Stabilizing variable selection and regression

Niklas Pfister, Evan G. Williams, Jonas Peters, Ruedi Aebersold, Peter Bühlmann

Research output: Contribution to journalJournal articleResearchpeer-review

15 Citations (Scopus)
33 Downloads (Pure)

Abstract

We consider regression in which one predicts a response Y with a set of predictors X across different experiments or environments. This is a common setup in many data-driven scientific fields, and we argue that statistical inference can benefit from an analysis that takes into account the distributional changes across environments. In particular, it is useful to distinguish between stable and unstable predictors, that is, predictors which have a fixed or a changing functional dependence on the response, respectively. We introduce stabilized regression which explicitly enforces stability and thus improves generalization performance to previously unseen environments. Our work is motivated by an application in systems biology. Using multiomic data, we demonstrate how hypothesis generation about gene function can benefit from stabilized regression. We believe that a similar line of arguments for exploit-ing heterogeneity in data can be powerful for many other applications as well. We draw a theoretical connection between multi-environment regression and causal models which allows to graphically characterize stable vs. unstable functional dependence on the response. Formally, we introduce the notion of a stable blanket which is a subset of the predictors that lies between the direct causal predictors and the Markov blanket. We prove that this set is op-timal in the sense that a regression based on these predictors minimizes the mean squared prediction error, given that the resulting regression generalizes to unseen new environments.

Original languageEnglish
JournalAnnals of Applied Statistics
Volume15
Issue number3
Pages (from-to)1220-1246
ISSN1932-6157
DOIs
Publication statusPublished - 2021

Keywords

  • Causality
  • Multiomic data
  • Regression
  • Variable selection

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