Speaker: Farzana Nasrin (U. Tennessee)
Title: Bayesian Topological Learning for Complex Data Analysis
Abstract: Classification is an important problem with multiple applications from materials science, and chemistry to biology and neuroscience. In this talk, we will approach the problem of classification by focusing on the shape of data and summarizing it with topological descriptors called persistence diagrams. Viewing persistence diagrams through the lenses of point processes, one could define a pertinent probabilistic framework and potentially quantify the uncertainty present in these summaries. Taking into account this framework and historical data, we will present a novel generalized Bayesian framework for persistent homology, which provides an effective, flexible and noise-resilient scheme to analyze and classify complex datasets. A closed form solution of the posterior distributions of persistence diagrams based on a family of conjugate priors will be provided, and Bayes factors on the space of persistence diagrams will be computed to yield robust classification results. An example of classifying high entropy alloy materials will demonstrate the applicability of this novel Bayesian classifier.