Massive parallelization boosts big Bayesian multidimensional scaling

TL;DR

This paper demonstrates how massive parallelization using CPUs and GPUs significantly accelerates Bayesian multidimensional scaling, enabling analysis of large-scale complex data such as viral spread patterns.

Contribution

It introduces a GPU-accelerated implementation of Bayesian MDS, extending its applicability to big data scenarios and providing an open-source library for practical use.

Findings

GPU acceleration achieves over 100-fold speedup in Bayesian MDS computations.

Bayesian MDS applied to influenza data reveals subtype H3N2's effective global spread.

Open-source MassiveMDS library facilitates scalable Bayesian MDS analysis.

Abstract

Big Bayes is the computationally intensive co-application of big data and large, expressive Bayesian models for the analysis of complex phenomena in scientific inference and statistical learning. Standing as an example, Bayesian multidimensional scaling (MDS) can help scientists learn viral trajectories through space-time, but its computational burden prevents its wider use. Crucial MDS model calculations scale quadratically in the number of observations. We partially mitigate this limitation through massive parallelization using multi-core central processing units, instruction-level vectorization and graphics processing units (GPUs). Fitting the MDS model using Hamiltonian Monte Carlo, GPUs can deliver more than 100-fold speedups over serial calculations and thus extend Bayesian MDS to a big data setting. To illustrate, we employ Bayesian MDS to infer the rate at which different seasonal influenza virus subtypes use worldwide air traffic to spread around the globe. We examine 5392 viral sequences and their associated 14 million pairwise distances arising from the number of commercial airline seats per year between viral sampling locations. To adjust for shared evolutionary history of the viruses, we implement a phylogenetic extension to the MDS model and learn that subtype H3N2 spreads most effectively, consistent with its epidemic success relative to other seasonal influenza subtypes. Finally, we provide MassiveMDS, an open-source, stand-alone C++ library and rudimentary R package, and discuss program design and high-level implementation with an emphasis on important aspects of computing architecture that become relevant at scale.