  Learning representations purely from observations concerns the problem of
learning a low-dimensional, compact representation which is beneficial to
prediction models. Under the hypothesis that the intrinsic latent factors
follow some casual generative models, we argue that by learning a causal
representation, which is the minimal sufficient causes of the whole system, we
can improve the robustness and generalization performance of machine learning
models. In this paper, we develop a learning method to learn such
representation from observational data by regularizing the learning procedure
with mutual information measures, according to the hypothetical factored causal
graph. We theoretically and empirically show that the models trained with the
learned causal representations are more robust under adversarial attacks and
distribution shifts compared with baselines. The supplementary materials are
available at https://github.com/ymy $4323460 / \mathrm{CaRI} /$.
