Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Thursday, Apr 14, 2022
Time: 4:00PM
Location: JWB 335
Jeff Calder
University of Minnesota
Title |
Boundary estimation and Hamilton-Jacobi equations on point clouds |
Abstract |
This talk will discuss recent work on estimating the boundary of a domain from iid samples, and on solving Hamilton-Jacobi equations on graphs. We’ll present a method for boundary estimation that is scalable to large datasets in high dimensional settings, and provide statistical guarantees that the method identifies all samples within a desired distance of the boundary. We’ll show that the method can be used to solve PDEs on point clouds with Dirichlet boundary conditions, which has applications to problems like data depth and machine learning. We will also present some work on robust approximations of graph distances via the solution of particular Hamilton-Jacobi equations on graphs, and discuss applications to data depth and semi-supervised learning. This is joint work with Dejan Slepcev, Sangmin Park, and Mahmood Ettehad. |
Differential Equations
Data Science and Machine Learning