arXiv：cs.LG· Song Liu·· 3 小时前
**title_zh:** 面向解耦流的自足独立成分分析
Self-sufficient Independent Component Analysis for Demixing Flows
AI 导读
**summary_zh:** 研究提出一种自足信号学习准则：给定已恢复信号的其余取值，观测其他信号不应改变其缺失值的条件分布，并将其形式化为条件 KL 散度最小化。算法无需先验分布与似然函数，通过顺序学习解混流模型，并证明了理想化 Wasserstein 梯度流变体下总相关的局部下降，完全避开不稳定的对抗训练。玩具与真实数据集实验验证了有效性。
正文
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.
| Comments: | Added identifiability theorem, columnwise projection step, and additional experiments. Revised positioning of the method |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2512.00665 [stat.ML] |
| (or arXiv:2512.00665v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2512.00665 arXiv-issued DOI via DataCite |
Submission history
From: Song Liu Dr. [view email]
[v1]
Sat, 29 Nov 2025 23:10:16 UTC (1,141 KB)
[v2]
Thu, 8 Oct 2026 17:45:00 UTC (1,267 KB)
来源：arXiv：cs.LG · arxiv.org