Linear Independent Component Analysis via Optimal Transport

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 measure non-Gaussianity using the squared Wasserstein distance $W_2^2$ to a standard Gaussian.

We prove that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized when the projection recovers an independent component.

Based on this observation, we propose the OT-ICA algorithm which finds this projection by gradient-based optimization.

Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods for different distributions of the latent variables.

Application to EEG artifact removal and econometric price discovery confirm OT-ICA can be used for applied ICA tasks without distributional assumptions.