Cursive: The Trace from the Curse of Dimensionality
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.
Related
- The Llog L-Luxemburg Discrepancy for Nonnegative Weights Suffers from the Curse of Dimensionality
- The curse of dimensionality for geometric L1-discrepancies with nonnegative weights
- Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity
- Residual neural networks overcome the curse of dimensionality for semilinear heat equations
- Finite Expression Approximation of High-Dimensional PDEs Without the Curse of Dimensionality
BibTeX
@misc{chen2026cursive,
title = {{Cursive: The Trace from the Curse of Dimensionality}},
author = {Hao Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08610},
eprint = {2609.08610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08610},
}
RIS
TY - UNPB
TI - Cursive: The Trace from the Curse of Dimensionality
AU - Hao Chen
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08610
UR - https://arxiv.org/abs/2609.08610
AB - 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.
ER -