Linear Independent Component Analysis via Optimal Transport

2026-07-15

AI Summary

This work proposes a novel approach to independent component analysis (ICA) by introducing the Wasserstein distance from optimal transport theory to directly quantify the discrepancy between linear projections and the standard Gaussian distribution. Unlike traditional ICA methods that rely on surrogate measures of non-Gaussianity, which are often inaccurate or require strong distributional assumptions, the proposed method optimizes the projection directions by maximizing the Wasserstein distance via gradient-based optimization, thereby recovering independent source signals without predefined proxy functions or parametric assumptions. This leads to a more accurate and principled measure of non-Gaussianity. Experimental results demonstrate that the method outperforms classical ICA algorithms on synthetic data and achieves promising performance in real-world applications, including EEG artifact removal and price discovery in econometrics.

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. 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.

Problem

• Independent Component Analysis
• Non-Gaussianity
• Negentropy
• Linear Mixtures
• Source Separation

Innovation

• Optimal Transport
• Independent Component Analysis
• Wasserstein Distance
• Non-Gaussianity
• Gradient-based Optimization