Stabilizing variable selection and regression

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