Self-concordant analysis for logistic regression
Machine Learning
2009-10-27 v1 Statistics Theory
Statistics Theory
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 -norm and regularization by the -norm, showing that new results for binary classification through logistic regression can be easily derived from corresponding results for least-squares regression.
Cite
@article{arxiv.0910.4627,
title = {Self-concordant analysis for logistic regression},
author = {Francis Bach},
journal= {arXiv preprint arXiv:0910.4627},
year = {2009}
}