OT-ICA uses optimal transport to recover independent components

The authors propose OT-ICA, a new algorithm for Linear Independent Component Analysis that measures non-Gaussianity using the squared Wasserstein distance to a standard Gaussian instead of proxy contrast functions. They prove that this distance is maximized when projections recover an independent component and implement the method via gradient-based optimization.

• Replaces intractable negentropy optimization with squared Wasserstein distance $W_2^2$.
• Maximizes Wasserstein distance between standard normal and linear data projections.
• Outperforms proxy-based methods on simulated data across different latent variable distributions.
• Successfully applied to EEG artifact removal and econometric price discovery without distributional assumptions.

OT-ICA provides a viable alternative for applied ICA tasks by avoiding the need for distributional assumptions required by classical methods.