Learning Counterfactually Invariant Predictors

Invariance, or equivariance to certain data transformations, has proven essential in numerous applications of machine learning (ML), since it can lead to better generalization capabilities [Arjovsky et al., 2019, Bloem-Reddy and Teh, 2020, Chen et al., 2020]. For instance, in image recognition, predictions ought to remain unchanged under scaling, translation, or rotation of the input image. Data augmentation, an early heuristic to promote such invariances, has become indispensable for successfully training deep neural networks (DNNs) [Shorten and Khoshgoftaar, 2019, Xie et al., 2020]. Well-known examples of "invariance by design" include convolutional neural networks (CNNs) for translation invariance [Krizhevsky et al., 2012], group equivariant NNs for general group transformations [Cohen and Welling, 2016], recurrent neural networks (RNNs) and transformers for sequential data [Vaswani et al., 2017], DeepSet [Zaheer et al., 2017] for sets, and graph neural networks (GNNs) for different types of geometric structures [Battaglia et al., 2018]. Many applications in modern ML, however, call for arguably stronger notions of invariance based on causality. This case has been made for image classification, algorithmic fairness [Hardt et al., 2016, Mitchell et al., 2021], robustness [Bühlmann, 2020], and out-of-distribution generalization [Lu et al., 2021]. The goal is invariance with respect to hypothetical manipulations of the data generating process (DGP). Various works develop methods that assume observational distributions (across environments or between training and test) to be governed by shared causal mechanisms, but differ due to various types of distribution shifts encoded by the causal model [Arjovsky et al., 2019, Bühlmann, 2020, Heinze-Deml et al., 2018, Makar et al., 2022, Part of this work was done while Francesco Quinzan visited the Max Planck Institute for Intelligent Systems, Tübingen, Germany.