LADE Meeting: Karthik Viswanathan (UvA)

Information Maximizing Persistent Homology

Abstract

Persistent homology (PH) is a mathematical tool in computational topology that measures the topological features of data such as loops and voids that persist across multiple scales with applications ranging from biological networks to cosmology. We represent the data in the form of a persistent diagram that keeps track of the length scales at which the topological features are created and destroyed. It is possible that we lose information about the dataset while we construct the persistence diagram. In this talk, I’ll explore how to quantify the information content of the persistent diagram with respect to the dataset. It can then be seen that the hyperparameters used to build this filtered simplicial complex can be optimized to maximize the Fisher information of the corresponding persistence summaries. This algorithm may be useful for integrating topological information into statistical inference. In an experimental setup, we show that in some cases topology can provide optimal summaries, in the sense that the Cramer-Rao bound is saturated.

Date
Sep 20, 2023 11:30 AM — 12:30 PM
Event
LADE Meeting
Location
Sala Riunioni RIT, Area Science Park
Località Padriciano 99, Trieste, 34149
Area Science Park - RIT
Area Science Park - RIT
Research Institute

The Institute of Research and Innovation Technology (RIT) at Area Science Park carries out cutting-edge research and provides services and consulting to public and private-sector users through its three laboratories equipped with state-of-the-art technology.