# A Class of Algorithms for General Instrumental Variable Models

arXiv: https://arxiv.org/abs/2006.06366 · HTML: https://mlsanity.com/paper/2006.06366/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 28 of 28)

- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [Consistency of Neural Causal Partial Identification](https://mlsanity.com/paper/2405.15673/) (2024)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [Targeted Sequential Indirect Experiment Design](https://mlsanity.com/paper/2405.19985/) (2024)
- [Learning Representations of Instruments for Partial Identification of Treatment Effects](https://mlsanity.com/paper/2410.08976/) (2024)
- [The Causal Marginal Polytope for Bounding Treatment Effects](https://mlsanity.com/paper/2202.13851/) (2022)
- [Approximate Causal Effect Identification under Weak Confounding](https://mlsanity.com/paper/2306.13242/) (2023)
- [IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning](https://mlsanity.com/paper/2605.12924/) (2026)
- [Algorithmic Recourse in Partially and Fully Confounded Settings Through Bounding Counterfactual Effects](https://mlsanity.com/paper/2106.11849/) (2021)
- [Distributional Instrumental Variable Method](https://mlsanity.com/paper/2502.07641/) (2025)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation](https://mlsanity.com/paper/2510.25128/) (2025)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)
- [Combining Interventional and Observational Data Using Causal Reductions](https://mlsanity.com/paper/2103.04786/) (2021)
- [Game-Theoretic Algorithms for Conditional Moment Matching](https://mlsanity.com/paper/2208.09551/) (2022)
- [Bounding Causal Effects with Leaky Instruments](https://mlsanity.com/paper/2404.04446/) (2024)
- [Machine learning the first stage in 2SLS: Practical guidance from bias decomposition and simulation](https://mlsanity.com/paper/2505.13422/) (2025)

## Abstract (arXiv)

Causal treatment effect estimation is a key problem that arises in a variety of real-world settings, from personalized medicine to governmental policy making. There has been a flurry of recent work in machine learning on estimating causal effects when one has access to an instrument. However, to achieve identifiability, they in general require one-size-fits-all assumptions such as an additive error model for the outcome. An alternative is partial identification, which provides bounds on the causal effect. Little exists in terms of bounding methods that can deal with the most general case, where the treatment itself can be continuous. Moreover, bounding methods generally do not allow for a continuum of assumptions on the shape of the causal effect that can smoothly trade off stronger background knowledge for more informative bounds. In this work, we provide a method for causal effect bounding in continuous distributions, leveraging recent advances in gradient-based methods for the optimization of computationally intractable objective functions. We demonstrate on a set of synthetic and real-world data that our bounds capture the causal effect when additive methods fail, providing a useful range of answers compatible with observation as opposed to relying on unwarranted structural assumptions.