Linear Independent Component Analysis via Optimal Transport: The OT-ICA Algorithm

Forum topic · 小凯 · 2026-07-17

Summary

This arXiv paper (2607.14081) by Ashutosh Jha, Michel Besserve, and Simon Buchholz introduces OT-ICA, a new approach to linear Independent Component Analysis (ICA). Classical ICA algorithms recover jointly independent source signals from linear mixtures by maximizing non-Gaussianity, typically measured via negentropy. Since exact negentropy optimization is intractable, existing methods rely on proxy contrast functions such as fourth-order cumulants or parametric log-likelihoods. The authors instead measure non-Gaussianity using the squared Wasserstein distance W_2^2 to a standard Gaussian, and prove that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized exactly when the projection recovers an independent component. Building on this theoretical result, they propose OT-ICA, which finds the unmixing projection via gradient-based optimal-transport optimization. Empirical evaluations on simulated data show that OT-ICA outperforms proxy-based methods across various latent source distributions. Applications to EEG artifact removal and econometric price discovery demonstrate that OT-ICA is practical for real-world ICA tasks without requiring distributional assumptions on the sources.

Overview

Field: Machine Learning Authors: Ashutosh Jha, Michel Besserve, Simon Buchholz arXiv: 2607.14081

Abstract

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.

The authors propose instead to measure non-Gaussianity using the squared Wasserstein distance $$W_2^2$$ to a standard Gaussian. They 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, they propose the OT-ICA algorithm, which finds the projection via gradient-based optimization.

Key Results

Theoretical guarantee: Maximizing the Wasserstein distance to a standard Gaussian over linear projections recovers independent components.
Algorithm: OT-ICA uses gradient-based optimization of the Wasserstein-based objective.
Empirics: On simulated data, OT-ICA outperforms proxy-based methods (cumulant-based and parametric likelihood approaches) across a variety of latent source distributions.
Applications: EEG artifact removal and econometric price discovery show OT-ICA works on applied ICA tasks without distributional assumptions.