PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Identifying Cause and Effect on Discrete Data using Additive Noise Models
Jonas Peters, Dominik Janzing and Bernhard Schölkopf
MLR Workshop and Conference Proceedings Volume 9: AISTATS 2010, Thirteenth International Conference on Artificial Intelligence and Statistics Volume 9, pp. 597-604, 2010.


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) + Ñ, Ñ ⊥ 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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:7808
Deposited By:Jonas Peters
Deposited On:17 March 2011