CONFIDENCE SETS FOR PERSISTENCE DIAGRAMS

• 成果类型: Article
• 署名作者: Fasy, Brittany Terese; Lecci, Fabrizio; Rinaldo, Alessandro; Wasserman, Larry; Balakrishnan, Sivaraman; Singh, Aarti
• 署名单位: Tulane University; Carnegie Mellon University; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1252
• 发表日期: 2014
• 页码: 2301-2339
• 关键词: nonparametric-estimation; density estimators; TOPOLOGY; HOMOLOGY; support

摘要

Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be topological noise, and those with a long lifetime are considered to be topological signal. In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to separate topological signal from topological noise.