用最优传输距离衡量非高斯性，提升独立成分分析精度。
Linear Independent Component Analysis via Optimal Transport
- 以平方Wasserstein距离替代传统非高斯性度量
- 在多种分布下均优于基于四阶累积量的方法
- 无需分布假设，适用于脑电去噪与价格发现
线性独立成分分析（ICA）旨在从线性混合中恢复相互独立的源信号。经典方法通过最大化非高斯性（以负熵衡量）实现，但精确优化不可行，故采用代理对比函数（如四阶累积量）或参数化似然。本文提出使用数据线性投影与标准高斯分布间的平方Wasserstein距离 $W_2^2$ 来度量非高斯性。理论上证明：当投影恢复出一个独立成分时，该距离达到最大。据此提出OT-ICA算法，通过梯度优化寻找该投影。在模拟数据上的实证表明，OT-ICA在不同潜在变量分布下均优于传统代理方法。应用于脑电伪迹去除与计量经济学价格发现任务，验证其无需分布假设即可有效执行实际ICA任务。
原文摘要 · Abstract (English)
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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