Jeff Calder, from the University of Minnesota, will present a hybrid talk at the Applied Mathematics Colloquium.

Title: Partial differential equations and graph-based learning

Abstract: Graph-based learning is concerned with applying machine learning (e.g., classification, clustering, or regression) to graph-structured data. A graph structure encodes interdependencies among constituents, such as social media users, images, videos, or physical or biological agents, and provides a convenient representation of high dimensional data that has proven to be highly effective in machine learning. In this talk, we will show how machine learning problems on graphs can be interpreted as numerical schemes for solving partial differential equations (PDEs). This connection between PDEs and graph-based learning allows us to utilize theoretical and computational tools from the field of PDEs to study machine learning problems and develop new algorithms. This talk will focus in particular on our recent work on active learning, where we will show how a PDE-based analysis leads to a new algorithm with rigorous performance guarantees, and on robust approximations of graph distance functions via Hamilton-Jacobi equations on graphs.

Bio: Jeff Calder is an Associate Professor of Mathematics at the University of Minnesota. His research involves interactions between partial differential equations (PDE), numerical analysis, applied probability, and computer science. He is interested in both the rigorous analysis of PDE, and the development and implementation of algorithms.

Please email [email protected] ahead of time for the Zoom link.