Computational Techniques for High-Dimensional Nonparametric Bayes

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Anjishnu Banerjee*+
• Keywords: Dimension reduction ; Map Reduce ; Random Projection ; Matrix Approximation ; Nonparamteric Bayes ; Gaussian Process

Abstract

A common problem in high dimensional Bayesian non parametric problems is the computational complexity. An example being in the context of Gaussian processes, inversion of the large covariance matrix (needed for likelihood evaluation), which practically infeasible and extremely numerically unstable for large $n$. We propose a general class of algorithms for parallelizing computations in a variety of nonparametric settings, borrowing from apparently unrelated recent developments in random linear algebra, machine learning and computer science. They enable us to dramatically speed up computations, improving efficiency by several orders of magnitude. We providing some motivating results which provide guarantees of approximation accuracy and convergence in the approximation settings. We also provide some illustrations to give a flavor of the gains and what becomes possible in freeing up the computational bottlenecks.