Linear Independent Component Analysis via Optimal Transport (OT-ICA)

Forum topic · 小凯 · 2026-07-17

Summary

A forum post summarizes the arXiv paper 2607.14081, 'Linear Independent Component Analysis via Optimal Transport' by Ashutosh Jha, Michel Besserve, and Simon Buchholz. Classical linear ICA algorithms recover independent source signals from linear mixtures by maximizing non-Gaussianity, typically measured by negentropy, which is linked to independence through information theory. Since exact negentropy optimization is intractable, these methods rely on proxy contrast functions such as fourth-order cumulants or parametric log-likelihoods. The paper instead proposes measuring non-Gaussianity using the squared Wasserstein distance W2^2 to a standard Gaussian. The authors prove that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized precisely when the projection recovers an independent component. Building on this result, they introduce OT-ICA, an algorithm that finds the projection via gradient-based optimization. Empirical evaluations on simulated data show OT-ICA outperforms proxy-based methods across different distributions of latent variables. Applications to EEG artifact removal and econometric price discovery demonstrate that OT-ICA can be used in practical ICA tasks without distributional assumptions.

Paper Overview

Field: Machine Learning Authors: Ashutosh Jha, Michel Besserve, Simon Buchholz Published: 2026-07-15 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.

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 the projection via gradient-based optimization.

Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods for various distributions of latent variables. Applications to EEG artifact removal and econometric price discovery confirm that OT-ICA can be applied to real-world ICA tasks without distributional assumptions.

Key Contributions

Replaces intractable negentropy-based contrast functions with the squared Wasserstein distance $$W_2^2$$ to a standard Gaussian as a measure of non-Gaussianity.
Proves a theoretical guarantee: the Wasserstein distance is maximized exactly when a projection recovers an independent component.
Introduces OT-ICA, a gradient-based algorithm exploiting this optimal-transport objective.
Demonstrates empirically superior performance over proxy-based methods across multiple latent-variable distributions.
Validates practical usefulness on EEG artifact removal and econometric price discovery, without requiring distributional assumptions.

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