On Approximation Guarantees for Greedy Low Rank Optimization
On Approximation Guarantees for Greedy Low Rank Optimization
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发表时间：
2017-03
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通讯作者：
Rajiv Khanna;Ethan R. Elenberg;A. Dimakis;J. Ghosh;S. Negahban
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作者：
Rajiv Khanna;Ethan R. Elenberg;A. Dimakis;J. Ghosh;S. Negahban
我们提供了新的近似保证贪婪的低秩矩阵估计的标准假设下的限制强凸性和光滑性。我们的新的分析还揭示了以前未知的低秩估计和组合优化之间的连接，以至于我们的界限让人想起相应的近似界次模最大化。此外，我们还提供统计恢复保证。最后，我们提出了经验比较贪婪估计与既定的基线上的两个重要的现实世界的问题。
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.