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December 2014 Confidence sets for persistence diagrams
Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, Aarti Singh
Ann. Statist. 42(6): 2301-2339 (December 2014). DOI: 10.1214/14-AOS1252

Abstract

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.

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Brittany Terese Fasy. Fabrizio Lecci. Alessandro Rinaldo. Larry Wasserman. Sivaraman Balakrishnan. Aarti Singh. "Confidence sets for persistence diagrams." Ann. Statist. 42 (6) 2301 - 2339, December 2014. https://doi.org/10.1214/14-AOS1252

Information

Published: December 2014
First available in Project Euclid: 20 October 2014

zbMATH: 1310.62059
MathSciNet: MR3269981
Digital Object Identifier: 10.1214/14-AOS1252

Subjects:
Primary: 62G05 , 62G20
Secondary: 62H12

Keywords: Density estimation , Persistent homology , topology

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 6 • December 2014
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