On Causal Discovery with Cyclic Additive Noise Models

Material for “ On Causal Discovery with Cyclic Additive Noise Models ”

Nonlinear causal discovery with additive noise models

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 less nonlinear, raising some doubts as ...

Justifying Additive Noise Model-Based Causal Discovery via Algorithmic Information Theory

A recent method for causal discovery is in many cases able to infer whether X causes Y or Y causes X for just two observed variables X and Y . It is based on the observation that there exist (non-Gaussian) joint distributions P (X,Y ) for which Y may be written as a function of X up to an additive noise term that is independent of X and no such model exists from Y to X . Whenever this is the ca...

Dependence Minimizing Regression with Model Selection for Non-Linear Causal Inference under Non-Gaussian Noise

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model through minimization of an estimator of the squaredloss mutual information b...

Distinguishing cause from effect using observational data: methods and benchmarks Distinguishing cause from effect using observational data: methods and benchmarks

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 . This was often considered to be impossible. Nevertheless, several approaches for addressing this bivariate causal discov...