Identifying confounders using additive noise models
Dominik Janzing, Jonas Peters, Joris Mooij and Bernhard Schölkopf
In: The 25th Conference on Uncertainty in Artificial Intelligence (UAI 2009), 18-21 Jun 2009, Montreal, Canada.
We propose a method for inferring the existence of a latent common cause
("confounder") of two observed random variables. The method assumes that the two effects of the confounder are (possibly nonlinear) functions of the confounder plus independent, additive noise. We discuss under which conditions the model is identifiable (up to an arbitrary reparameterization of the confounder) from the joint distribution of the effects. We state and prove a theoretical result that provides evidence for the conjecture that the model is generically identifiable under suitable technical conditions. In addition, we propose a practical method to estimate the confounder from a finite i.i.d.\ sample of the effects and illustrate that the method works well on both simulated and real-world data.