Fast Big Data Spatial Process Regression Using Hierarchical Modeling

• Activity Number: 64 - Computational Advances in Bayesian Inference
• Type: Contributed
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Pallavi Ray* and Debdeep Pati and Anirban Bhattacharya
• Companies: Eli Lilly and Company and Texas A&M University and Texas A&M University
• Keywords: Hierarchical modeling; Divide-and-conquer; Gaussian Process; Elliptical Slice sampling

Abstract

We propose a divide-and-conquer based algorithm for spatial data where the subgroups are represented by partitions in a regular grid. In order to induce coherence and to facilitate borrowing of information across multiple subgroups, we incorporate a hierarchical model on group-specific functions. This approach yet fails to scale for datasets with very large number of observations. As a remedy, we propose a novel approach for sampling from the posterior distribution of the Gaussian process (GP) assumed for the common mean of each subgroup. The proposed method uses the special structure of the covariance matrix for the GP, which is Block Toeplitz with Toeplitz Blocks (BTTB) and employs Fast Fourier Transform (FFT) and elliptical slice sampling. Inducing dependence through hierarchical modeling in conjunction with a novel algorithm to sample from the posterior distribution of the mean of each subgroup results in a fast regression algorithm with a better accuracy in prediction that can handle datasets with very large number of observations. This resolves potential issues associated with the original divide-and-conquer method and the regular hierarchical Gaussian process regression.