arXiv：cs.LG· Ashutosh Jha, Michel Besserve, Simon Buchholz·· 4 小时前AI 评分37
基于最优传输的线性独立成分分析（OT-ICA）
Linear Independent Component Analysis via Optimal Transport
AI 导读
研究者提出用标准高斯分布的平方 L2-Wasserstein 距离作为线性 ICA 的对比函数，并给出 OT-ICA 算法。理论证明该距离在投影恢复独立成分时取最大值，且在源正则条件下与真实混合存在明确间隔；对平滑密度源具有 √N 一致性与渐近正态闭式方差，对含原子源则估计精确。模拟数据显示 OT-ICA 优于基于代理对比函数的方法，并已应用于线性因果解耦与 EEG 伪影去除。
正文
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 use the squared $L_2$-Wasserstein distance to a standard Gaussian as the ICA contrast. We show that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized when the projection recovers an independent component, and that under a regularity condition on the sources this maximum is separated from every genuine mixture by an explicit margin. We uncover the advantageous properties of the resulting estimator: for sources with a smooth density it is $\sqrt{N}$-consistent and asymptotically normal with a closed-form variance, whereas for a source with an atom the contrast has a kink at the true direction, which makes the estimator exact with probability tending to one. The proposed OT-ICA algorithm finds this projection by gradient-based optimization. Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods and that the $W_2^2$ contrast provides more robust signal than proxy contrasts in measuring non-Gaussianity for different distributional mixtures of the latent variables. Application to linear causal disentanglement and EEG artifact removal, along with further applications detailed in the appendix, confirms OT-ICA can be used for applied ICA tasks without distributional assumptions.
| Comments: | 49 pages, 16 figures. A preliminary version appeared at the 9th Workshop on Tractable Probabilistic Modeling (TPM), UAI 2026 |
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2607.14081 [cs.LG] |
| (or arXiv:2607.14081v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.14081 arXiv-issued DOI via DataCite |
Submission history
From: Ashutosh Jha [view email]
[v1]
Wed, 15 Jul 2026 17:56:11 UTC (492 KB)
[v2]
Wed, 7 Oct 2026 10:04:37 UTC (706 KB)
来源：arXiv：cs.LG · arxiv.org