Learning towards Robustness in Causally-Invariant Predictors

We propose to learn an invariant causal predictor that is robust to distributional shifts, in the supervised regression scenario. Based on a disentangled causal factorization that describes the underlying data generating process, we attribute the distributional shifts to mutation of generating factors, which covers a wide range of cases of distributional shifts as we do not make prior specifications on the causal structure or the source of mutation. Under this causal framework, we identify a set of invariant predictors based on the do-operator. We provide a sufficient and necessary condition for a predictor to be min-max optimal, i.e., minimizes the worst-case quadratic loss among all domains. This condition is justifiable under the Markovian and faithfulness assumptions, thus inspiring a practical algorithm to identify the optimal predictor. For empirical estimation, we propose a permutation-regeneration scheme guided by a local causal discovery procedure. The utility and effectiveness of our method are demonstrated in simulation data and two real-world applications: Alzheimer's disease diagnosis and gene function prediction.