NDLI: On Estimation of Functional Causal Models: Post-Nonlinear Causal Model as an Example

Content Provider	IEEE Xplore Digital Library
Author	Kun Zhang Zhikun Wang Scholkopf, B.
Copyright Year	2013
Description	Author affiliation: Dept. Empirical Inference, Max-Planck Inst. for Intell. Syst., Tubingen, Germany (Kun Zhang; Zhikun Wang; Scholkopf, B.)
Abstract	Compared to constraint-based causal discovery, causal discovery based on functional causal models is able to identify the whole causal model under appropriate assumptions. Functional causal models represent the effect as a function of the direct causes together with an independent noise term. Examples include the linear non-Gaussian a cyclic model (LiNGAM), nonlinear additive noise model, and post-nonlinear (PNL) model. Currently there are two ways to estimate the parameters in the models, one is by dependence minimization, and the other is maximum likelihood. In this paper, we show that for any a cyclic functional causal model, minimizing the mutual information between the hypothetical cause and the noise term is equivalent to maximizing the data likelihood with a flexible model for the distribution of the noise term. We then focus on estimation of the PNL causal model, and propose to estimate it with the warped Gaussian process with the noise modeled by the mixture of Gaussians. As a Bayesian nonparametric approach, it outperforms the previous one based on mutual information minimization with nonlinear functions represented by multilayer perceptrons, we also show that unlike the ordinary regression, estimation results of the PNL causal model are sensitive to the assumption on the noise distribution. Experimental results on both synthetic and real data support our theoretical claims.
Sponsorship	Toshiba
Starting Page	139
Ending Page	146
File Size	631460
Page Count	8
File Format	PDF
e-ISBN	9781479931422
DOI	10.1109/ICDMW.2013.162
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-12-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Additive noise mutual information minimization Functional causal model Warped Gaussian processes Nonlinear distortion Gaussian processes maximum likelihood Minimization Data models Post-nonlinear causal model Mutual information Causal discovery
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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