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Causal Reasoning by Evaluating the Complexity of Conditional Densities with Kernel Methods




We propose a method to quantify the complexity of conditional probability measures by a Hilbert space seminorm of the logarithm of its density. The concept of reproducing kernel Hilbert spaces (RKHSs) is a flexible tool to define such a seminorm by choosing an appropriate kernel. We present several examples with artificial data sets where our kernel-based complexity measure is consistent with our intuitive understanding of complexity of densities. The intention behind the complexity measure is to provide a new approach to inferring causal directions. The idea is that the factorization of the joint probability measure P(effect, cause) into P(effect|cause)P(cause) leads typically to "simpler" and "smoother" terms than the factorization into P(cause|effect)P(effect). Since the conventional constraint-based approach of causal discovery is not able to determine the causal direction between only two variables, our inference principle can in particular be useful when combined with other existing methods. We provide several simple examples with real-world data where the true causal directions indeed lead to simpler (conditional) densities.

Author(s): Sun, X. and Janzing, D. and Schölkopf, B.
Journal: Neurocomputing
Volume: 71
Number (issue): 7-9
Pages: 1248-1256
Year: 2008
Month: March
Day: 0

Department(s): Empirical Inference
Bibtex Type: Article (article)

Digital: 0
DOI: 10.1016/j.neucom.2007.12.023
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Causal Reasoning by Evaluating the Complexity of Conditional Densities with Kernel Methods},
  author = {Sun, X. and Janzing, D. and Sch{\"o}lkopf, B.},
  journal = {Neurocomputing},
  volume = {71},
  number = {7-9},
  pages = {1248-1256},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = mar,
  year = {2008},
  month_numeric = {3}