Towards a Learning Theory of Cause-Effect Inference
This addresses the challenge of cause-effect inference for researchers in machine learning and statistics, offering a novel learning-based approach with extensions to multi-variable cases.
The paper tackles the problem of causal inference by framing it as learning to classify probability distributions, using kernel mean embeddings and a binary classifier to distinguish causal directions, achieving state-of-the-art results with generalization bounds for consistency and learning rates.
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 $X_i \times Y_i$, and $l_i$ is a binary label indicating whether "$X_i \to Y_i$" or "$X_i \leftarrow Y_i$". 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.