# Causal Inference with Conditional Instruments using Deep Generative Models

arXiv: https://arxiv.org/abs/2211.16246 · HTML: https://mlsanity.com/paper/2211.16246/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (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)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [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)
- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Ivy: Instrumental Variable Synthesis for Causal Inference](https://mlsanity.com/paper/2004.05316/) (2020)

## Built on by (most cited first, 6 of 6)

- [Instrumental Variables in Causal Inference and Machine Learning: A Survey](https://mlsanity.com/paper/2212.05778/) (2022)
- [Conditional Instrumental Variable Regression with Representation Learning for Causal Inference](https://mlsanity.com/paper/2310.01865/) (2023)
- [Causal Prompting for Implicit Sentiment Analysis with Large Language Models](https://mlsanity.com/paper/2507.00389/) (2025)
- [Debiased Contrastive Representation Learning for Mitigating Dual Biases in Recommender Systems](https://mlsanity.com/paper/2408.09646/) (2024)
- [Interaction-Data-guided Conditional Instrumental Variables for Debiasing Recommender Systems](https://mlsanity.com/paper/2408.09651/) (2024)
- [Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data](https://mlsanity.com/paper/2411.17774/) (2024)

## Abstract (arXiv)

The instrumental variable (IV) approach is a widely used way to estimate the causal effects of a treatment on an outcome of interest from observational data with latent confounders. A standard IV is expected to be related to the treatment variable and independent of all other variables in the system. However, it is challenging to search for a standard IV from data directly due to the strict conditions. The conditional IV (CIV) method has been proposed to allow a variable to be an instrument conditioning on a set of variables, allowing a wider choice of possible IVs and enabling broader practical applications of the IV approach. Nevertheless, there is not a data-driven method to discover a CIV and its conditioning set directly from data. To fill this gap, in this paper, we propose to learn the representations of the information of a CIV and its conditioning set from data with latent confounders for average causal effect estimation. By taking advantage of deep generative models, we develop a novel data-driven approach for simultaneously learning the representation of a CIV from measured variables and generating the representation of its conditioning set given measured variables. Extensive experiments on synthetic and real-world datasets show that our method outperforms the existing IV methods.