Identifying confounders using additive noise models

TL;DR

This paper introduces a method to detect and estimate latent confounders affecting two variables, assuming a nonlinear additive noise model, with theoretical guarantees and practical effectiveness demonstrated on real data.

Contribution

The paper presents a novel approach for confounder inference using additive noise models, including identifiability conditions and a practical estimation method.

Findings

The model is generically identifiable under certain conditions.

The proposed estimation method performs well on simulated data.

The method is effective on real-world datasets.

Abstract

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.