# Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition

arXiv: https://arxiv.org/abs/2107.05884 · HTML: https://mlsanity.com/paper/2107.05884/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 61 references that are in the map.
- First posted on arXiv 13 Jul 2021.

## Builds on (most cited first, 21 of 21)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Counterfactual VQA: A Cause-Effect Look at Language Bias](https://mlsanity.com/paper/2006.04315/) (2020)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [A Survey on Data Collection for Machine Learning: a Big Data -- AI Integration Perspective](https://mlsanity.com/paper/1811.03402/) (2018)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Towards Bayesian Deep Learning: A Framework and Some Existing Methods](https://mlsanity.com/paper/1608.06884/) (2016)
- [Stable Prediction across Unknown Environments](https://mlsanity.com/paper/1806.06270/) (2018)
- [Machine Learning for the Geosciences: Challenges and Opportunities](https://mlsanity.com/paper/1711.04708/) (2017)
- [Adversarial Generalized Method of Moments](https://mlsanity.com/paper/1803.07164/) (2018)
- [A Unified View of Causal and Non-causal Feature Selection](https://mlsanity.com/paper/1802.05844/) (2018)
- [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)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)
- [Learning Decomposed Representation for Counterfactual Inference](https://mlsanity.com/paper/2006.07040/) (2020)
- [Variable-lag Granger Causality and Transfer Entropy for Time Series Analysis](https://mlsanity.com/paper/2002.00208/) (2020)
- [Causal Decision Trees](https://mlsanity.com/paper/1508.03812/) (2015)
- [Dual Instrumental Variable Regression](https://mlsanity.com/paper/1910.12358/) (2019)

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

- [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)
- [Instrumental Variable-Driven Domain Generalization with Unobserved Confounders](https://mlsanity.com/paper/2110.01438/) (2021)
- [Causal Inference with Conditional Instruments using Deep Generative Models](https://mlsanity.com/paper/2211.16246/) (2022)
- [Adaptive Instrument Design for Indirect Experiments](https://mlsanity.com/paper/2312.02438/) (2023)
- [Disentangled Representation Learning for Causal Inference with Instruments](https://mlsanity.com/paper/2412.04641/) (2024)
- [Structure Causal Models and LLMs Integration in Medical Visual Question Answering](https://mlsanity.com/paper/2505.02703/) (2025)
- [Learning Instrumental Variable from Data Fusion for Treatment Effect Estimation](https://mlsanity.com/paper/2208.10912/) (2022)
- [Self-Distilled Disentangled Learning for Counterfactual Prediction](https://mlsanity.com/paper/2406.05855/) (2024)
- [Instrumental Variable Learning for Chest X-ray Classification](https://mlsanity.com/paper/2305.12070/) (2023)
- [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)
- [Pareto-Optimal Estimation and Policy Learning on Short-term and Long-term Treatment Effects](https://mlsanity.com/paper/2403.02624/) (2024)
- [Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data](https://mlsanity.com/paper/2411.17774/) (2024)
- [Sequential Treatment Effect Estimation with Unmeasured Confounders](https://mlsanity.com/paper/2505.09113/) (2025)
- [Disentangled Instrumental Variables for Causal Inference with Networked Observational Data](https://mlsanity.com/paper/2602.07765/) (2026)
- [Towards causal effect estimation with learned instrument representations](https://mlsanity.com/paper/2602.10370/) (2026)
- [Proximal Causal Learning under Unmeasured Confounding](https://mlsanity.com/paper/2610.04519/) (2026)

## Abstract (arXiv)

Instrumental variables (IVs), sources of treatment randomization that are conditionally independent of the outcome, play an important role in causal inference with unobserved confounders. However, the existing IV-based counterfactual prediction methods need well-predefined IVs, while it is an art rather than science to find valid IVs in many real-world scenes. Moreover, the predefined hand-made IVs could be weak or erroneous by violating the conditions of valid IVs. These thorny facts hinder the application of the IV-based counterfactual prediction methods. In this paper, we propose a novel Automatic Instrumental Variable decomposition (AutoIV) algorithm to automatically generate representations serving the role of IVs from observed variables (IV candidates). Specifically, we let the learned IV representations satisfy the relevance condition with the treatment and exclusion condition with the outcome via mutual information maximization and minimization constraints, respectively. We also learn confounder representations by encouraging them to be relevant to both the treatment and the outcome. The IV and confounder representations compete for the information with their constraints in an adversarial game, which allows us to get valid IV representations for IV-based counterfactual prediction. Extensive experiments demonstrate that our method generates valid IV representations for accurate IV-based counterfactual prediction.