NDLI: Penalized Bregman divergence for large-dimensional regression and classification

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Penalized Bregman divergence for large-dimensional regression and classification

Content Provider	PubMed Central
Author	Zhang, Chunming Jiang, Yuan Chai, Yi
Copyright Year	2010
Abstract	Regularization methods are characterized by loss functions measuring data fits and penalty terms constraining model parameters. The commonly used quadratic loss is not suitable for classification with binary responses, whereas the loglikelihood function is not readily applicable to models where the exact distribution of observations is unknown or not fully specified. We introduce the penalized Bregman divergence by replacing the negative loglikelihood in the conventional penalized likelihood with Bregman divergence, which encompasses many commonly used loss functions in the regression analysis, classification procedures and machine learning literature. We investigate new statistical properties of the resulting class of estimators with the number pn of parameters either diverging with the sample size n or even nearly comparable with n, and develop statistical inference tools. It is shown that the resulting penalized estimator, combined with appropriate penalties, achieves the same oracle property as the penalized likelihood estimator, but asymptotically does not rely on the complete specification of the underlying distribution. Furthermore, the choice of loss function in the penalized classifiers has an asymptotically relatively negligible impact on classification performance. We illustrate the proposed method for quasilikelihood regression and binary classification with simulation evaluation and real-data application.
Related Links	http://dx.doi.org/10.1093/biomet/asq033
Ending Page	566
Page Count	16
Starting Page	551
File Format	PDF
ISSN	00063444
e-ISSN	14643510
Journal	Biometrika
Issue Number	3
Volume Number	97
Language	English
Publisher	Oxford University Press
Publisher Date	2010-09-01
Access Restriction	Open
Rights Holder	Oxford University Press
Subject Keyword	Agricultural and Biological Sciences (miscellaneous) Statistics, Probability and Uncertainty Statistics and Probability Applied Mathematics Agricultural and Biological Sciences(all) Mathematics(all) Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability Agricultural and Biological Sciences Statistics, Probability and Uncertainty

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