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The theory and application of networks: from mathematical machine learning to simplicial complexes
Special Events| Speaker: | Sanjukta Krishnagopal, Berkeley AI Research Lab, University of California, Berkeley Department of Mathematics, University of California, Los Angeles |
| Location: | 1147 MSB |
| Start time: | Tue, Jan 16 2024, 4:00PM |
Networks are ubiquitous in nature and appropriate for mathematical investigation of various systems. In this talk I will discuss some aspects at the intersection of mathematics, machine learning, and networks to introduce interdisciplinary methods with wide application.First, I will discuss some recent advances in mathematical machine learning for prediction on graphs. Machine learning is often a black box. Here I will present some exact theoretical results on the dynamics of weights while training graph neural networks using graphons - a limiting function of a graph with infinitely many nodes. Next, I will use these ideas to present a new method for predictive and personalized medicine applications with remarkable success in prediction of Parkinson's subtype five years in advance.Then, I will discuss some work on higher-order models of graphs: simplicial complexes - that can capture simultaneous many-body interactions. I will present some results on spectral theory of simplicial complexes, as well as introduce a mathematical framework for studying the topology and dynamics of multilayer simplicial complexes using Hodge theory, and discuss applications of such interdisciplinary methods to studying bias in society, opinion dynamics, hate speech in social media.
Reception is at 3:30pm, immediately before the talk, in the lobby of MSB