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Inferring Causal Directions by Evaluating the Complexity of Conditional Distributions




We propose a new approach to infer the causal structure that has generated the observed statistical dependences among n random variables. The idea is that the factorization of the joint measure of cause and effect into P(cause)P(effect|cause) leads typically to simpler conditionals than non-causal factorizations. To evaluate the complexity of the conditionals we have tried two methods. First, we have compared them to those which maximize the conditional entropy subject to the observed first and second moments since we consider the latter as the simplest conditionals. Second, we have fitted the data with conditional probability measures being exponents of functions in an RKHS space and defined the complexity by a Hilbert-space semi-norm. Such a complexity measure has several properties that are useful for our purpose. We describe some encouraging results with both methods applied to real-world data. Moreover, we have combined constraint-based approaches to causal discovery (i.e., methods using only information on conditional statistical dependences) with our method in order to distinguish between causal hypotheses which are equivalent with respect to the imposed independences. Furthermore, we compare the performance to Bayesian approaches to causal inference.

Author(s): Sun, X. and Janzing, D. and Schölkopf, B.
Year: 2006
Month: December
Day: 0

Department(s): Empirical Inference
Bibtex Type: Talk (talk)

Digital: 0
Event Name: NIPS 2006 Workshop on Causality and Feature Selection
Event Place: Whistler, BC, Canada
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Inferring Causal Directions by Evaluating the Complexity of Conditional Distributions},
  author = {Sun, X. and Janzing, D. and Sch{\"o}lkopf, B.},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = dec,
  year = {2006},
  month_numeric = {12}