# IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning

arXiv: https://arxiv.org/abs/2605.12924 · HTML: https://mlsanity.com/paper/2605.12924/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 68 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 29 of 29)

- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [TabICL: A Tabular Foundation Model for In-Context Learning on Large Data](https://mlsanity.com/paper/2502.05564/) (2025)
- [TabDPT: Scaling Tabular Foundation Models on Real Data](https://mlsanity.com/paper/2410.18164/) (2024)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Statistical Foundations of Prior-Data Fitted Networks](https://mlsanity.com/paper/2305.11097/) (2023)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Foundation Models for Causal Inference via Prior-Data Fitted Networks](https://mlsanity.com/paper/2506.10914/) (2025)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [On the definition of a confounder](https://mlsanity.com/paper/1304.0564/) (2013)
- [Flexible sensitivity analysis for observational studies without observable implications](https://mlsanity.com/paper/1809.00399/) (2018)
- [A General Method for Deriving Tight Symbolic Bounds on Causal Effects](https://mlsanity.com/paper/2003.10702/) (2020)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [Towards Causal Foundation Model: on Duality between Causal Inference and Attention](https://mlsanity.com/paper/2310.00809/) (2023)
- [Black Box Causal Inference: Effect Estimation via Meta Prediction](https://mlsanity.com/paper/2503.05985/) (2025)
- [Nonparametric Bounds and Sensitivity Analysis of Treatment Effects](https://mlsanity.com/paper/1503.01598/) (2015)
- [Covariate-assisted bounds on causal effects with instrumental variables](https://mlsanity.com/paper/2301.12106/) (2023)
- [Challenges in Statistics: A Dozen Challenges in Causality and Causal Inference](https://mlsanity.com/paper/2508.17099/) (2025)
- [Causal Inference through a Witness Protection Program](https://mlsanity.com/paper/1406.0531/) (2014)
- [Amortized Inference of Causal Models via Conditional Fixed-Point Iterations](https://mlsanity.com/paper/2410.06128/) (2024)
- [Learning Representations of Instruments for Partial Identification of Treatment Effects](https://mlsanity.com/paper/2410.08976/) (2024)
- [Frequentist Consistency of Prior-Data Fitted Networks for Causal Inference](https://mlsanity.com/paper/2603.12037/) (2026)

## Built on by (most cited first, 3 of 3)

- [Computational Identifiability](https://mlsanity.com/paper/2606.19361/) (2026)
- [Causal Foundation Models](https://mlsanity.com/paper/2609.03003/) (2026)
- [ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding](https://mlsanity.com/paper/2610.08078/) (2026)

## Abstract (arXiv)

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.