Linear Independent Component Analysis via Optimal Transport
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Computer Science > Machine Learning
Title:Linear Independent Component Analysis via Optimal Transport
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 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.
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2607.14081 [cs.LG] |
| (or arXiv:2607.14081v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.14081
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