Towards a Learning Theory of Causation

Опубликовано 27 июня 2016, 21:21

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(S i ,l i )} i=1 n , where each S i is a sample drawn from the probability distribution of X i × Y i , and l i is a binary label indicating whether “ X i to Y i ” or “ X i ≤ftarrow Y i ”. Given these data, we build a causal inference rule in two steps. First, we featurize each S i 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.