[论文] Linear Independent Component Analysis via Optimal Transport

论文概要

研究领域: ML
作者: Ashutosh Jha, Michel Besserve, Simon Buchholz
发布时间: 2026-07-15
arXiv: 2607.14081

中文摘要

线性独立成分分析（ICA）从其线性混合中恢复联合独立的源信号。为实现此目标，经典ICA算法尝试最大化非高斯性，用负熵度量，这与信息论中的独立性相关。由于精确负熵优化难以处理，它们依赖代理对比函数，如四阶累积量，和参数化对数似然。我们改为使用到标准高斯的平方Wasserstein距离\(W_2^2\)来度量非高斯性。我们证明，当投影恢复独立成分时，标准正态分布与数据线性投影之间的Wasserstein距离被最大化。基于这一观察，我们提出OT-ICA算法，通过基于梯度的优化找到该投影。在模拟数据上的实证评估表明，对于潜变量的不同分布，OT-ICA优于基于代理的方法。在EEG伪影去除和经济计量价格发现中的应用证实OT-ICA可用于应用ICA任务而无需分布假设。

原文摘要

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 ...

自动采集于 2026-07-17

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