Sublinear algorithms for penalized logistic regression in massive datasets

Abstract

Penalized logistic regression (PLR) is a widely used supervised learning model. In this paper, we consider its applications in large-scale data problems and resort to a stochastic primal-dual approach for solving PLR. In particular, we employ a random sampling technique in the primal step and a multiplicative weights method in the dual step. This technique leads to an optimization method with sublinear dependency on both the volume and dimensionality of training data. We develop concrete algorithms for PLR with ℓ 2-norm and ℓ 1-norm penalties, respectively. Experimental results over several large-scale and high-dimensional datasets demonstrate both efficiency and accuracy of our algorithms. © 2012 Springer-Verlag.