# Identifiability of Sparse Causal Effects using Instrumental Variables

arXiv: https://arxiv.org/abs/2203.09380 · HTML: https://mlsanity.com/paper/2203.09380/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [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)
- [Instrumental Variables Estimation with Some Invalid Instruments and its Application to Mendelian Randomization](https://mlsanity.com/paper/1401.5755/) (2014)
- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Distributional robustness of K-class estimators and the PULSE](https://mlsanity.com/paper/2005.03353/) (2020)
- [Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression](https://mlsanity.com/paper/1307.6701/) (2013)

## Built on by (most cited first, 9 of 9)

- [Towards Trustworthy and Aligned Machine Learning: A Data-centric Survey with Causality Perspectives](https://mlsanity.com/paper/2307.16851/) (2023)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants](https://mlsanity.com/paper/2506.05202/) (2025)
- [Boosted Control Functions: Distribution generalization and invariance in confounded models](https://mlsanity.com/paper/2310.05805/) (2023)
- [Stable Blanket with Hidden Variables and Cycles](https://mlsanity.com/paper/2605.01856/) (2026)
- [Partially Specified Causal Simulations](https://mlsanity.com/paper/2309.10514/) (2023)
- [Learning Robust Intervention Representations with Delta Embeddings](https://mlsanity.com/paper/2508.04492/) (2025)
- [Many Experiments, Few Repetitions, Unpaired Data, and Sparse Effects: Is Causal Inference Possible?](https://mlsanity.com/paper/2601.15254/) (2026)
- [Causal Cellular Context Transfer Learning (C3TL): An Efficient Architecture for Prediction of Unseen Perturbation Effects](https://mlsanity.com/paper/2603.13051/) (2026)

## Abstract (arXiv)

Exogenous heterogeneity, for example, in the form of instrumental variables can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this paper, we consider linear models in which the causal effect from covariates X on a response Y is sparse. We provide conditions under which the causal coefficient becomes identifiable from the observed distribution. These conditions can be satisfied even if the number of instruments is as small as the number of causal parents. We also develop graphical criteria under which identifiability holds with probability one if the edge coefficients are sampled randomly from a distribution that is absolutely continuous with respect to Lebesgue measure and Y is childless. As an estimator, we propose spaceIV and prove that it consistently estimates the causal effect if the model is identifiable and evaluate its performance on simulated data. If identifiability does not hold, we show that it may still be possible to recover a subset of the causal parents.