Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Wednesday, January 26, 2022 - 16:00 to 17:00
Location: 
on Zoom

Speaker Info

Institution: 
University of Hawaii at Manoa
Abstract: 

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology (PH) is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). However, a sufficiently large amount of PDs that allow performing statistical analyses is typically unavailable or requires inordinate computational resources. In this talk, I will present a novel sampling method for random persistence diagram generation (RPDG) that augments topological summaries of the data, thus facilitating statistical inference with a limited amount of data. RPDG is underpinned by (i) a model based on pairwise interacting point processes for inference of PDs, and (ii) by a reversible jump Markov chain Monte Carlo algorithm for generating samples of PDs. This framework is applicable to a wide variety of datasets. I will present an application to a materials science problem.