Wald Memorial Award & Lecture, Part I

This talk develops algorithmic causality learning techniques from the data that are collected from heterogeneous environments. We pursue the maximum set of invariant variables such that the regression function on this set of quasi-causal variables remains the same across different environments, but including one or more noncausal or endogenously spurious variables will cause regression functions to vary across different environments. To realize this idea, we proposed a Neural Adversial Invariant Learning (NAIL) framework, in which the unknown regression is represented by a Relu network, and invariance across multiple environments is tested using adversarial neural networks. Leveraging the representation power of neural networks, we introduce neural causal networks based on a focused adversarial invariance regularization (FAIR) and its novel training algorithm. It is shown that FAIR-NN can find the invariant variables and causal variables under the structural causal model and that the resulting procedure is adaptive to low-dimensional composition structures. The combinatorial optimization problem is implemented by a Gumble approximation with decreased temperature and stochastic approximations. The procedures are convincingly demonstrated using simulated examples and two real data examples: causal discovery in a physical system and transfer learning to unseen environments. (Joint work with Cong Fang, Yihong Gu, and Peter Buelhmann)