# Valid Causal Inference with (Some) Invalid Instruments

arXiv: https://arxiv.org/abs/2006.11386 · HTML: https://mlsanity.com/paper/2006.11386/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 19 of 19)

- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [Instrumental Variables in Causal Inference and Machine Learning: A Survey](https://mlsanity.com/paper/2212.05778/) (2022)
- [Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data](https://mlsanity.com/paper/2206.01931/) (2022)
- [Estimating Causal Effects using a Multi-task Deep Ensemble](https://mlsanity.com/paper/2301.11351/) (2023)
- [Ancestral Instrument Method for Causal Inference without Complete Knowledge](https://mlsanity.com/paper/2201.03810/) (2022)
- [Causal Inference with Conditional Instruments using Deep Generative Models](https://mlsanity.com/paper/2211.16246/) (2022)
- [Disentangled Representation Learning for Causal Inference with Instruments](https://mlsanity.com/paper/2412.04641/) (2024)
- [Learning Instrumental Variable from Data Fusion for Treatment Effect Estimation](https://mlsanity.com/paper/2208.10912/) (2022)
- [Instrument Space Selection for Kernel Maximum Moment Restriction](https://mlsanity.com/paper/2106.03340/) (2021)
- [Causal Effect Estimation with Variational AutoEncoder and the Front Door Criterion](https://mlsanity.com/paper/2304.11969/) (2023)
- [Causal Imitation Learning under Expert-Observable and Expert-Unobservable Confounding](https://mlsanity.com/paper/2502.07656/) (2025)
- [VLUCI: Variational Learning of Unobserved Confounders for Counterfactual Inference](https://mlsanity.com/paper/2308.00904/) (2023)
- [Bounding Causal Effects with Leaky Instruments](https://mlsanity.com/paper/2404.04446/) (2024)
- [Identification and Estimation of the Bi-Directional MR with Some Invalid Instruments](https://mlsanity.com/paper/2407.07933/) (2024)
- [Sequential Treatment Effect Estimation with Unmeasured Confounders](https://mlsanity.com/paper/2505.09113/) (2025)
- [Towards causal effect estimation with learned instrument representations](https://mlsanity.com/paper/2602.10370/) (2026)
- [TabCF: Distributional Control Function Estimation with Tabular Foundation Models](https://mlsanity.com/paper/2605.05993/) (2026)

## Abstract (arXiv)

Instrumental variable methods provide a powerful approach to estimating causal effects in the presence of unobserved confounding. But a key challenge when applying them is the reliance on untestable "exclusion" assumptions that rule out any relationship between the instrument variable and the response that is not mediated by the treatment. In this paper, we show how to perform consistent IV estimation despite violations of the exclusion assumption. In particular, we show that when one has multiple candidate instruments, only a majority of these candidates---or, more generally, the modal candidate-response relationship---needs to be valid to estimate the causal effect. Our approach uses an estimate of the modal prediction from an ensemble of instrumental variable estimators. The technique is simple to apply and is "black-box" in the sense that it may be used with any instrumental variable estimator as long as the treatment effect is identified for each valid instrument independently. As such, it is compatible with recent machine-learning based estimators that allow for the estimation of conditional average treatment effects (CATE) on complex, high dimensional data. Experimentally, we achieve accurate estimates of conditional average treatment effects using an ensemble of deep network-based estimators, including on a challenging simulated Mendelian Randomization problem.