发表机构
The George Washington University; Montana Technological University; University of Ljubljana（乔治华盛顿大学; 蒙大拿理工大学; 卢布尔雅那大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对持久性图总体，提出固定预算下局部均值对比的同时推断方法，利用加性界标响应和高斯乘子自助校准置信区间，在模拟中实现94%-98%覆盖，并应用于MUTAG基准识别差异区域。
AI 中文摘要
许多针对持久性图总体的两样本检验仅评估全局差异，而未识别出生-死亡平面中导致这些差异的区域。我们研究当可用图数量固定时，局部均值对比的同时推断。这些对比是在多个中心和半径的$\ell_\infty$邻域内，期望加权特征质量的差异。我们使用加性界标响应来估计这些对比。高斯乘子自助法校准同时置信区间，同时允许组间协方差不等。区间排除零的邻域构成一幅具有近似族wise误差控制的图谱，选择原始区间的子集进行展示可保留其联合覆盖保证。在同时覆盖事件上，每个报告的邻域都位于其半径两倍范围内，且包含均值测度差异的支撑。一个几何结果给出了位移特征产生非零对比的充分半径条件。对充分检测阈值的比较量化了减少测试坐标数量与为独立预试验保留观测之间的权衡。在每类40至120张图的模拟中，带在严格零假设和均值相等但协方差不等两种情形下均实现了94%-98%的同时覆盖。在后一种情形下，置换最大值和Moon与Lazar的两阶段持久性图像检验的合并t实现分别在多达32%和26%的运行中拒绝。在固定预算模拟中，将三分之一的观测用于预试验以选择界标或半径，其定位变化的情况少于在单一半径下使用预设网格的情况。在MUTAG基准上，局部化区域集中于稠环系统的环上，这是一种探索性解读。
英文摘要
Many two-sample tests for populations of persistence diagrams assess global differences without identifying the regions of the birth-death plane that contribute to them. We study simultaneous inference for local mean contrasts when the number of available diagrams is fixed. They are differences in expected weighted feature mass within $\ell_\infty$ neighborhoods at several centers and radii. We estimate these contrasts using additive landmark responses. A Gaussian multiplier bootstrap calibrates simultaneous confidence intervals while allowing unequal group covariances. The neighborhoods whose intervals exclude zero form a map with approximate family-wise error control, and selecting a subset of original intervals for display preserves their joint coverage guarantee. On the simultaneous coverage event, every reported neighborhood lies within twice its radius of the support of the mean-measure difference. A geometric result gives sufficient radius conditions for a displaced feature to produce a nonzero contrast. A comparison of sufficient detection thresholds quantifies the tradeoff between reducing the number of tested coordinates and reserving observations for an independent pilot. In simulations with 40 to 120 diagrams per class, the bands achieved 94%-98% simultaneous coverage under both the strict null and equal means with unequal covariances. In the latter setting, a permutation maximum and the pooled-t implementation of the two-stage persistence-image test of Moon and Lazar rejected in up to 32% and 26% of runs, respectively. In the fixed-budget simulations, spending a third of the observations on a pilot to choose landmarks or radii located changes less often than a prespecified grid at a single radius. On the MUTAG benchmark, the localized region concentrates on rings of fused-ring systems, an exploratory reading.
Comments45 pages, 9 figures. Appendices with proofs and additional experiments. Under review
