# Multiple Causal Inference with Latent Confounding

arXiv: https://arxiv.org/abs/1805.08273 · HTML: https://mlsanity.com/paper/1805.08273/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2018.

## Built on by (most cited first, 14 of 14)

- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning](https://mlsanity.com/paper/2303.12703/) (2023)
- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [Causal Estimation with Functional Confounders](https://mlsanity.com/paper/2102.08533/) (2021)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [Causal Contrastive Learning for Counterfactual Regression Over Time](https://mlsanity.com/paper/2406.00535/) (2024)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [DoGR: Disaggregated Gaussian Regression for Reproducible Analysis of Heterogeneous Data](https://mlsanity.com/paper/2108.13581/) (2021)
- [Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data](https://mlsanity.com/paper/2310.10559/) (2023)
- [Multi-treatment Effect Estimation from Biomedical Data](https://mlsanity.com/paper/2112.07574/) (2021)
- [A/B testing under Interference with Partial Network Information](https://mlsanity.com/paper/2404.10547/) (2024)
- [Shrinkage priors for Bayesian Substitute Confounders](https://mlsanity.com/paper/2606.18535/) (2026)

## Abstract (arXiv)

Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treatments in the presence of unobserved confounding. We develop two assumptions based on shared confounding between treatments and independence of treatments given the confounder. Together, these assumptions lead to a confounder estimator regularized by mutual information. For this estimator, we develop a tractable lower bound. To recover treatment effects, we use the residual information in the treatments independent of the confounder. We validate on simulations and an example from clinical medicine.