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False Discovery and Its Control in Low Rank Estimation

Taeb, Armeen and Shah, Parikshit and Chandrasekaran, Venkat (2020) False Discovery and Its Control in Low Rank Estimation. Journal of the Royal Statistical Society: Series B, 82 (4). pp. 997-1027. ISSN 1369-7412. https://resolver.caltech.edu/CaltechAUTHORS:20190626-161131951

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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 with variable selection, we lack a formal framework to assess true or false discoveries in low rank estimation; in particular, the key source of difficulty is that the standard notion of a discovery is a discrete notion 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 analyse 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 with previous approaches via numerical experiments.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1111/rssb.12387DOIArticle
https://arxiv.org/abs/1810.08595arXivDiscussion Paper
ORCID:
AuthorORCID
Taeb, Armeen0000-0002-5647-3160
Additional Information:© 2020 Royal Statistical Society. Version of Record online: 18 July 2020.
Subject Keywords:Algebraic geometry; Determinantal varieties; Model selection; Regularization; Stability selection; Testing
Issue or Number:4
Record Number:CaltechAUTHORS:20190626-161131951
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190626-161131951
Official Citation:Taeb, A., Shah, P. and Chandrasekaran, V. (2020), False discovery and its control in low rank estimation. J. R. Stat. Soc. B, 82: 997-1027. doi:10.1111/rssb.12387
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96759
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:27 Jun 2019 01:45
Last Modified:12 Aug 2020 15:00

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