Greedy Column Subset Selection: New Bounds and Distributed Algorithms

TL;DR

This paper improves theoretical understanding and develops a distributed algorithm for greedy column subset selection, demonstrating its effectiveness through analysis and empirical validation.

Contribution

It provides new approximation guarantees for the greedy algorithm and introduces the first distributed implementation with provable performance bounds.

Findings

Improved approximation guarantee for greedy column subset selection.

First distributed algorithm with provable approximation factors.

Empirical validation confirms effectiveness of the distributed approach.

Abstract

The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy algorithm has been shown to be quite effective in practice. However, theoretical guarantees on its performance have not been explored thoroughly, especially in a distributed setting. In this paper, we study the greedy algorithm for the column subset selection problem from a theoretical and empirical perspective and show its effectiveness in a distributed setting. In particular, we provide an improved approximation guarantee for the greedy algorithm which we show is tight up to a constant factor, and present the first distributed implementation with provable approximation factors. We use the idea of randomized composable core-sets, developed recently in the context of submodular maximization. Finally, we validate the effectiveness of this distributed algorithm via an empirical study.