Towards a Learning Theory of Cause-Effect Inference

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection ${(Si,li)}{i=1}^n$, where each $Si$ is a sample drawn from the probability distribution of $Xi \times Yi$, and $li$ is a binary label indicating whether "$Xi \to Yi$" or "$Xi \leftarrow Yi$". Given these data, we build a causal inference rule in two steps. First, we featurize each $Si$ using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.