Causal Inference by Choosing Graphs with Most Plausible Markov Kernels.
Xiaohai Sun, Dominik Janzing and Bernhard Schölkopf
In: 9th International Symposium on Artificial Intelligence and Mathematics, 4-6 Jan 2006, Fort Lauderdale, Florida.
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.