# Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders

arXiv: https://arxiv.org/abs/2210.05446 · HTML: https://mlsanity.com/paper/2210.05446/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Nested Counterfactual Identification from Arbitrary Surrogate Experiments](https://mlsanity.com/paper/2107.03190/) (2021)
- [The Sensitivity of Counterfactual Fairness to Unmeasured Confounding](https://mlsanity.com/paper/1907.01040/) (2019)
- [Estimation of causal effects with multiple treatments: a review and new ideas](https://mlsanity.com/paper/1701.05132/) (2017)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Estimating Categorical Counterfactuals via Deep Twin Networks](https://mlsanity.com/paper/2109.01904/) (2021)
- [NCoRE: Neural Counterfactual Representation Learning for Combinations of Treatments](https://mlsanity.com/paper/2103.11175/) (2021)
- [Integrating overlapping datasets using bivariate causal discovery](https://mlsanity.com/paper/1910.11356/) (2019)
- [Leveraging directed causal discovery to detect latent common causes](https://mlsanity.com/paper/1910.10174/) (2019)
- [Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders](https://mlsanity.com/paper/2005.11528/) (2020)
- [Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables](https://mlsanity.com/paper/1506.03880/) (2015)
- [MultiVerse: Causal Reasoning using Importance Sampling in Probabilistic Programming](https://mlsanity.com/paper/1910.08091/) (2019)
- [Multiply Robust Causal Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2105.09254/) (2021)

## Built on by (most cited first, 10 of 10)

- [Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding](https://mlsanity.com/paper/2302.10625/) (2023)
- [Contrastive representations of high-dimensional, structured treatments](https://mlsanity.com/paper/2411.19245/) (2024)
- [Non-parametric identifiability and sensitivity analysis of synthetic control models](https://mlsanity.com/paper/2301.07656/) (2023)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [The Hardness of Validating Observational Studies with Experimental Data](https://mlsanity.com/paper/2503.14795/) (2025)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Identification of Average Causal Effects in Confounded Additive Noise Models](https://mlsanity.com/paper/2407.10014/) (2024)
- [Estimating Joint Interventional Distributions from Marginal Interventional Data](https://mlsanity.com/paper/2409.01794/) (2024)
- [Local Interference: Removing Interference Bias in Semi-Parametric Causal Models](https://mlsanity.com/paper/2503.18756/) (2025)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)

## Abstract (arXiv)

The ability to answer causal questions is crucial in many domains, as causal inference allows one to understand the impact of interventions. In many applications, only a single intervention is possible at a given time. However, in some important areas, multiple interventions are concurrently applied. Disentangling the effects of single interventions from jointly applied interventions is a challenging task -- especially as simultaneously applied interventions can interact. This problem is made harder still by unobserved confounders, which influence both treatments and outcome. We address this challenge by aiming to learn the effect of a single-intervention from both observational data and sets of interventions. We prove that this is not generally possible, but provide identification proofs demonstrating that it can be achieved under non-linear continuous structural causal models with additive, multivariate Gaussian noise -- even when unobserved confounders are present. Importantly, we show how to incorporate observed covariates and learn heterogeneous treatment effects. Based on the identifiability proofs, we provide an algorithm that learns the causal model parameters by pooling data from different regimes and jointly maximizing the combined likelihood. The effectiveness of our method is empirically demonstrated on both synthetic and real-world data.