Bayesian Manifold Learning

• Activity Number: 328
• Type: Invited
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): David B. Dunson*+
• Companies: Duke University
• Keywords: big data ; nonparametric Bayes ; manifold learning ; dimensionality reduction ; scalable computation ; geometry

Abstract

When faced with huge data sets, dimensionality reduction is crucial. Common approaches based on linear dimension reduction, such as PCA/factor analysis etc, have clear limitations motivating an increasing literature on non-linear alternatives. One view is to suppose that the big data are concentrated near a much lower dimensional manifold or even combination of manifolds. Many machine learning methods have been developed for manifold learning, but such approaches lack a global characterization of the lower-dimensional subspace accounting for uncertainty. We attempt to address this gap using probabilistic Bayesian methods to place priors on lower dimensional subspaces (e.g., manifolds in one special case), which lead to optimality properties and are tractable to compute even in huge data settings. These methods are illustrated with several very cool applications to massive imaging of famous paintings and to emerging neuroimaging technologies in which the number of pixels can be upwards of 100 billion or more. Careful use of distributed and cloud computing is key is such settings.