STABILIZING VARIABLE SELECTION AND REGRESSION

• 成果类型: Article
• 署名作者: Pfister, Niklas; Williams, Evan G.; Peters, Jonas; Aebersold, Ruedi; Buehlmann, Peter
• 署名单位: University of Copenhagen; University of Luxembourg; Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/21-AOAS1487
• 发表日期: 2021
• 页码: 1220-1246
• 关键词: Causal Inference; INDEPENDENCE

摘要

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 exploiting 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 optimal 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.