[Paper Review] A Short Note on Gaussian Process Modeling for Large Datasets using Graphics Processing Units

Mark Franey, Pritam Ranjan+1 more|arXiv (Cornell University)|Mar 6, 2012

Gaussian Processes and Bayesian Inference20 references18 citations

TL;DR

This paper demonstrates that Gaussian process (GP) modeling for large datasets can achieve up to 150x speedup by leveraging GPU acceleration via CUDA, reducing computation time from hours to minutes. The authors implement a CPU+GPU heterogeneous system to accelerate matrix inversion and determinant calculations—key bottlenecks in GP likelihood evaluation—showcasing significant performance gains without compromising model accuracy.

ABSTRACT

The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central processing units (CPUs), and thus provide a great deal of promise for computationally intensive statistical applications. Fitting complex statistical models with a large number of parameters and/or for large datasets is often very computationally expensive. In this study, we focus on Gaussian process (GP) models -- statistical models commonly used for emulating expensive computer simulators. We demonstrate that the computational cost of implementing GP models can be significantly reduced by using a CPU+GPU heterogeneous computing system over an analogous implementation on a traditional computing system with no GPU acceleration. Our small study suggests that GP models are fertile ground for further implementation on CPU+GPU systems.

Motivation & Objective

• Address the high computational cost of fitting Gaussian process models on large datasets, particularly due to O(n³) matrix operations.
• Explore the feasibility and performance benefits of using GPU acceleration (via CUDA) for statistical modeling workloads.
• Demonstrate that heterogeneous CPU+GPU systems can drastically reduce runtime for GP model fitting compared to traditional CPU-only implementations.
• Provide a proof-of-concept for GPU acceleration in computationally intensive statistical applications, particularly in computer experiments and emulator fitting.

Proposed method

• Implement Gaussian process regression using the power exponential correlation function with p = 1.95 to reduce near-singularity issues in large n designs.
• Use maximum likelihood estimation (MLE) to fit hyper-parameters, requiring repeated computation of matrix determinant and inverse of the correlation matrix R.
• Accelerate matrix inversion and determinant calculations using NVIDIA’s CUDA toolkit on GPU hardware, leveraging single-precision floating-point parallelism.
• Compare CPU-only and CPU+GPU implementations using identical model specifications and data, with timing measured on a heterogeneous computing platform.
• Employ matrix factorization techniques (e.g., LU, QR) to improve numerical stability and reduce computational overhead during likelihood evaluation.
• Use single-precision arithmetic on GPU to maximize speed, with subsequent double-precision refinement possible for improved accuracy.

Experimental results

Research questions

• RQ1 Can GPU acceleration significantly reduce the computational time required to fit Gaussian process models on large datasets?
• RQ2 How does the performance of a CPU+GPU heterogeneous system compare to a CPU-only system in terms of runtime for GP likelihood evaluation?
• RQ3 What are the practical limits of GPU acceleration in GP modeling, particularly as dataset size increases beyond n = 1000?
• RQ4 To what extent do differences in floating-point precision (single vs. double) affect the accuracy of estimated hyper-parameters in GPU-accelerated GP models?
• RQ5 Can GPU acceleration be effectively combined with existing statistical optimization techniques to further improve scalability in large-scale GP modeling?

Key findings

• For n = 4064, the GPU-accelerated implementation reduced computation time from approximately 45 hours (CPU-only) to 18 minutes (GPU), achieving a speedup of over 150x.
• At n = 1024, the GPU implementation completed the likelihood evaluation in 96.19 seconds, compared to 13,325.86 seconds on the CPU, representing a 138x speedup.
• The CUDA implementation achieved consistent speedups across all tested dataset sizes (64, 256, 1024, 4064), with the largest gains observed at larger n.
• Despite using single-precision arithmetic on the GPU, the estimated hyper-parameters (μ, σ²z, and -2logLθ) were close to those from the CPU-only implementation, indicating acceptable accuracy.
• The study confirms that matrix inversion and determinant computation—O(n³) operations—are the primary bottlenecks in GP modeling and are highly amenable to GPU parallelization.
• The results suggest that GPU acceleration is a viable and highly effective approach for scaling GP models to large datasets, especially in computer experiment and simulator emulation contexts.