Confidence sets for persistence diagrams
Statistics Theory
2014-11-21 v3 Computational Geometry
Machine Learning
Statistics Theory
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.
Cite
@article{arxiv.1303.7117,
title = {Confidence sets for persistence diagrams},
author = {Brittany Terese Fasy and Fabrizio Lecci and Alessandro Rinaldo and Larry Wasserman and Sivaraman Balakrishnan and Aarti Singh},
journal= {arXiv preprint arXiv:1303.7117},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/14-AOS1252 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)