Bregman Distance to L1 Regularized Logistic Regression

TL;DR

This paper explores the connection between Bregman distances and L1-regularized logistic regression, proposing a new primal-dual algorithm within a generalized entropy framework for improved parameter estimation.

Contribution

It introduces a novel formulation of L1-regularized logistic regression as Bregman distance minimization and develops a primal-dual optimization algorithm for parameter learning.

Findings

Bregman distance framework generalizes L1-regularized logistic regression.

A primal-dual method effectively estimates model parameters.

Enhanced understanding of the relationship between entropy measures and regularized models.

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.