# Estimating Treatment Effects with Independent Component Analysis

arXiv: https://arxiv.org/abs/2507.16467 · HTML: https://mlsanity.com/paper/2507.16467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 72 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 30 of 32)

- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Scalable Causal Discovery with Score Matching](https://mlsanity.com/paper/2304.03382/) (2023)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [Causal Discovery with Score Matching on Additive Models with Arbitrary Noise](https://mlsanity.com/paper/2304.03265/) (2023)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Cross-Entropy Is All You Need To Invert the Data Generating Process](https://mlsanity.com/paper/2410.21869/) (2024)
- [Orthogonal Machine Learning: Power and Limitations](https://mlsanity.com/paper/1711.00342/) (2017)
- [Independent Innovation Analysis for Nonlinear Vector Autoregressive Process](https://mlsanity.com/paper/2006.10944/) (2020)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Estimation of Causal Effects of Multiple Treatments in Observational Studies with a Binary Outcome](https://mlsanity.com/paper/2001.06483/) (2020)
- [Large Dimensional Independent Component Analysis: Statistical Optimality and Computational Tractability](https://mlsanity.com/paper/2303.18156/) (2023)
- [Do Finetti: On Causal Effects for Exchangeable Data](https://mlsanity.com/paper/2405.18836/) (2024)
- [Score matching through the roof: linear, nonlinear, and latent variables causal discovery](https://mlsanity.com/paper/2407.18755/) (2024)
- [An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis](https://mlsanity.com/paper/2311.18048/) (2023)
- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [It's Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation](https://mlsanity.com/paper/2507.02275/) (2025)
- [On the Identifiability of Sparse ICA without Assuming Non-Gaussianity](https://mlsanity.com/paper/2408.10353/) (2024)
- [Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators](https://mlsanity.com/paper/2306.07918/) (2023)
- [Double Machine Learning for Causal Inference under Shared-State Interference](https://mlsanity.com/paper/2504.08836/) (2025)
- [Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments](https://mlsanity.com/paper/2506.11756/) (2025)

## Abstract (arXiv)

Independent Component Analysis (ICA) uses a measure of non-Gaussianity to identify latent sources from data and estimate their mixing coefficients (Shimizu et al., 2006). Meanwhile, higher-order Orthogonal Machine Learning (OML) exploits non-Gaussian treatment noise to provide more accurate estimates of treatment effects in the presence of confounding nuisance effects (Mackey et al., 2018). Remarkably, we find that the two approaches rely on the same moment conditions for consistent estimation. We then seize upon this connection to show how ICA can be effectively used for treatment effect estimation. Specifically, we prove that linear ICA can consistently estimate multiple treatment effects, even in the presence of Gaussian confounders, and identify regimes in which ICA is provably more sample-efficient than OML for treatment effect estimation. Our synthetic demand estimation experiments confirm this theory and demonstrate that linear ICA can accurately estimate treatment effects even in the presence of nonlinear nuisance.