发表机构
The University of Tokyo; RIKEN; University of Bristol（东京大学; 理化学研究所; 布里斯托尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出零通量准则，将流匹配扩展到离散分布，通过局部概率通量判断分布是否相同，并实现高效估计与高维分布偏移的稳定跟踪。
AI 中文摘要
比较两个高维离散分布一直是一项具有挑战性的任务，因为状态空间呈指数增长且交互作用变化复杂。最近的一项工作建议通过使用流匹配在两个连续分布之间训练的向量场来比较分布。当且仅当两个分布相同时，所得向量场在中点处消失。然而，这种基于流的标准并不自然地适用于离散分布。我们将这一原理扩展到离散域，并引入了\emph{零通量}准则，这是一种基于局部概率通量的差异度量。在独立耦合下，我们证明当且仅当两个分布相同时，所有局部概率通量在中点处消失。该差异度量将联合分布差异分解为更小的局部贡献，并且可以从样本中高效估计。我们为我们的估计器建立了有限样本误差界。在合成和真实分类数据上的实验表明，该方法能够可靠地恢复稀疏依赖信号，并在高维中稳定跟踪分布偏移。
英文摘要
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.
