Learning Theory Approach to Minimum Error Entropy Criterion

Ting Hu, Jun Fan, Qiang Wu, Ding-Xuan Zhou

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm when an approximation of Rényi's entropy (of order 2) by Parzen windowing is minimized. This learning algorithm involves a Parzen windowing scaling parameter. We present a learning theory approach for this MEE algorithm in a regression setting when the scaling parameter is large. Consistency and explicit convergence rates are provided in terms of the approximation ability and capacity of the involved hypothesis space. Novel analysis is carried out for the generalization error associated with Rényi's entropy and a Parzen windowing function, to overcome technical difficulties arising from the essential differences between the classical least squares problems and the MEE setting. An involved symmetrized least squares error is introduced and analyzed, which is related to some ranking algorithms.
Original languageEnglish
Pages (from-to)377–397
JournalJournal of Machine Learning Research
Volume14
Issue number1
Publication statusPublished - Jan 2013

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