Controlling for discrete unmeasured confounding in nonlinear causal models
Patrick Burauel, Frederick Eberhardt, Michel Besserve
TL;DR
The paper tackles unmeasured discrete confounding in nonlinear causal models by reframing the confounded cause–effect system as a latent-variable model with a Gaussian-mixture prior and a piecewise affine mapping to observed data, enabling identifiability of the causal mechanism up to an invertible affine reparameterization. Building on identifiability results for latent variable models with piecewise affine mappings, it shows that the average causal effect E[Y|do(X=x)] can be recovered from observational data despite latent confounding. The authors implement a flow-based model, DeconFlow, that enforces the causal direction via triangular transforms and allows sampling from backdoor latents to perform do-calculus adjustments. Through synthetic experiments in linear and nonlinear settings and a real-world twin-birth dataset, the method demonstrates reduced bias and improved estimation of causal effects when discrete confounding is present. This work bridges causal inference with deep latent-variable identifiability, while acknowledging limitations related to model class assumptions and outlining paths for future extension to richer graphs and other estimands.
Abstract
Unmeasured confounding is a major challenge for identifying causal relationships from non-experimental data. Here, we propose a method that can accommodate unmeasured discrete confounding. Extending recent identifiability results in deep latent variable models, we show theoretically that confounding can be detected and corrected under the assumption that the observed data is a piecewise affine transformation of a latent Gaussian mixture model and that the identity of the mixture components is confounded. We provide a flow-based algorithm to estimate this model and perform deconfounding. Experimental results on synthetic and real-world data provide support for the effectiveness of our approach.