Abstract

Many problems in machine learning require the classification of high dimensional data. One methodology to approach such problems is to construct a graph whose vertices are identified with data points, with edges weighted according to some measure of affinity between the data points. Algorithms such as spectral clustering, probit classification and the Bayesian level set method can all be applied in this setting. The goal of the talk is to describe these algorithms for classification, and analyze them in the limit of large data sets. Doing so leads to interesting problems in the calculus of variations, Bayesian inverse problems and in Monte Carlo Markov Chain, all of which will be highlighted in the talk. These limiting problems give insight into the structure of the classification problem, and algorithms for it.    

Collaboration with:  
Andrea Bertozzi (UCLA)
Michael Luo (UCLA)
Kostas Zygalakis (Edinburgh)
https://arxiv.org/abs/1703.08816  
and  
Matt Dunlop (Caltech)
Dejan Slepcev (CMU)
Matt Thorpe (Cambridge)
(forthcoming paper)