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arXiv · 1810.08595

False Discovery and Its Control in Low Rank Estimation

Armeen Taeb·Parikshit Shah·Venkat Chandrasekaran
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Abstract

Models specified by low-rank matrices are ubiquitous in contemporary applications. In many of these problem domains, the row/column space structure of a low-rank matrix carries information about some underlying phenomenon, and it is of interest in inferential settings to evaluate the extent to which the row/column spaces of an estimated low-rank matrix signify discoveries about the phenomenon. However, in contrast to variable selection, we lack a formal framework to assess true/false discoveries in low-rank estimation; in particular, the key source of difficulty is that the standard notion of a discovery is a discrete one that is ill-suited to the smooth structure underlying low-rank matrices. We address this challenge via a geometric reformulation of the concept of a discovery, which then enables a natural definition in the low-rank case. We describe and analyze a generalization of the Stability Selection method of Meinshausen and B\"uhlmann to control for false discoveries in low-rank estimation, and we demonstrate its utility compared to previous approaches via numerical experiments.

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Armeen Taeb, Parikshit Shah, Venkat Chandrasekaran. 2018-10-19. False Discovery and Its Control in Low Rank Estimation. https://arxiv.org/abs/1810.08595

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