Consistency analysis of an empirical minimum error entropy algorithm
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Pages (from-to) | 164-189 |
Journal / Publication | Applied and Computational Harmonic Analysis |
Volume | 41 |
Issue number | 1 |
Online published | 23 Dec 2014 |
Publication status | Published - Jul 2016 |
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Abstract
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the bandwidth parameter tends to 0 at an appropriate rate. The regression consistency, which requires the learned function to approximate the regression function, however, is a complicated issue. We prove that the error entropy consistency implies the regression consistency for homoskedastic models where the noise is independent of the input variable. But for heteroskedastic models, a counterexample is used to show that the two types of consistency do not coincide. A surprising result is that the regression consistency is always true, provided that the bandwidth parameter tends to infinity at an appropriate rate. Regression consistency of two classes of special models is shown to hold with fixed bandwidth parameter, which further illustrates the complexity of regression consistency of MEE. Fourier transform plays crucial roles in our analysis.
Research Area(s)
- Error entropy consistency, Learning theory, Minimum error entropy, Regression consistency, Rényi's entropy
Citation Format(s)
Consistency analysis of an empirical minimum error entropy algorithm. / Fan, Jun; Hu, Ting; Wu, Qiang et al.
In: Applied and Computational Harmonic Analysis, Vol. 41, No. 1, 07.2016, p. 164-189.
In: Applied and Computational Harmonic Analysis, Vol. 41, No. 1, 07.2016, p. 164-189.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review