发表机构
Università della Svizzera italiana; University of Milano-Bicocca（瑞士意大利大学; 米兰比可卡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出非参数加权持续强度回归方法，建立其理论与估计性质，经模拟验证后用于分析脑动脉树径向几何随年龄的变化。
AI 中文摘要
持续图总结数据的多尺度拓扑结构，在应用中常与协变量成对出现。我们开发非参数方法与理论，用于估计欧几里得协变量条件下的期望加权持续图。将每个加权图表示为紧窗口上的有限随机测度，我们将其条件期望的密度作为回归目标，即条件加权持续强度。对于条件双核估计量，我们建立了有限样本上确界范数率（匹配极小极大下界）、部分最优传输中的一致率，以及用于带宽选择的无偏风险交叉验证准则。对解析已知强度的模拟验证了该理论，且表明在精确强度设计中，交叉验证能选择出最优带宽候选。该方法通过研究脑动脉树的径向几何如何随年龄变化得到说明。
英文摘要
Persistence diagrams summarize the multiscale topological structure of data, and in applications they often arrive paired with covariates. We develop nonparametric methodology and theory for estimating the expected weighted persistence diagram conditional on a Euclidean covariate. Representing each weighted diagram as a finite random measure on a compact window, we take the density of its conditional expectation as the regression target, the conditional weighted persistence intensity. For a conditional double-kernel estimator we establish finite-sample sup-norm rates with a matching minimax lower bound, uniform rates in partial optimal transport, and an unbiased-risk cross-validation criterion for bandwidth selection. Simulations with analytically known intensities corroborate the theory and show that cross-validation selects the oracle candidate bandwidth in the exact-intensity design. The method is illustrated by studying how radial geometry in cerebral artery trees varies with age.
