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arXiv · 0910.4627

Self-concordant analysis for logistic regression

Francis Bach
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Abstract

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 $\ell_2$-norm and regularization by the $\ell_1$-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. 2009-10-24. Self-concordant analysis for logistic regression. https://arxiv.org/abs/0910.4627

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