropy;    Renyi entropy;    information potential;   

DOI  :  10.3390/e16042223

来源: mdpi

【 摘 要 】

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).

MSC Codes: 62B10

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland