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Confidence sets for persistence diagrams

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arxiv 1303.7117 v3 pith:SJIWAMQI submitted 2013-03-28 math.ST cs.CGcs.LGstat.TH

Brittany Terese Fasy , Fabrizio Lecci , Alessandro Rinaldo , Larry Wasserman , Sivaraman Balakrishnan , Aarti Singh This is my paper · ORCID
classification math.STcs.CGcs.LGstat.TH
keywords topologicalconfidenceconsideredfeatureshomologymethodnoisepersistent
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features

    stat.ML 2026-06 unverdicted novelty 7.0 of 10

    STRAND treats persistence diagrams as survival data to derive a calibrated two-sample test, interpretable effect sizes, and a 1-Wasserstein-stable feature vector from one representation.

  2. Topology of Out-of-Distribution Examples in Deep Neural Networks

    cs.LG 2025-01 conditional novelty 6.0 of 10

    Out-of-distribution images show longer average H0 persistence lifetimes in a ResNet18 embedding layer than in-distribution training and test images.

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