arXiv：cs.LG（机器学习，全量分类）· Leyang Wang, Yakun Wang, Song Liu, Taiji Suzuki·· 7 小时前AI 评分38
Zero Flux：基于流的高维离散分布比较准则
Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions
AI 导读
研究者提出 Zero Flux 准则，将基于流匹配的连续分布比较方法扩展到离散领域，通过局部概率通量衡量两个高维离散分布的差异。在独立耦合下，当且仅当两分布相同时，中点处所有局部概率通量消失。该差异可分解为局部贡献并从样本高效估计，研究给出了有限样本误差界，在合成与真实类别数据上实现了稀疏依赖信号的可靠恢复和高维分布偏移的稳定追踪。
正文
Abstract:Comparing two high-dimensional discrete distributions has always been a challenging task due to the exponentially growing state space and complex changes in interactions. A recent work suggests comparing distributions through a vector field trained using flow matching between two continuous distributions. The resulting vector field at mid-point vanishes if and only if two distributions identical. However, such a flow-based criterion does not naturally apply to discrete distributions. We extend this principle to the discrete domain and introduce the \emph{Zero Flux} criterion, a discrepancy based on local probability fluxes. Under independent coupling, we show that all local probability fluxes vanish at the midpoint if and only if two distributions are the same. This discrepancy decomposes the joint distributional difference into smaller, local contributions and can be efficiently estimated from samples. We establish finite sample error bounds for our estimator. Experiments on synthetic and real categorical data demonstrate reliable recovery of sparse dependence signals and stable tracking of distribution shifts in high dimensions.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.01472 [stat.ML] |
| (or arXiv:2610.01472v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01472 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Leyang Wang [view email]
[v1]
Thu, 1 Oct 2026 11:13:49 UTC (6,677 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org