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False Discovery and Its Control in Low Rank Estimation

Taeb, Armeen and Shah, Parikshit and Chandrasekaran, Venkat (2018) False Discovery and Its Control in Low Rank Estimation. . (Unpublished)

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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 Bühlmann to control for false discoveries in low-rank estimation, and we demonstrate its utility compared to previous approaches via numerical experiments.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Taeb, Armeen0000-0002-5647-3160
Subject Keywords:algebraic geometry, determinantal varieties, testing, model selection, regularization, stability selection
Record Number:CaltechAUTHORS:20190626-161131951
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96759
Deposited By: Tony Diaz
Deposited On:27 Jun 2019 01:45
Last Modified:03 Oct 2019 21:25

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