Provable Deterministic Leverage Score Sampling

Dimitris Papailiopoulos; Anastasios Kyrillidis; Christos Boutsidis

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arXiv · 1404.1530

Provable Deterministic Leverage Score Sampling

Dimitris Papailiopoulos·Anastasios Kyrillidis·Christos Boutsidis

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Abstract

We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain provable guarantees, previous work requires randomized sampling of the columns with probabilities proportional to their leverage scores. In this work, we provide a novel theoretical analysis of deterministic leverage score sampling. We show that such deterministic sampling can be provably as accurate as its randomized counterparts, if the leverage scores follow a moderately steep power-law decay. We support this power-law assumption by providing empirical evidence that such decay laws are abundant in real-world data sets. We then demonstrate empirically the performance of deterministic leverage score sampling, which many times matches or outperforms the state-of-the-art techniques.

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BibTeX RIS

Dimitris Papailiopoulos, Anastasios Kyrillidis, Christos Boutsidis. 2014-04-06. Provable Deterministic Leverage Score Sampling. https://arxiv.org/abs/1404.1530

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