GPU-Accelerated Hierarchical Bayesian Inference with Application to Modeling Cosmic Populations: CUDAHM

TL;DR

CUDAHM is a GPU-accelerated framework enabling large-scale hierarchical Bayesian inference for demographic modeling, significantly speeding up computations for massive datasets in astronomy.

Contribution

It introduces a novel GPU-based computational framework for hierarchical Bayesian inference, leveraging conditional independence and parallel processing to handle large datasets efficiently.

Findings

Accurate density deconvolution for 300,000 objects in ~1 hour

Supports complex demographic models with uncertainties

Utilizes GPU parallelism for scalable Bayesian inference

Abstract

We describe a computational framework for hierarchical Bayesian inference with simple (typically single-plate) parametric graphical models that uses graphics processing units (GPUs) to accelerate computations, enabling deployment on very large datasets. Its C++ implementation, CUDAHM (CUDA for Hierarchical Models) exploits conditional independence between instances of a plate, facilitating massively parallel exploration of the replication parameter space using the single instruction, multiple data architecture of GPUs. It provides support for constructing Metropolis-within-Gibbs samplers that iterate between GPU-accelerated robust adaptive Metropolis sampling of plate-level parameters conditional on upper-level parameters, and Metropolis-Hastings sampling of upper-level parameters on the host processor conditional on the GPU results. CUDAHM is motivated by demographic problems in astronomy, where density estimation and linear and nonlinear regression problems must be addressed for populations of thousands to millions of objects whose features are measured with possibly complex uncertainties. We describe a thinned latent point process framework for modeling such demographic data. We demonstrate accurate GPU-accelerated parametric conditional density deconvolution for simulated populations of up to 300,000 objects in ~1 hour using a single NVIDIA Tesla K40c GPU. Supplementary material provides details about the CUDAHM API and the demonstration problem.