# Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders

arXiv: https://arxiv.org/abs/2005.11528 · HTML: https://mlsanity.com/paper/2005.11528/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2020.

## Built on by (most cited first, 7 of 7)

- [Identifying Representations for Intervention Extrapolation](https://mlsanity.com/paper/2310.04295/) (2023)
- [Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2210.05446/) (2022)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [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)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)
- [Incorporating Interventional Independence Improves Robustness against Interventional Distribution Shift](https://mlsanity.com/paper/2507.05412/) (2025)

## Abstract (arXiv)

We propose an approach to estimate the effect of multiple simultaneous interventions in the presence of hidden confounders. To overcome the problem of hidden confounding, we consider the setting where we have access to not only the observational data but also sets of single-variable interventions in which each of the treatment variables is intervened on separately. We prove identifiability under the assumption that the data is generated from a nonlinear continuous structural causal model with additive Gaussian noise. In addition, we propose a simple parameter estimation method by pooling all the data from different regimes and jointly maximizing the combined likelihood. We also conduct comprehensive experiments to verify the identifiability result as well as to compare the performance of our approach against a baseline on both synthetic and real-world data.