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On the Identifiability of the Post-Nonlinear Causal Model

2009

Conference Paper

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By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situations in which the model is not identifiable, we provide sufficient conditions for its identifiability. Simulations are given to support the theoretical results. Moreover, in the case of more than two variables, we show that the whole causal structure can be found by applying the PNL causal model to each structure in the Markov equivalent class and testing if the disturbance is independent of the direct causes for each variable. In this way the exhaustive search over all possible causal structures is avoided.

Author(s): Zhang, K. and Hyvärinen, A.
Journal: Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009)
Pages: 647-655
Year: 2009
Month: June
Day: 0
Editors: Bilmes, J. , A. Y. Ng, D. A. McAllester
Publisher: AUAI Press

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009)
Event Place: Montréal, Canada

Address: Corvallis, OR, USA
Digital: 0
ISBN: 978-0-9749039-5-8
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{6721,
  title = {On the Identifiability of the Post-Nonlinear Causal Model},
  author = {Zhang, K. and Hyv{\"a}rinen, A.},
  journal = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009)},
  pages = {647-655},
  editors = {Bilmes, J. , A. Y. Ng, D. A. McAllester},
  publisher = {AUAI Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Corvallis, OR, USA},
  month = jun,
  year = {2009},
  month_numeric = {6}
}