Open Access
2010 Self-concordant analysis for logistic regression
Francis Bach
Electron. J. Statist. 4: 384-414 (2010). DOI: 10.1214/09-EJS521


Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature, namely self-concordant functions, to provide simple extensions of theoretical results for the square loss to the logistic loss. We apply the extension techniques to logistic regression with regularization by the 2-norm and regularization by the 1-norm, showing that new results for binary classification through logistic regression can be easily derived from corresponding results for least-squares regression.


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Francis Bach. "Self-concordant analysis for logistic regression." Electron. J. Statist. 4 384 - 414, 2010.


Published: 2010
First available in Project Euclid: 22 April 2010

zbMATH: 1329.62324
MathSciNet: MR2645490
Digital Object Identifier: 10.1214/09-EJS521

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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