Linear Independent Component Analysis via Optimal Transport

TL;DR — A new linear ICA method (OT-ICA) that measures non-Gaussianity via the squared Wasserstein-2 distance to a standard Gaussian instead of classical proxy contrasts, giving a distribution-agnostic way to recover independent source signals.

• Replaces negentropy proxies (fourth-order cumulants, parametric log-likelihoods) with the optimal-transport distance $W_2^2$ between a standard normal and linear projections of the data.
• Provides a theoretical result: this Wasserstein distance is maximized exactly when the projection recovers an independent component; OT-ICA optimizes it via gradient descent.
• On simulated data, OT-ICA reportedly outperforms proxy-based methods across different latent-variable distributions.
• Demonstrated on applied tasks—EEG artifact removal and econometric price discovery—without requiring distributional assumptions.