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At the heart of causal structure learning from observational data lies adeceivingly simple question: given two statistically dependent randomvariables, which one has a causal effect on the other? This is impossible toanswer using statistical dependence testing alone and requires that we makeadditional assumptions. We propose several fast and simple criteria fordistinguishing cause and effect in pairs of discrete or continuous randomvariables. The intuition behind them is that predicting the effect variableusing the cause variable should be `simpler' than the reverse -- differentnotions of `simplicity' giving rise to different criteria. We demonstrate theaccuracy of the criteria on synthetic data generated under a broad family ofcausal mechanisms and types of noise.

Inferring Causal Direction from Observational Data: A Complexity Approach