- Tuesday, April 11, 2017, 3:15pm, 119 Physics, CTMS Adventures In Theory Lectures Seminar
Uncertainty Quantification in the Classification of High Dimensional Data
Andrew Stuart (University of Warwick)
- We provide a unified framework for graph based semi-supervised
learning which brings together
a variety of methods which have been introduced in different
communities within the mathematical sciences; the unification
is through an inverse problems formulation.
We study probit classification, 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 machine learning.
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. Finally we study continuum
limits of the problem formulations, and algorithms, arising in the
infinite data limit.
AL Bertozzi, X Luo (UCLA)
KC Zygalakis (Edinburgh)
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