On Approximation Guarantees for Greedy Low Rank Optimization

TL;DR

This paper establishes new approximation guarantees for greedy low rank matrix estimation, revealing connections to combinatorial optimization and providing statistical recovery guarantees, supported by empirical comparisons on real-world problems.

Contribution

It introduces novel approximation bounds for greedy low rank estimation, linking it to submodular maximization and offering statistical guarantees.

Findings

New approximation bounds similar to submodular maximization

Statistical recovery guarantees established

Empirical results show competitive performance

Abstract

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminiscent of corresponding approximation bounds in submodular maximization. Additionally, we also provide statistical recovery guarantees. Finally, we present empirical comparison of greedy estimation with established baselines on two important real-world problems.