Self-concordant analysis for logistic regression
Self-concordant analysis for logistic regression
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DOI：
10.1214/09-ejs521
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发表时间：
2010-01-01
影响因子：
1.1
通讯作者：
Bach, Francis
中科院分区：
文献类型：
--
作者：
Bach, Francis
大多数回归的非渐近理论工作都是针对平方损失进行的，其中估计量可以通过封闭形式的表达式获得。在本文中，我们使用和扩展工具，从凸优化文献，即自协调函数，提供简单的扩展的理论结果的平方损失的逻辑损失。我们将扩展技术应用于逻辑回归，通过l（2）-范数和l（1）-范数进行正则化，表明通过逻辑回归进行二进制分类的新结果可以很容易地从最小二乘回归的相应结果中得出。
Most of the non-asymptotic theoretical work in regression 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 l(2)-norm and regularization by the l(1)-norm, showing that new results for binary classification through logistic regression can be easily derived from corresponding results for least-squares regression.