Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning

Shimeng Huang; Matthew Robinson; Francesco Locatello

cs.LGFeb 23, 2026

Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning

Authors: Shimeng Huang, Matthew Robinson, Francesco Locatello

Organizations: Institute of Science and Technology Austria (ISTA)

Abstract

Mendelian Randomization (MR) is a prominent observational epidemiological research method designed to address unobserved confounding when estimating causal effects. However, core assumptions -- particularly the independence between instruments and unobserved confounders -- are often violated due to population stratification or assortative mating. Leveraging the increasing availability of multi-environment data, we propose a representation learning framework that exploits cross-environment invariance to recover latent exogenous components of genetic instruments. We provide theoretical guarantees for identifying these latent instruments under various mixing mechanisms and demonstrate the effectiveness of our approach through simulations and semi-synthetic experiments using data from the All of Us Research Hub.

Figures & tables

Panel of Figure 1 — Figure 1: Left: DAG with disentangled latent variables that generate $Z$ , where $U_{2}$ and $U_{3}$ , if observed, are valid instruments for $D$ with respect to $Y$ . Right: ADMG without considering the disentangled latent variables, $Z_{1}$ to $Z_{3}$ are all invalid instruments due to $Z_{1}$ ’s violation of exchangability. 2 2 2 DAG: directly acyclic graph. ADMG: acyclic directed mixed graph.

Panel of Figure 2 — Figure 2: Illustration of our general setup where $Z$ is a complex, entangled instrument containing some valid information (represented by $W$ ) as IV for $D$ with respect to $Y$ , and some invalid information (represented by $V$ ). $V$ and $W$ are not directly observed and are not necessarily subvectors of $Z$ .

Figure 3: Bias of estimated ACE based on different estimators based on semi-synthetic experiments using genetic variants from AoU biobank.

Figure 4: Bias comparison under different mixing functions (Polynomials of degree $1$ - $3$ and invertible MLP). Our methods remain unbiased while all other methods exhibit large bias.

Figure 5: Estimation bias given misspecified latent dimensions ( $\hat{p}$ ) when the true dimension is $p=2$ . Our methods remain unbiased for under-specified and moderately over-specified dimensions of $\widehat{W}$ .

Figure 6: Estimation bias with and without including an independence loss. Both 2SLS and PO-2SLS estimators are unbiased when independence loss is included, while PO-2SLS is not unbiased when independence loss is excluded.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 7 — Figure 7: DAG induced by the SCM in Example C.5

Figure 8: Distributions of the latent variables. The first component ( $C0$ ) (obtained from real data) is used as the true $V$ and the rest of the components (simulated) are used as true $W$ .

Panel of Figure 9 — Figure 9: Left: Estimation bias in a $3$ -population experiment given different mixing functions. Right: Estimation bias when using different invariance losses given a polynomial mixing of degree $3$ .

Instrumental Variable Estimation

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Unobserved confounding is a fundamental challenge in causal inference from observational data. This article develops a mixture-learning perspective, viewing latent confounders as sources of heterogeneity that induce mixture structure in observed data. Under suitable structural and identifiability assumptions, recovering the mixing distribution and component mechanisms enables estimation of interventional distributions and causal estimands. Using variants of Bernoulli mixtures as a running example, we contextualize mixture-learning techniques and their structural assumptions, and connect them to causal inference in panel-data settings, including latent factor models and synthetic interventions.We then consider high-dimensional exponential-family mixtures with dependent outcome trajectories, moving beyond counterfactual means to model counterfactual distributions. We situate this perspective relative to complementary approaches for unobserved confounding. Together, these ideas provide a bridge between mixture learning and causal inference, connecting recent advances in high-dimensional mixture learning to scalable identification and estimation of causal effects while raising new challenges for mixture learning.

Abstract

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