Causal discovery with continuous 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 ...

On Causal Discovery with Cyclic Additive Noise Models

We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussian-noise case. We also propose a method to learn such models from observational data. In the acyclic case, the method reduces to ordinary regression, but in...

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

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...