# Linear Independent Component Analysis via Optimal Transport

arXiv: https://arxiv.org/abs/2607.14081 · HTML: https://mlsanity.com/paper/2607.14081/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 63 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Function Classes for Identifiable Nonlinear Independent Component Analysis](https://mlsanity.com/paper/2208.06406/) (2022)
- [Projection Robust Wasserstein Distance and Riemannian Optimization](https://mlsanity.com/paper/2006.07458/) (2020)
- [Sliced Iterative Normalizing Flows](https://mlsanity.com/paper/2007.00674/) (2020)
- [Iterative Gaussianization: from ICA to Random Rotations](https://mlsanity.com/paper/1602.00229/) (2016)
- [Faster independent component analysis by preconditioning with Hessian approximations](https://mlsanity.com/paper/1706.08171/) (2017)
- [A proof of the Caffarelli contraction theorem via entropic regularization](https://mlsanity.com/paper/1904.06053/) (2019)
- [Blind Source Separation with Optimal Transport Non-negative Matrix Factorization](https://mlsanity.com/paper/1802.05429/) (2018)
- [Wasserstein Projection Pursuit of Non-Gaussian Signals](https://mlsanity.com/paper/2302.12693/) (2023)
- [Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussian](https://mlsanity.com/paper/2607.12832/) (2026)
- [R-Estimation for Asymmetric Independent Component Analysis](https://mlsanity.com/paper/1304.3073/) (2013)
- [Independent component analysis in the light of Information Geometry](https://mlsanity.com/paper/2212.10429/) (2022)

## Abstract (arXiv)

Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize non-Gaussianity, measured by negentropy, which is linked to independence by information theory. Because exact negentropy optimization is intractable, they rely on proxy contrast functions, such as fourth-order cumulants and parametric log-likelihoods. We propose instead to use the squared L2-Wasserstein distance to a standard Gaussian as the ICA contrast. We show that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized when the projection recovers an independent component, and that under a regularity condition on the sources this maximum is separated from every genuine mixture by an explicit margin. We uncover the advantageous properties of the resulting estimator: for sources with a smooth density it is √N-consistent and asymptotically normal with a closed-form variance, whereas for a source with an atom the contrast has a kink at the true direction, which makes the estimator exact with probability tending to one. The proposed OT-ICA algorithm finds this projection by gradient-based optimization. Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods and that the W22 contrast provides more robust signal than proxy contrasts in measuring non-Gaussianity for different distributional mixtures of the latent variables. Application to linear causal disentanglement and EEG artifact removal, along with further applications detailed in the appendix, confirms OT-ICA can be used for applied ICA tasks without distributional assumptions.