Statistical Persistent Homology
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 as one varies a tuning parameter. Features with short lifetimes are informally considered to be “topological noise.” In our work, we attempt bring some statistical ideas to persistent homology. In particular, we have derived confidence intervals that allow us to separate topological signal from topological noise.
Statistical Inference For Persistent Homology: Confidence Sets for Persistence Diagrams
Brittany Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, Aarti Singh
On the Bootstrap for Persistence Diagrams and Landscapes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, Larry Wasserman
Stochastic Convergence of Persistence Landscapes and Silhouettes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman