Cursive：从维度灾难的轨迹
Cursive: The Trace from the Curse of Dimensionality
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中文总结 AI 辅助
本文提出Cursive研究计划，探讨高维数据中关系信息在统计摘要中的丢失，并追溯基于图、秩、核和相异度的方法如何围绕此问题设计，以改进多种统计任务。
中文摘要 AI 辅助
现代数据日益高维或非欧几里得。随着维度增长，观测之间关系中可能出现新的统计模式，而传统的统计摘要可能无法保留它们所携带的信号。本文围绕这一观察命名并组织了一个研究计划，称之为Cursive。Cursive询问在形成摘要时哪些关系信息丢失，以及应如何围绕该信息重新设计分析。典型例子是广义边数检验，它保留两个样本内边数，其相反的偏差可能在经典的样本间计数中相互抵消。本文追溯了同样的设计问题如何导致了基于图、基于图的秩、核函数和相异度分布的任务特定方法，用于检验、变点检测、协变量平衡评估、聚类、分类和生成模型评估。
英文摘要
Modern data are increasingly high-dimensional or non-Euclidean. As dimension grows, new statistical patterns can emerge in the relations among observations, while a conventional statistical summary may fail to retain the signal they carry. This paper names and organizes a research program around this observation, calling it Cursive. Cursive asks which relational information is lost when the summary is formed and how the analysis should be redesigned around that information. The canonical example is the generalized edge-count test, which keeps the two within-sample edge counts whose opposing deviations can cancel in the classical between-sample count. This paper traces how the same design question has led to task-specific methods built from graphs, graph-based ranks, kernels, and dissimilarity profiles for testing, change-point detection, covariate-balance assessment, clustering, classification, and generative-model evaluation.
发表机构
- University of California, Davis（加州大学戴维斯分校）
机构由 AI 辅助整理，请以论文原文为准。
