Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Chen, Hao
Institution: University of California, Davis
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7212060582
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