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Invariant Gaussian Process Latent Variable Models and Application in Causal Discovery

2010

Conference Paper

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In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challenging problem. However, generally in such models the observation noise is assumed to be independent across data dimensions, and consequently the noise dependencies are ignored. In this paper we focus on the Gaussian process latent variable model (GPLVM), from which we develop an extended model called invariant GPLVM (IGPLVM), which can adapt to arbitrary noise covariances. With the Gaussian process prior put on a particular transformation of the latent nonlinear functions, instead of the original ones, the algorithm for IGPLVM involves almost the same computational loads as that for the original GPLVM. Besides its potential application in causal discovery, IGPLVM has the advantage that its estimated latent nonlinear manifold is invariant to any nonsingular linear transformation of the data. Experimental results on both synthetic and realworld data show its encouraging performance in nonlinear manifold learning and causal discovery.

Author(s): Zhang, K. and Schölkopf, B. and Janzing, D.
Book Title: Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence
Journal: Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Sixth Conference (UAI 2010)
Pages: 717-724
Year: 2010
Month: July
Day: 0
Editors: P Gr{\"u}nwald and P Spirtes
Publisher: AUAI Press

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

Event Name: UAI 2010
Event Place: Catalina Island, CA, USA

Address: Corvallis, OR, USA
Digital: 0
ISBN: 978-0-9749039-6-5
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{6629,
  title = {Invariant Gaussian Process Latent Variable Models and Application in Causal Discovery},
  author = {Zhang, K. and Sch{\"o}lkopf, B. and Janzing, D.},
  journal = {Uncertainty in Artificial Intelligence: Proceedings of the Twenty-Sixth Conference (UAI 2010)},
  booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence},
  pages = {717-724},
  editors = {P Gr{\"u}nwald and P Spirtes},
  publisher = {AUAI Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Corvallis, OR, USA},
  month = jul,
  year = {2010},
  month_numeric = {7}
}