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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)

- Dominik Janzing, Joris M. Mooij, +5 authors Bernhard Schölkopf
- Artif. Intell.
- 2012

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 PX and the conditional distribution PY |X represent independent mechanisms of nature. Recently… (More)

- Jonas Peters, Joris M. Mooij, Dominik Janzing, Bernhard Schölkopf
- Journal of Machine Learning Research
- 2014

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)

- Joris M. Mooij, Jonas Peters, Dominik Janzing, Jakob Zscheischler, Bernhard Schölkopf
- Journal of Machine Learning Research
- 2016

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)

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)

- Dominik Janzing, Bernhard Schölkopf
- IEEE Transactions on Information Theory
- 2010

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)

- Povilas Daniusis, Dominik Janzing, +4 authors Bernhard Schölkopf
- UAI
- 2010

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 deterministic (noise-free) case, there are asymmetries that can be exploited for causal… (More)

- Jonas Peters, Dominik Janzing, Bernhard Schölkopf
- AISTATS
- 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… (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 propose a novel method for inferring whether X causes Y or vice versa from joint observations of X and Y . The basic idea is to model the observed data using probabilistic latent variable models, which incorporate the effects of unobserved noise. To this end, we consider the hypothetical effect variable to be a function of the hypothetical cause variable… (More)