Fast Overlapping Group Lasso

TL;DR

This paper introduces an efficient optimization method for the overlapping group Lasso, enabling feature selection in complex overlapping group structures, demonstrated on gene expression data with improved computational performance.

Contribution

It reveals key properties of the proximal operator for overlapping group Lasso and proposes a gradient descent-based algorithm for efficient optimization.

Findings

Effective optimization of overlapping group Lasso achieved.

Algorithm demonstrated on breast cancer gene expression data.

Results show improved efficiency and effectiveness.

Abstract

The group Lasso is an extension of the Lasso for feature selection on (predefined) non-overlapping groups of features. The non-overlapping group structure limits its applicability in practice. There have been several recent attempts to study a more general formulation, where groups of features are given, potentially with overlaps between the groups. The resulting optimization is, however, much more challenging to solve due to the group overlaps. In this paper, we consider the efficient optimization of the overlapping group Lasso penalized problem. We reveal several key properties of the proximal operator associated with the overlapping group Lasso, and compute the proximal operator by solving the smooth and convex dual problem, which allows the use of the gradient descent type of algorithms for the optimization. We have performed empirical evaluations using the breast cancer gene expression data set, which consists of 8,141 genes organized into (overlapping) gene sets. Experimental results demonstrate the efficiency and effectiveness of the proposed algorithm.