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          Institute: MPI für Intelligente Systeme (ehemals Max-Planck-Institut für Metallforschung)     Collection: Abt. Schölkopf (Empirical Inference)     Display Documents



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ID: 596090.0, MPI für Intelligente Systeme (ehemals Max-Planck-Institut für Metallforschung) / Abt. Schölkopf (Empirical Inference)
Causal inference on discrete data using additive noise models
Authors:Peters, J.; Janzing, D.; Schölkopf, B.
Language:English
Date of Publication (YYYY-MM-DD):2011-12-01
Title of Journal:IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume:33
Issue / Number:12
Start Page:2436
End Page:2450
Review Status:not specified
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. The case of two random variables is particularly challenging since no (conditional) independences can be exploited. Recent methods that are based on additive noise models suggest the following principle: Whenever the joint distribution {\bf P}^{(X,Y)} admits such a model in one direction, e.g., Y=f(X)+N, N \perp\kern-6pt \perp X, but does not admit the reversed model X=g(Y)+\tilde{N}, \tilde{N} \perp\kern-6pt \perp Y, one infers the former direction to be causal (i.e., X\rightarrow Y). Up to now, these approaches only dealt with continuous variables. In many situations, however, the variables of interest are discrete or even have only finitely many states. In this work, we extend the notion of additive noise models to these cases. We prove that it almost never occurs that additive noise models can be fit in both directions. We further propose an efficient algorithm that is able to perform this way of causal inference on finite samples of discrete variables. We show that the algorithm works on both synthetic and real data sets.
External Publication Status:published
Document Type:Article
Communicated by:Heide Klooz
Affiliations:MPI für Intelligente Systeme/Abt. Schölkopf
Identifiers:URL:http://www.kyb.tuebingen.mpg.de/fileadmin/user_upl...
LOCALID:PetersJS2011
DOI:10.1109/TPAMI.2011.71
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