IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning
Authors: Vahid Balazadeh, Hamidreza Kamkari, Medha Barath, Ricardo Silva, Rahul G. Krishnan
Organizations: University of Toronto · Vector Institute · MIT CSAIL · University College London
Abstract
The instrumental-variables (IV) setting is standard for partial identification of causal effects when unobserved confounding makes point identification impossible. Existing approaches face methodological bottlenecks: closed-form bound estimands are required -- e.g., Balke-Pearl equations in binary IV -- and even when available, designing accurate estimators requires manual effort tailored to each estimand. While direct Bayesian inference of the causal effects, instead of the bounds, circumvents these challenges, it is often computationally intensive and suffers from high prior sensitivity or under-dispersed posteriors. As a remedy, we introduce IV-ICL, an amortized Bayesian in-context learning method that learns the marginal posterior distribution of the causal effects directly and derives bounds as its quantiles. Unlike standard variational inference that optimizes exclusive KL divergence, amortized Bayesian inference minimizes the expected inclusive KL, a mass-covering objective. We empirically observe that optimizing inclusive KL can recover the entire identified set across diverse data-generating processes, while exclusive-KL (e.g. with variational inference) of the same Bayesian formulation collapses onto a single mode and fails to cover the identified set. We evaluate IV-ICL on synthetic and semi-synthetic IV benchmarks and show it produces intervals that are more reliably valid and more informative compared to efficient semi-parametric, Bayesian, and plug-in baselines, at 20-500x lower inference time. Beyond methodology, we propose a procedure to convert randomized controlled trials into IV benchmarks with provably preserved ground-truth causal effects that enables a more realistic evaluation of partial-identification methods.
Instrumental-variable (IV) regression enables causal estimation under endogeneity, but modern IV problems often involve nonlinear structural effects and high-dimensional covariates. Existing nonlinear IV methods directly learn the causal relation in observed feature space or rely on learned representations within two-stage or moment-based procedures, which can struggle when the causal information is embedded in a high-dimensional representation. We propose BGM-IV, a latent Bayesian generative modeling approach that reframes nonlinear IV regression as posterior inference in a causally structured latent space. BGM-IV infers latent components that separately capture shared confounding structure, outcome-specific variation, treatment-specific variation, and covariate-only nuisance information. To account for endogeneity, BGM-IV replaces the confounded outcome likelihood with an IV-integrated pseudo-likelihood that averages over instrument-induced treatment values within the latent model. Across various benchmark datasets, BGM-IV remains competitive in the classical low-dimensional regime and performs best in high-dimensional covariate regimes. Together, these results show that structured latent generative modeling provides a principled and effective strategy to nonlinear IV estimation with rich covariates. The code of BGM-IV is available at https://github.com/liuq-lab/BGM-IV.
Causal queries are often only partially identifiable from observational data, and experiments that could tighten the resulting bounds are typically costly. We study the problem of selecting, prior to observing experimental outcomes, a cost-constrained subset of experiments that maximally tightens bounds on a target query. We formalize this as the max-potency problem, where epistemic potency measures the worst-case reduction in bound width guaranteed by an experiment, and show that this problem is NP-hard via a reduction from 0-1 knapsack. Building on the polynomial-programming framework of Duarte et al. (2023), we give a general procedure for evaluating epistemic potency in discrete settings. To control the super-exponential search space, we introduce two graphical pruning criteria that depend only on the causal graph and the query: a novel path-interception rule that exploits district structure to certify zero potency in linear time, and an identifiability check based on the ID algorithm. On Erdos-Renyi random graphs and 11 bnlearn benchmark networks, the two criteria together prune 50-88% of candidate experiments on average without solving a single polynomial program. For the general subset search, we show that ID-pruned experiments are combinatorially inert, yielding a super-exponential reduction in the number of subsets evaluated. We close with an end-to-end demonstration on observational NHANES data, selecting optimal experiments for estimating the effect of physical activity on diabetes.
We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.
Phevos Paschalidis, Constantinos Daskalakis, Devavrat Shah