Towards a Learning Theory of Cause-Effect Inference

author: Krikamol Muandet, Max Planck Institute for Intelligent Systems, Max Planck Institute
published: Dec. 5, 2015,   recorded: October 2015,   views: 2046

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We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(Si,li)}ni=1, 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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