Here is another fascinating aspect of randomization, detecting causation from correlation: The Randomized Causation Coefficient by David Lopez-Paz, Krikamol Muandet and Benjamin Recht

We are interested in learning causal relationships between pairs of random variables, purely from observational data. To effectively address this task, the state-of-the-art relies on strong assumptions regarding the mechanisms mapping causes to effects, such as invertibility or the existence of additive noise, which only hold in limited situations. On the contrary, this short paper proposes to learn how to perform causal inference directly from data, and without the need of feature engineering. In particular, we pose causality as a kernel mean embedding classification problem, where inputs are samples from arbitrary probability distributions on pairs of random variables, and labels are types of causal relationships. We validate the performance of our method on synthetic and real-world data against the state-of-the-art. Moreover, we submitted our algorithm to the ChaLearn's "Fast Causation Coefficient Challenge" competition, with which we won the fastest code prize and ranked third in the overall leaderboard.

The code is on David Lopez-Paz's page.

Also relevant: The Randomized Dependence Coefficient by David Lopez-Paz, Philipp Hennig and Bernhard Schölkopf. Attendant code is also on David Lopez-Paz's page.

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