Greedy Column Subset Selection: New Bounds and Distributed Algorithms
The problem of matrix 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, our theoretical guarantees on its performance have not been ex- plored thoroughly, especially in a distributed set- ting. 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 par- ticular, we provide an improved approximation guarantee for the greedy algorithm, and present the first distributed implementation of this algo- rithm with provable approximation factors. We use the idea of randomized composable core- sets, developed recently in the context of sub- modular maximization. Finally, we validate the effectiveness of this distributed algorithm via an empirical study.