On Approximation Guarantees for Greedy Low Rank Optimization
Machine Learning
2017-03-09 v1 Information Theory
Machine Learning
math.IT
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.
Keywords
Cite
@article{arxiv.1703.02721,
title = {On Approximation Guarantees for Greedy Low Rank Optimization},
author = {Rajiv Khanna and Ethan Elenberg and Alexandros G. Dimakis and Sahand Negahban},
journal= {arXiv preprint arXiv:1703.02721},
year = {2017}
}