Contrastive Learning Recovers Causal Features for Instrumental Variable Regression

Gabin Agbalé, Stefan Harmeling, Alexander Marx

Keywords: Causal Representation Learning, Contrastive Learning, Instrument Variable Regression

TL;DR: We introduce a contrastive learning framework to recover latent treatment variables for Instrumental Variable regression, enabling causal effect estimation from nonlinear transformations.

Abstract: Instrumental Variable (IV) regression is an established technique for estimating causal effects in the presence of unobserved confounders. A core IV assumption is that we have access to an external variable---called the instrument---which directly influences the treatment variable. In this work, we consider a more challenging yet realistic setting where the treatment is high-dimensional but admits a latent structure, through which it interacts with the outcome. To overcome this problem, we leverage insights from the Independently Modulated Component Analysis (IMCA), which is a framework that relaxes the independence assumption in Independent Component Analysis (ICA). Specifically, we propose a general contrastive learning framework to recover the latent features up to an affine transformation which may be related to the instrument by a (non-)linear function. We prove that the recovered representation is compatible with standard IV techniques. Empirically, we demonstrate the effectiveness of our method using control function and two-stage least squares (2SLS) estimators and evaluate the robustness of the learned estimators in distribution shift setting.

Primary Area: causal reasoning

Submission Number: 18799