# Identification of Average Causal Effects in Confounded Additive Noise Models

arXiv: https://arxiv.org/abs/2407.10014 · HTML: https://mlsanity.com/paper/2407.10014/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 13 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Estimating average causal effects from patient trajectories](https://mlsanity.com/paper/2203.01228/) (2022)
- [Efficient Intervention Design for Causal Discovery with Latents](https://mlsanity.com/paper/2005.11736/) (2020)
- [What can be estimated? Identifiability, estimability, causal inference and ill-posed inverse problems](https://mlsanity.com/paper/1904.02826/) (2019)
- [Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2210.05446/) (2022)
- [Learning Joint Nonlinear Effects from Single-variable Interventions in the Presence of Hidden Confounders](https://mlsanity.com/paper/2005.11528/) (2020)
- [Causal Inference in the Presence of Interference in Sponsored Search Advertising](https://mlsanity.com/paper/2010.07458/) (2020)
- [Collaborative Causal Discovery with Atomic Interventions](https://mlsanity.com/paper/2106.03028/) (2021)
- [Causal Identification with Additive Noise Models: Quantifying the Effect of Noise](https://mlsanity.com/paper/2110.08087/) (2021)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Additive noise models (ANMs) are an important setting studied in causal inference. Most of the existing works on ANMs assume causal sufficiency, i.e., there are no unobserved confounders. This paper focuses on confounded ANMs, where a set of treatment variables and a target variable are affected by an unobserved confounder that follows a multivariate Gaussian distribution. We introduce a novel approach for estimating the average causal effects (ACEs) of any subset of the treatment variables on the outcome and demonstrate that a small set of interventional distributions is sufficient to estimate all of them. In addition, we propose a randomized algorithm that further reduces the number of required interventions to poly-logarithmic in the number of nodes. Finally, we demonstrate that these interventions are also sufficient to recover the causal structure between the observed variables. This establishes that a poly-logarithmic number of interventions is sufficient to infer the causal effects of any subset of treatments on the outcome in confounded ANMs with high probability, even when the causal structure between treatments is unknown. The simulation results indicate that our method can accurately estimate all ACEs in the finite-sample regime. We also demonstrate the practical significance of our algorithm by evaluating it on semi-synthetic data.