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We consider regression in which one predicts a response $Y$ with a set ofpredictors $X$ across different experiments or environments. This is a commonsetup in many data-driven scientific fields and we argue that statisticalinference can benefit from an analysis that takes into account thedistributional changes across environments. In particular, it is useful todistinguish between stable and unstable predictors, i.e., predictors which havea fixed or a changing functional dependence on the response, respectively. Weintroduce stabilized regression which explicitly enforces stability and thusimproves generalization performance to previously unseen environments. Our workis motivated by an application in systems biology. Using multiomic data, wedemonstrate how hypothesis generation about gene function can benefit fromstabilized regression. We believe that a similar line of arguments forexploiting heterogeneity in data can be powerful for many other applications aswell. We draw a theoretical connection between multi-environment regression andcausal models, which allows to graphically characterize stable versus unstablefunctional dependence on the response. Formally, we introduce the notion of astable blanket which is a subset of the predictors that lies between the directcausal predictors and the Markov blanket. We prove that this set is optimal inthe sense that a regression based on these predictors minimizes the meansquared prediction error given that the resulting regression generalizes tounseen new environments.

Stabilizing Variable Selection and Regression