Identifying confounders using additive noise models
This work addresses a fundamental issue in causal inference for researchers and practitioners, though it appears incremental as it builds on existing additive noise models.
The paper tackles the problem of inferring latent common causes (confounders) between two observed variables by assuming additive noise models, and it provides theoretical identifiability results and a practical estimation method that performs well on simulated and real-world data.
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.