# Conditional Instrumental Variable Regression with Representation Learning for Causal Inference

arXiv: https://arxiv.org/abs/2310.01865 · HTML: https://mlsanity.com/paper/2310.01865/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity](https://mlsanity.com/paper/1911.09260/) (2019)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Instrumental Variables: An Econometrician's Perspective](https://mlsanity.com/paper/1410.0163/) (2014)
- [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)

## Built on by (most cited first, 8 of 8)

- [Causal Prompting for Implicit Sentiment Analysis with Large Language Models](https://mlsanity.com/paper/2507.00389/) (2025)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [When to Trust: A Causality-Aware Calibration Framework for Accurate Knowledge Graph Retrieval-Augmented Generation](https://mlsanity.com/paper/2601.09241/) (2026)
- [Interaction-Data-guided Conditional Instrumental Variables for Debiasing Recommender Systems](https://mlsanity.com/paper/2408.09651/) (2024)
- [FairDRL-ST: Disentangled Representation Learning for Fair Spatio-Temporal Mobility Prediction](https://mlsanity.com/paper/2508.07518/) (2025)
- [Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data](https://mlsanity.com/paper/2411.17774/) (2024)
- [Disentangled Instrumental Variables for Causal Inference with Networked Observational Data](https://mlsanity.com/paper/2602.07765/) (2026)
- [Addressing Instrument-Outcome Confounding in Mendelian Randomization through Representation Learning](https://mlsanity.com/paper/2602.19782/) (2026)

## Abstract (arXiv)

This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved confounders. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV) are commonly used to eliminate confounding bias, including the bias caused by unobserved confounders, but they rely on the linearity assumption. Besides, the strict condition of unconfounded instruments posed on a standard IV is too strong to be practical. To address these challenging and practical problems of the standard IV method (linearity assumption and the strict condition), in this paper, we use a conditional IV (CIV) to relax the unconfounded instrument condition of standard IV and propose a non-linear CIV regression with Confounding Balancing Representation Learning, CBRL.CIV, for jointly eliminating the confounding bias from unobserved confounders and balancing the observed confounders, without the linearity assumption. We theoretically demonstrate the soundness of CBRL.CIV. Extensive experiments on synthetic and two real-world datasets show the competitive performance of CBRL.CIV against state-of-the-art IV-based estimators and superiority in dealing with the non-linear situation.