Uncertainty quantification in graph-based classification of high dimensional data

Andrea L. Bertozzi, Xiyang Luo, Andrew M. Stuart, Konstantinos Zygalakis

Research output: Contribution to journalArticlepeer-review

Abstract

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we introduce, develop algorithms for, and investigate the properties of, a variety of Bayesian models for the task of binary classification; via the posterior distribution on the classification labels, these methods automatically give measures of uncertainty. The methods are all based around the graph formulation of semi-supervised learning.
We provide a unified framework which brings together a variety of methods which have been introduced in different communities within the mathematical sciences. We study probit classification in the graph-based setting, generalize the level-set method for Bayesian inverse problems to the classification setting, and generalize the Ginzburg-Landau optimization-based classifier to a Bayesian setting; we also show that the probit and level set approaches are natural relaxations of the harmonic function approach introduced in [Zhu et al 2003].
We introduce efficient numerical methods, suited to large data-sets, for both MCMC-based sampling as well as gradient-based MAP estimation. Through numerical experiments we study classification accuracy and uncertainty quantification for our models; these experiments showcase a suite of datasets commonly used to evaluate graph-based semi-supervised learning algorithms.
Original languageEnglish
Pages (from-to)568-595
Number of pages28
JournalSIAM/ASA Journal on Uncertainty Quantification
Volume6
Issue number2
Early online date26 Apr 2018
DOIs
Publication statusPublished - Apr 2018

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