arXiv：cs.LG· Steve Huntsman·· 4 小时前
用距离草图实现高效二次熵计算
Efficient quadratic entropy with distance sketches
AI 导读
研究人员提出一种可扩展方法，用于近似任意分布 p 与负类型距离 d 的二次熵 p^T d p，针对欧几里得和球面测地线情形，利用随机特征嵌入与投影显著降低计算复杂度。
正文
Abstract:We detail scalable methods for approximating the quadratic entropy $p^T d p$ for arbitrary distributions $p$ and common distances $d$ of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where $d$ is held constant while $p$ varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.
| Comments: | Code for reproducing results in LaTeX comments |
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST); Computation (stat.CO) |
| MSC classes: | 94A17 (Primary), 68W20, 65C05, 62R07 (Secondary) |
| Cite as: | arXiv:2610.11976 [stat.ML] |
| (or arXiv:2610.11976v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11976 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Steve Huntsman [view email]
[v1]
Thu, 8 Oct 2026 13:52:24 UTC (1,702 KB)
来源：arXiv：cs.LG · arxiv.org