Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces

Abstract

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.

References in corpus (5)

• Random geometric complexes
• Persistent Homology for Random Fields and Complexes
• Fréchet Means for Distributions of Persistence diagrams
• Crackle: The Persistent Homology of Noise
• Limit theorems for Betti numbers of random simplicial complexes

Cited by in corpus (5)

• Confidence sets for persistence diagrams
• Topological consistency via kernel estimation
• Probabilistic Fréchet Means for Time Varying Persistence Diagrams
• Parametric Inference using Persistence Diagrams: A Case Study in Population Genetics
• Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis