一维Wasserstein距离能同时捕捉密度差异与支撑集变化。
On the Information Processing of One-Dimensional Wasserstein Distances with Finite Samples
- 通过泊松过程建模，分离速率因子分析点态密度差异
- 在有限样本下仍能有效识别速率与支撑集的联合差异
- 适用于神经信号解码和氨基酸接触频率分析
利用Wasserstein距离——数据空间中样本间传输距离的总和——在测量两个潜在密度函数支撑集差异方面具有优势。然而，当支撑集显著重叠而密度存在显著逐点差异时，这种传输信息是否以及如何准确识别这些差异，尤其是在有限样本设置下的解析表征，仍不明确。本文通过泊松过程建模并分离速率因子，分析了一维Wasserstein距离在有限样本下的信息处理能力。结果表明，该距离能够捕捉逐点密度差异，并与支撑集差异信息协同。相关性质在神经脉冲序列解码和氨基酸接触频率数据中得到验证。结果显示，一维Wasserstein距离能有效突出与速率和支撑集相关的有意义密度差异。
原文摘要 · Abstract (English)
Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports significantly overlap while densities exhibit substantial pointwise differences, it remains unclear whether and how this transport information can accurately identify these differences, particularly their analytic characterization in finite-sample settings. We address this issue by conducting an analysis of the information processing capabilities of the one-dimensional Wasserstein distance with finite samples. By utilizing the Poisson process and isolating the rate factor, we demonstrate the capability of capturing the pointwise density difference with Wasserstein distances and how this information harmonizes with support differences. The analyzed properties are confirmed using neural spike train decoding and amino acid contact frequency data. The results reveal that the one-dimensional Wasserstein distance highlights meaningful density differences related to both rate and support.
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