# Sequential Underspecified Instrument Selection for Cause-Effect Estimation

arXiv: https://arxiv.org/abs/2302.05684 · HTML: https://mlsanity.com/paper/2302.05684/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 11 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [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)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [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)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [Detecting non-causal artifacts in multivariate linear regression models](https://mlsanity.com/paper/1803.00810/) (2018)
- [Identifiability of Sparse Causal Effects using Instrumental Variables](https://mlsanity.com/paper/2203.09380/) (2022)
- [Instrumental Variable Estimation for Compositional Treatments](https://mlsanity.com/paper/2106.11234/) (2021)
- [A Consistent Estimator for Confounding Strength](https://mlsanity.com/paper/2211.01903/) (2022)

## Built on by (most cited first, 4 of 4)

- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [Targeted Sequential Indirect Experiment Design](https://mlsanity.com/paper/2405.19985/) (2024)
- [Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants](https://mlsanity.com/paper/2506.05202/) (2025)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)

## Abstract (arXiv)

Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome indirectly via the treatment variable(s). Most IV applications focus on low-dimensional treatments and crucially require at least as many instruments as treatments. This assumption is restrictive: in the natural sciences we often seek to infer causal effects of high-dimensional treatments (e.g., the effect of gene expressions or microbiota on health and disease), but can only run few experiments with a limited number of instruments (e.g., drugs or antibiotics). In such underspecified problems, the full treatment effect is not identifiable in a single experiment even in the linear case. We show that one can still reliably recover the projection of the treatment effect onto the instrumented subspace and develop techniques to consistently combine such partial estimates from different sets of instruments. We then leverage our combined estimators in an algorithm that iteratively proposes the most informative instruments at each round of experimentation to maximize the overall information about the full causal effect.