Barycentric Gaussian Processes for Nonparametric Regression

• Activity Number: 18 - Optimal Transport and Scalable Bayes: A Fruitful Synergy?
• Type: Topic Contributed
• Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Cheng Li* and Sanvesh Srivastava and David B. Dunson
• Companies: National University of Singapore and The University of Iowa and Duke University
• Keywords: Gaussian process ; divide and conquer ; barycenter ; approximation error ; Markov chain Monte Carlo

Abstract

Complex dependencies between continuous random variables can be modeled by Bayesian nonparametric regression based on Gaussian process (GP). The flexibility of GP comes at the cost of intractable posterior computations when the sample size is large. Existing methods solve this problem by imposing low-rank and sparsity assumptions on the covariance or inverse-covariance matrix. However, accuracy of low-rank approximation can degrade quickly as the size of data increases. We develop a divide-and-conquer method for GP-based models. We first partition the data into smaller subsets such that fitting GP-based models is feasible for every subset. Then we modify the GP priors on all subsets and combine them into a global prior via their Wasserstein barycenter, which is analytically tractable. The BarGP prior from this divide-and-conquer procedure can be shown as a valid GP prior. We develop efficient sampling algorithms for finding the barycenter and updating the model parameters. We provide theoretical results that quantify the approximation error from the BarGP posterior to the true GP posterior, and compare its empirical performance with existing low-rank GP methods.