Confidence sets for persistence diagrams
Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, Aarti Singh
The Annals of Statistics · 2014 · Volume 42 · Issue 6
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.
Keywords
62G05, 62G20, 62H12, Density estimation, Persistent homology, topology
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