Bregman Distance to L1 Regularized Logistic Regression

2010/04/21 by Mithun Das Gupta, Thomas S. Huang, Gupta, Mithun Das +1
Computer Science · #FOS: Computer and information sciences #Machine Learning (cs.LG) #cs.LG

paper · pdf · doi:10.48550/arxiv.1004.3814

8 pages, 3 images, shorter version published in ICPR 2008 by same authors.

arxiv created 2010/04/21 · arxiv updated 2010/04/23

Abstract

In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We present a detailed study of Bregman Distance minimization, a family of generalized entropy measures associated with convex functions. We convert the L1-regularized logistic regression into this more general framework and propose a primal-dual method based algorithm for learning the parameters. We pose L1-regularized logistic regression into Bregman distance minimization and then apply non-linear constrained optimization techniques to estimate the parameters of the logistic model.

Related

• Box-constrained L0 Bregman-relaxations
• Exact continuous relaxations of l0-regularized criteria with non-quadratic data terms
• Robust estimation of parameters in logistic regression via solving the Cramer-von Mises type L2 optimization problem
• Optimization landscape of ℓ₀-Bregman relaxations
• Dual Newton Proximal Point Algorithm for Solution Paths of the L1-Regularized Logistic Regression