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Causal Relationship Prediction with Continuous Additive Noise Models

We consider the problem of learning causal relationships in continuous additive noise models (ANM) from a machine learning perspective. Causal discovery from ANMs has primarily focused on testing for independence between the residuals and the true parent set of a variable. We posit that this unique association between residuals and the true parent set can be leveraged with kernel mean embedding to predict causal relationships in observational data. In particular, we propose a framework that finds useful patterns and constructs the causal graph by predicting the true parent set of each variable. We present an analysis of the patterns from kernel mean embeddings that explains their discriminative ability in predicting causal relationships. Finally, we perform simulations that demonstrate the effectiveness of our method.