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Large-Scale Sparse Logistic Regression (Lassplore)

The lassplore package solves the following sparse logistic regression problem:

                                                           min         f(w, c) + ρ ||w||²

s.t.          ||w|₁ ≤ z                     (1)

where f(w, c) is the average logistic loss, ||w|| and ||w||₁ denote the 2-norm and 1-norm of the vector w, respectively.

The Matlab Code (version 1.0) can be downloaded here.

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Related Paper

Jun Liu, Jianhui Chen, and Jieping Ye. Large-Scale Sparse Logistic Regression. Technical report, Department of Computer Science and Engineering, Arizona State University, 2009.

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Background & Main Features

Sparse logistic regression embeds feature selection in the classification framework, and is attractive in many applications involving high-dimensional data, e.g., document classification, natural language processing, computer vision, and bioinformatics.

　

We propose the Lassplore algorithm for solving large-scale sparse logistic regression. Specifically, we formulate the problem as the l₁ ball constrained optimization problem (1), and propose to solve the problem using the Nesterov's first-order smooth optimal method. One of the critical issues in the use of Nesterov’s method is the estimation of the step size at each of the optimization iterations. Previous approaches either applies the constant step size which assumes that the Lipschitz gradient is known in advance, or requires a sequence of decreasing step size which leads to slow convergence in practice. In Lassplore, we employ an adaptive line search scheme which allows to tune the step size adaptively and meanwhile guarantees the optimal convergence rate.