Feature Clustering for Accelerating Parallel Coordinate Descent

TL;DR

This paper introduces a new family of block-greedy coordinate descent algorithms for large-scale L1-regularized problems, providing a unified convergence analysis and demonstrating improved parallelism through feature clustering.

Contribution

The paper proposes a novel block-greedy coordinate descent framework, unifies existing algorithms, and offers convergence analysis that highlights the benefits of feature clustering for parallelism.

Findings

Block-greedy algorithms include SCD, Greedy CD, Shotgun, and Thread-Greedy.

Clustering features improves parallelism and convergence.

Experimental results validate theoretical advantages across real-world datasets.

Abstract

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building upon previous work on coordinate descent algorithms for L1-regularized problems, we introduce a novel family of algorithms called block-greedy coordinate descent that includes, as special cases, several existing algorithms such as SCD, Greedy CD, Shotgun, and Thread-Greedy. We give a unified convergence analysis for the family of block-greedy algorithms. The analysis suggests that block-greedy coordinate descent can better exploit parallelism if features are clustered so that the maximum inner product between features in different blocks is small. Our theoretical convergence analysis is supported with experimental re- sults using data from diverse real-world applications. We hope that algorithmic approaches and convergence analysis we provide will not only advance the field, but will also encourage researchers to systematically explore the design space of algorithms for solving large-scale L1-regularization problems.