Self-sufficient Independent Component Analysis for Demixing Flows

Abstract:We study the problem of learning disentangled signals from data using non-linear Independent Component Analysis (ICA). Motivated by advances in self-supervised learning, we propose to learn self-sufficient signals: Given the remaining values of a recovered signal, observing other signals should not change the conditional distribution of its missing value. We formulate this problem as the minimization of a conditional KL divergence. Our algorithm is prior-free and likelihood-free in the sense that it prescribes neither parametric source densities nor an observation likelihood. To tackle the KL divergence minimization problem, we propose a sequential algorithm that learns a de-mixing flow model at each iteration, and prove local descent of the total correlation for its idealized Wasserstein-gradient-flow variant with exact velocities and a population projection condition. This approach completely avoids the unstable adversarial training, a common issue in minimizing the KL divergence. Experiments on toy and real-world datasets show the effectiveness of our method.

Added identifiability theorem, columnwise projection step, and additional experiments. Revised positioning of the method

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2512.00665 [stat.ML]

(or arXiv:2512.00665v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2512.00665 Focus to learn more arXiv-issued DOI via DataCite

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