---
title: "Linear Independent Component Analysis via Optimal Transport"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.14081v1"
permalink: "https://feed.astralor.com/items/itm_019fc74cb0e29c083c90f0b9"
published: "2026-07-15T17:56:11.000Z"
score: 76
channel: "ai"
tags: ["OT-ICA","Wasserstein Distance","Optimal Transport","ICA","Non-Gaussianity measure"]
---

# Linear Independent Component Analysis via Optimal Transport

## AI commentary

> What makes this paper noteworthy is its elegant redefinition of the core ICA metric through optimal transport, backed by solid theory and experiments. For readers working on unsupervised learning, signal processing, or causal discovery, it offers a new tool free from distributional assumptions. However, computational complexity may require further optimization for large-scale applications.

## At a glance

This paper proposes the OT-ICA algorithm, which uses the squared Wasserstein distance to measure non-Gaussianity instead of traditional proxies like negentropy. It proves that maximizing the Wasserstein distance between projected data and a standard Gaussian recovers independent components. Empirical evaluations show OT-ICA outperforms proxy-based methods across various latent distributions, and applications to EEG artifact removal and econometric price discovery demonstrate its practicality without distributional assumptions.

## Key points

- First to introduce optimal transport (Wasserstein distance) into linear ICA, replacing traditional non-Gaussianity proxies.
- Theoretical proof that maximizing Wasserstein distance is equivalent to recovering independent components.
- OT-ICA solves via gradient optimization without parametric assumptions on latent distributions.
- Validated on EEG artifact removal and price discovery tasks, demonstrating general applicability.

## Full text

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.

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