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The discovery of causal relationships between a set of observed variables is a fundamental problem in science. For continuous-valued data linear acyclic causal models with additive noise are often used because these models are well understood and there are well-known methods to fit them to data. In reality, of course, many causal relationships are more or(More)
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic(More)
Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when the sample size is one. We develop a theory how to generate causal graphs explaining similarities between single objects. To(More)
The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y. An example is to decide whether altitude causes temperature, or vice versa, given(More)
Motivated by causal inference problems, we propose a novel method for regression that minimizes the statistical dependence between regressors and residuals. The key advantage of this approach to regression is that it does not assume a particular distribution of the noise, i.e., it is non-parametric with respect to the noise distribution. We argue that the(More)
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the de-terministic (noise-free) case, there are asymmetries that can be exploited for causal(More)
While conventional approaches to causal inference are mainly based on conditional (in)dependences, recent methods also account for the shape of (conditional) distributions. The idea is that the causal hypothesis " X causes Y " imposes that the marginal distribution P X and the conditional distribution P Y |X represent independent mechanisms of nature.(More)
We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments , from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed(More)
We describe a method for inferring linear causal relations among multi-dimensional variables. The idea is to use an asymmetry between the distributions of cause and effect that occurs if the covariance matrix of the cause and the structure matrix mapping the cause to the effect are independently chosen. The method applies to both stochastic and(More)