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Nonlinear directed acyclic structure learning with weakly additive noise models

2009

Conference Paper

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The recently proposed emph{additive noise model} has advantages over previous structure learning algorithms, when attempting to recover some true data generating mechanism, since it (i) does not assume linearity or Gaussianity and (ii) can recover a unique DAG rather than an equivalence class. However, its original extension to the multivariate case required enumerating all possible DAGs, and for some special distributions, e.g. linear Gaussian, the model is invertible and thus cannot be used for structure learning. We present a new approach which combines a PC style search using recent advances in kernel measures of conditional dependence with local searches for additive noise models in substructures of the equivalence class. This results in a more computationally efficient approach that is useful for arbitrary distributions even when additive noise models are invertible. Experiments with synthetic and real data show that this method is more accurate than previous methods when data are nonlinear and/or non-Gaussian.

Author(s): Tillman, RE. and Gretton, A. and Spirtes, P.
Book Title: Advances in Neural Information Processing Systems 22
Journal: Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009
Pages: 1847-1855
Year: 2009
Day: 0
Editors: Bengio, Y. , D. Schuurmans, J. Lafferty, C. Williams, A. Culotta
Publisher: Curran

Department(s): Empirical Inference
Research Project(s): Causality (Causal Inference)
Bibtex Type: Conference Paper (inproceedings)

Address: Red Hook, NY, USA
Digital: 0
Event Name: 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009)
Event Place: Vancouver, BC, Canada
ISBN: 978-1-615-67911-9
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{6133,
  title = {Nonlinear directed acyclic structure learning with weakly additive noise models},
  author = {Tillman, RE. and Gretton, A. and Spirtes, P.},
  journal = {Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009},
  booktitle = {Advances in Neural Information Processing Systems 22},
  pages = {1847-1855},
  editors = {Bengio, Y. , D. Schuurmans, J. Lafferty, C. Williams, A. Culotta},
  publisher = {Curran},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Red Hook, NY, USA},
  year = {2009}
}