Fabrizio Lecci - Carnegie Mellon University

Title: Statistical Inference for Topological Data Analysis. Abstract: Topological Data Analysis (TDA) is an emerging area of research at the intersection of algebraic topology and computational geometry, aimed at describing, summarizing and analyzing possibly high-dimensional data using low-dimensional algebraic representations. Recent advances in computational topology have made it possible to actually compute topological invariants from data. These novel types of data summaries have been used successfully in a variety of applied problems, and their potential for high-dimensional statistical inference appears to be significant. In this talk, I will focus on the tools of persistent homology, the main method of TDA for measuring the topological features of shapes and functions at different resolutions. I will show how to construct confidence sets for the data summaries of persistence homology, and use them to separate topological signal from topological noise.