On Approximation Guarantees for Greedy Low Rank Optimization

Rajiv Khanna; Ethan Elenberg; Alexandros G. Dimakis; Sahand Negahban

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arXiv · 1703.02721

On Approximation Guarantees for Greedy Low Rank Optimization

Rajiv Khanna·Ethan Elenberg·Alexandros G. Dimakis·Sahand Negahban

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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.

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BibTeX RIS

Rajiv Khanna, Ethan Elenberg, Alexandros G. Dimakis, Sahand Negahban. 2017-03-08. On Approximation Guarantees for Greedy Low Rank Optimization. https://arxiv.org/abs/1703.02721

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