36 research outputs found
Causal Inference on Discrete Data using Additive Noise Models
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. We prove that whenever the
joint distribution \prob^{(X,Y)} admits such a model in one direction, e.g.
Y=f(X)+N, N \independent X, it does not admit the reversed model
X=g(Y)+\tilde N, \tilde N \independent 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. In an extensive experimental study we show that this
algorithm works both on synthetic and real data sets
Consistency of Causal Inference under the Additive Noise Model
We analyze a family of methods for statistical causal inference from sample
under the so-called Additive Noise Model. While most work on the subject has
concentrated on establishing the soundness of the Additive Noise Model, the
statistical consistency of the resulting inference methods has received little
attention. We derive general conditions under which the given family of
inference methods consistently infers the causal direction in a nonparametric
setting