Confidence sets for persistence diagrams

@article{Fasy2014ConfidenceSF,
  title={Confidence sets for persistence diagrams},
  author={Brittany Terese Fasy and Fabrizio Lecci and Alessandro Rinaldo and Larry A. Wasserman and Sivaraman Balakrishnan and Aarti Singh},
  journal={The Annals of Statistics},
  year={2014},
  volume={42}
}
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… 

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Optimal rates of convergence for persistence diagrams in Topological Data Analysis

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