# Bounding Causal Effects with Leaky Instruments

arXiv: https://arxiv.org/abs/2404.04446 · HTML: https://mlsanity.com/paper/2404.04446/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 87 references that are in the map.
- First posted on arXiv 5 Apr 2024.

## Builds on (most cited first, 23 of 23)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2002.04518/) (2020)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [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)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [Valid Causal Inference with (Some) Invalid Instruments](https://mlsanity.com/paper/2006.11386/) (2020)
- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)
- [Instrumental Variable Regression via Kernel Maximum Moment Loss](https://mlsanity.com/paper/2010.07684/) (2020)
- [Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Models](https://mlsanity.com/paper/1309.7004/) (2013)
- [Covariate-assisted bounds on causal effects with instrumental variables](https://mlsanity.com/paper/2301.12106/) (2023)
- [Semi-Instrumental Variables: A Test for Instrument Admissibility](https://mlsanity.com/paper/1301.2261/) (2013)
- [Causal Inference through a Witness Protection Program](https://mlsanity.com/paper/1406.0531/) (2014)
- [Bayesian inference for a covariance matrix](https://mlsanity.com/paper/1408.4050/) (2014)
- [Two Robust Tools for Inference about Causal Effects with Invalid Instruments](https://mlsanity.com/paper/2006.01393/) (2020)
- [A set of efficient methods to generate high-dimensional binary data with specified correlation structures](https://mlsanity.com/paper/2007.14080/) (2020)
- [MASSIVE: Tractable and Robust Bayesian Learning of Many-Dimensional Instrumental Variable Models](https://mlsanity.com/paper/2012.10141/) (2020)

## Abstract (arXiv)

Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the textitexclusion criterion, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides textitpartial identification in linear systems given a set of textitleaky instruments, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying textttR package, textttleakyIV, is available from textttCRAN.