Bayesian Computation for Persistent Homology

April 2, 2020
3:00
Speaker: Farzana Nasrin
Host: Lenore Cowen

Abstract

Abstract, a joint work with Vasileios Maroulas:

Persistent homology is a tool in topological data analysis for learning about the geometrical/topological structures by detecting different dimensional hole and storing their appearance disappearance scales in persistence diagrams. In this talk, we will present a Bayesian framework for persistent homology by relying on the independent and identically distributed cluster point process. This framework provides the flexibility to estimate the posterior cardinality of points in a persistence diagram and their posterior spatial distribution simultaneously. We present a closed form of the posterior intensity and cardinality under the assumption of conjugate families. Using this posterior calculation, we implement a Bayes factor algorithm to classify the actin filament networks of plant cells. However, due to the inherent complexity of real datasets, it is not always possible to obtain a closed form solution to the posterior distribution of persistence diagrams. We will address this by proposing an importance sampling scheme for estimating the posterior distributions of persistence diagrams.

You are invited to a Zoom meeting. When: Apr 2, 2020 03:00 PM Eastern Time (US and Canada)

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A recording of this colloquium is available at https://tufts.zoom.us/rec/share/3-l3FvLyrCRLW6fE8hv9RYM6GYHLX6a8gyIb_fUIz0f4d9Cr3O36E_munqYJCvsE?startTime=1585854132000