PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Distinguishing Cause and Effect via Second Order Exponential Models
Dominik / DJ Janzing, Xiaohai / XS Sun and Bernhard / BS Schoelkopf
ArXive 2009.

Abstract

We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a family of smooth densities and conditional densities by second order exponential models, i.e., by maximizing conditional entropy subject to first and second statistical moments. If some of the variables take only values in proper subsets of R^n, these conditionals can induce different families of joint distributions even for Markov-equivalent graphs. We consider the case of one binary and one real-valued variable where the method can distinguish between cause and effect. Using this example, we describe that sometimes a causal hypothesis must be rejected because P(effect|cause) and P(cause) share algorithmic information (which is untypical if they are chosen independently). This way, our method is in the same spirit as faithfulness-based causal inference because it also rejects non-generic mutual adjustments among DAG-parameters.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:6831
Deposited By:Dominik Janzing
Deposited On:08 March 2010