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Conference Paper

Causal Inference by Choosing Graphs with Most Plausible Markov Kernels

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Sun,  X
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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AIMath-2006-Sun.pdf
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Citation

Sun, X., Janzing, D., & Schölkopf, B. (2006). Causal Inference by Choosing Graphs with Most Plausible Markov Kernels. In Ninth International Symposium on Artificial Intelligence and Mathematics (AIMath 2006) (pp. 1-11).


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D317-D
Abstract
We propose a new inference rule for estimating causal structure that underlies the observed statistical dependencies among n random variables. Our method is based on comparing the conditional distributions of variables given their direct causes (the so-called Markov kernels") for all hypothetical causal directions and choosing the most plausible one. We consider those Markov kernels most plausible, which maximize the (conditional) entropies constrained by their observed first moment (expectation) and second moments (variance and covariance with its direct causes) based on their given domain. In this paper, we discuss our inference rule for causal relationships between two variables in detail, apply it to a real-world temperature data set with known causality and show that our method provides a correct result for the example.