# Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussian

arXiv: https://arxiv.org/abs/2607.12832 · HTML: https://mlsanity.com/paper/2607.12832/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Faster independent component analysis by preconditioning with Hessian approximations](https://mlsanity.com/paper/1706.08171/) (2017)
- [Independent Component Analysis via Distance Covariance](https://mlsanity.com/paper/1306.4911/) (2013)
- [Wasserstein Projection Pursuit of Non-Gaussian Signals](https://mlsanity.com/paper/2302.12693/) (2023)
- [Distribution-free joint independence testing and robust independent component analysis using optimal transport](https://mlsanity.com/paper/2211.15639/) (2022)
- [Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHS](https://mlsanity.com/paper/2405.13153/) (2024)

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

- [Linear Independent Component Analysis via Optimal Transport](https://mlsanity.com/paper/2607.14081/) (2026)
- [How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM](https://mlsanity.com/paper/2608.15840/) (2026)

## Abstract (arXiv)

We study the squared 2-Wasserstein distance to the standard Gaussian as a non-Gaussianity criterion and use it for linear Independent Component Analysis (ICA) and causal discovery in Linear Non-Gaussian Acyclic Models (LiNGAM). Unlike commonly used parametric contrasts and approximations of information-theoretic quantities, this criterion requires no distributional regularity beyond finite second moments, involves neither approximation nor tuning parameters, and can be computed exactly and efficiently from empirical order statistics. Our analysis relies on a strict subadditivity property of the 2-Wasserstein distance to the Gaussian. At the population level, we prove exact identification of the ICA unmixing matrix, up to signed permutation, and give an analogous characterization of causal orders through sequential least-squares residuals. We then define empirical plug-in estimators and prove distribution-free uniform convergence under finite-moment assumptions, before detailing three practical solvers: a Picard-style orthogonal optimizer for ICA, an exhaustive dynamic program for causal order search, and a greedy order search variant. Empirically, we demonstrate competitive performance for both tasks and provide open-source implementations for source separation and causal discovery.