Identifying confounders using additive noise models
Dominik Janzing, Jonas Peters, Joris Mooij, Bernhard Schoelkopf
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.
PDF Link: /papers/09/p249-janzing.pdf
AUTHOR = "Dominik Janzing
and Jonas Peters and Joris Mooij and Bernhard Schoelkopf",
TITLE = "Identifying confounders using additive noise models",
BOOKTITLE = "Proceedings of the Twenty-Fifth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-09)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2009",
PAGES = "249--257"