OT-ICA Recasts Linear Independent Component Analysis Through Optimal Transport

Lead

Independent Component Analysis (ICA) is a long-standing problem in signal processing and machine learning: given only linear mixtures of several hidden signals, can we recover the underlying mutually independent sources? A new arXiv paper by Ashutosh Jha, Michel Besserve, and Simon Buchholz, titled “Linear Independent Component Analysis via Optimal Transport,” proposes a different answer to a central part of this problem. Instead of relying on conventional proxy contrast functions for non-Gaussianity, the authors turn to optimal transport.

Key points

• A new way to measure non-Gaussianity: Classical ICA is often motivated by maximizing non-Gaussianity, with negentropy providing an information-theoretic link to independence. But exact negentropy optimization is generally intractable. Practical methods therefore use substitutes such as fourth-order cumulants or parametric log-likelihoods. This paper proposes using the squared Wasserstein distance $W_2^2$ between a linear projection of the data and a standard Gaussian distribution.

• A theoretical bridge to source recovery: The authors prove that, for linear projections of the observed data, the Wasserstein distance from a standard normal distribution is maximized when the projection recovers an independent component. This gives the familiar ICA principle—seek the most non-Gaussian projection—a new formulation grounded in optimal transport geometry.

• The OT-ICA algorithm: Building on this observation, the paper introduces OT-ICA, which searches for the relevant projection through gradient-based optimization. The key distinction is that the optimization objective is not a hand-crafted statistical proxy, but the Wasserstein-distance criterion connected to the authors’ theoretical result.

• Empirical validation across tasks: On simulated data, the paper reports that OT-ICA outperforms proxy-based methods across different latent-variable distributions. The authors also apply the method to EEG artifact removal and econometric price discovery, arguing that it can support applied ICA workflows without imposing distributional assumptions.

Why it matters

The paper is notable because it revisits a classic algorithmic framework through a modern optimal transport lens. In real-world blind source separation, assuming a convenient parametric distribution for the hidden sources can be restrictive, and low-order statistical proxies may behave differently across distributions. A Wasserstein-based objective offers a more direct way to compare projected data with Gaussian structure.

The abstract does not settle all practical questions, such as computational cost, scaling behavior, or performance against a broader range of contemporary baselines. Still, the contribution is conceptually clear: OT-ICA replaces traditional proxy measures of non-Gaussianity with an optimal transport distance, and links that choice to the recovery of independent components.

Source: arXiv