---
title: "基于最优传输的线性独立成分分析"
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距离","最优传输","独立成分分析","非高斯性度量"]
---

# 基于最优传输的线性独立成分分析

## AI 点评

> 这篇论文最值得关注的地方是用最优传输理论重新定义了独立成分分析的核心度量，理论优雅且实验扎实。对于从事无监督学习、信号处理或因果发现的读者来说，它提供了一种摆脱分布假设束缚的新工具。不过需要注意计算复杂度，在实际大规模应用中可能需要进一步优化。

## 速览

本文提出OT-ICA算法，利用平方Wasserstein距离替代传统ICA中的非高斯性度量（如负熵），通过最大化投影数据与标准正态分布的Wasserstein距离来恢复独立成分。理论证明该度量与独立成分恢复等价，实验表明OT-ICA在多种潜变量分布下优于基于代理函数的经典方法，并在EEG伪迹去除和计量经济学价格发现等实际任务中展示出无需分布假设的实用性。

## 关键点

- 首次将最优传输理论（Wasserstein距离）引入线性ICA，替代传统非高斯性代理函数。
- 理论证明Wasserstein距离最大化等价于独立成分恢复。
- OT-ICA通过梯度优化求解，无需对潜变量分布做参数化假设。
- 在EEG伪迹去除与价格发现任务中验证了算法的通用性与效果。

## 全文

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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引用前请核对原文;本文由星际流动整理:https://feed.astralor.com/items/itm_019fc74cb0e29c083c90f0b9