Towards causality-aware predictions in static anticausal machine learning tasks: the linear structural causal model case

We propose a counterfactual approach to train ``causality-aware" predictive models that are able to leverage causal information in static anticausal machine learning tasks (i.e., prediction tasks where the outcome influences the features). In applications plagued by confounding, the approach can be used to generate predictions that are free from the influence of observed confounders. In applications involving observed mediators, the approach can be used to generate predictions that only capture the direct or the indirect causal influences. Mechanistically, we train supervised learners on (counterfactually) simulated features which retain only the associations generated by the causal relations of interest. We focus on linear models, where analytical results connecting covariances, causal effects, and prediction mean squared errors are readily available. Quite importantly, we show that our approach does not require knowledge of the full causal graph. It suffices to know which variables represent potential confounders and/or mediators. We discuss the stability of the method with respect to dataset shifts generated by selection biases and validate the approach using synthetic data experiments.