Papers › Towards a Learning Theory of Cause-Effect Inference
Towards a Learning Theory of Cause-Effect Inference
David Lopez-Paz, Krikamol Muandet, Bernhard Schölkopf, Ilya Tolstikhin
We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(Sᵢ,lᵢ)}ᵢ₌₁ⁿ, where each Sᵢ is a sample drawn from the probability distribution of Xᵢ ×Yᵢ, and lᵢ is a binary label indicating whether "Xᵢ →Yᵢ" or "Xᵢ ←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.
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