SIAM Mathematics of Data Science (MDS20) Distinguished Lecture Series: Andrea Bertozzi

/ May 19, 2020/

Graphical Models in Machine Learning, Networks, and Uncertainty Quantification

Abstract: This talk is an overview of recent work graph models for classification using similarity graphs, for community detection in networks, and for the subgraph isomorphism problem in multichannel networks. The equivalence between the graph mincut problem and total variation minimization on the graph allows one to cast graph-cut variational problems in the language of total variation minimization, thus creating a parallel between low dimensional data science problems in Euclidean space (e.g. image segmentation) and high dimensional clustering. Semi-supervised learning with a small amount of training data can be carried out in this framework with diverse applications ranging from hyperspectral pixel classification to identifying activity in police body worn video. It can also be extended to the context of uncertainty quantification with Gaussian noise models. The problem of community detection in networks also has a graph-cut structure and algorithms are presented for the use of threshold dynamics for modularity optimization. With efficient methods, this allows for the use of network modularity for unsupervised machine learning problems with unknown number of classes. Finally we discuss a different class of graph problem – namely identifying template structure in large world graphs and how combinatorial filtering methods can be structured to efficiently attack this problem.

Andrea L. Bertozzi, University of California, Los Angeles, U.S.

This is one of seven virtual plenary talks originally scheduled for the 2020 SIAM Conference on Mathematics of Data Science. For more information on this session, visit https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=69236. To view the virtual program and register for other invited plenary talks, minitutorial talks, and minisymposia, please visit the MDS20 website at https://www.siam.org/conferences/cm/conference/mds20.