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#### Identifying Cause and Effect on Discrete Data using Additive Noise Models

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##### Citation

Peters, J., Janzing, D., & Schölkopf, B. (2010). Identifying Cause and Effect on
Discrete Data using Additive Noise Models.* Proceedings of the Thirteenth International Conference
on Artificial Intelligence and Statistics (AISTATS 2010),* 597-604.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C040-6

##### Abstract

Inferring the causal structure of a set of random
variables from a finite sample of the
joint distribution is an important problem
in science. Recently, methods using additive
noise models have been suggested to approach
the case of 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.
Whenever the joint distribution P(X;Y ) admits
such a model in one direction, e.g. Y =
f(X) + N; N ? X, it does not admit the
reversed model X = g(Y ) + ~N ; ~N ? Y as
long as the model is chosen in a generic way.
Based on these deliberations we propose an
efficient new algorithm that is able to distinguish
between cause and effect for a finite
sample of discrete variables. We show that
this algorithm works both on synthetic and
real data sets.