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What's the right complexity measure for inferring causal relations?

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If X causes Y for two random variables X and Y, we expect that the factorization of P(X,Y) into P(X)P(Y|X) is simpler than the non-causal factorization P(Y)P(X|Y). This is because P(Y|X) describes the causal mechanism while P(X|Y) is “only a mathematical expression”.

Discussions have shown that a lot of researchers agree on this intuition. Since we would like to use this principle for inferring causal directions, we are left with two problems:

(1) what does “simple” mean?

(2) is there any deeper justification for this principle?

Our answer to question (2) is a clear “yes” if complexity vs simplicity is measured in terms of Kolmogorov complexity: I will present a theory of causal inference that generalizes the framework of Bayesian networks to algorithmic instead of statistical conditional dependences. I will show that our theory implies the above inference principle. However, since Kolmogorov complexity is uncomputable we still need complexity measures that are appropriate for practical implementations.

I will present some first small steps towards this challenging goal.

This talk is part of the Statistics series.

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