On Approximation Guarantees for Greedy Low Rank Optimization

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Rajiv Khanna, Ethan R. Elenberg, Alexandros G. Dimakis, Joydeep Ghosh, Sahand Negahban ;
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1837-1846, 2017.

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 provide also provide statistical recovery guarantees. Finally, we present empirical comparison of greedy estimation with established baselines on two important real-world problems.

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