Title:  Providing Statistical Guarantees for Topological Summaries of Data

Abstract:
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.  In this talk, I will define some of the existing topological summaries of data, and show how we can provide statistical guarantees of these summaries.
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