Statistical Computational Topology
Overview
Persistent homology is a method for probing topological properties of point clouds and function. 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.” I am interested in bringing statistical ideas to persistent homology in order to distinguish topological signal from topological noise and to derive meaningful, yet computable, summaries of large datasets. For more information, please see the CMU TopStat website.
Publications and Preprints
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“Statistical Inference For Persistent Homology: Confidence Sets For Persistence Diagrams” by Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, and Aarti Singh. To appear: Annals of Statistics. [arXiv:1303.7117] [BibTeX]
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“Stochastic Convergence of Persistence Landscapes and Silhouettes” by Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, and Larry Wasserman. Conference: Proceedings of SoCG 2014. In submission: Journal of Computational Geometry. [arXiv:1312.0308] [BibTeX]
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“Subsampling Methods for Persistent Homology” by Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, and Larry Wasserman. Work in progress. [arXiv:1406.1901] [BibTeX]
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“On the Bootstrap for Persistence Diagrams and Landscapes” by Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, and Larry Wasserman. Journal: Modeling and Analysis of Information Systems. [arXiv:1311.0376] [BibTeX]
Presentations and Posters