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Information-geometric approach to inferring causal directions This publication appears in: Artificial Intelligence Authors: D. Janzing, J. Mooij and J. Lemeire Volume: 182 Pages: 1-31 Publication Date: Jan. 2012
Abstract: While conventional approaches to causal inference are mainly based on conditional
(in)dependences, recent methods also account for the shape of (conditional) distributions.
The idea is that the causal hypothesis "X causes Y " imposes that the marginal distribution
P(X) and the conditional distribution P(Y |X) represent independent mechanisms of nature.
Recently it has been postulated that the shortest description of the joint distribution P X,Y
should therefore be given by separate descriptions of P(X) and P(Y |X) . Since description
length in the sense of Kolmogorov complexity is uncomputable, practical implementations
rely on other notions of independence. Here we define independence via orthogonality
in information space. This way, we can explicitly describe the kind of dependence that
occurs between P(Y) and P(X|Y) making the causal hypothesis "Y causes X" implausible.
Remarkably, this asymmetry between cause and effect becomes particularly simple if X
and Y are deterministically related. We present an inference method that works in this
case. We also discuss some theoretical results for the non-deterministic case although it is
not clear how to employ them for a more general inference method. External Link.
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