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Parallel Gaussian process with kernel approximation in CUDA

Davide Carminati

TL;DR

A parallel implementation in CUDA/C++ of the Gaussian process with a decomposed kernel relies on parallelizing the computation of the predictive posterior statistics on a GPU using CUDA and its libraries.

Abstract

This paper introduces a parallel implementation in CUDA/C++ of the Gaussian process with a decomposed kernel. This recent formulation, introduced by Joukov and Kulić (2022), is characterized by an approximated -- but much smaller -- matrix to be inverted compared to plain Gaussian process. However, it exhibits a limitation when dealing with higher-dimensional samples which degrades execution times. The solution presented in this paper relies on parallelizing the computation of the predictive posterior statistics on a GPU using CUDA and its libraries. The CPU code and GPU code are then benchmarked on different CPU-GPU configurations to show the benefits of the parallel implementation on GPU over the CPU.

Parallel Gaussian process with kernel approximation in CUDA

TL;DR

A parallel implementation in CUDA/C++ of the Gaussian process with a decomposed kernel relies on parallelizing the computation of the predictive posterior statistics on a GPU using CUDA and its libraries.

Abstract

This paper introduces a parallel implementation in CUDA/C++ of the Gaussian process with a decomposed kernel. This recent formulation, introduced by Joukov and Kulić (2022), is characterized by an approximated -- but much smaller -- matrix to be inverted compared to plain Gaussian process. However, it exhibits a limitation when dealing with higher-dimensional samples which degrades execution times. The solution presented in this paper relies on parallelizing the computation of the predictive posterior statistics on a GPU using CUDA and its libraries. The CPU code and GPU code are then benchmarked on different CPU-GPU configurations to show the benefits of the parallel implementation on GPU over the CPU.
Paper Structure (9 sections, 18 equations, 1 figure, 1 table)

This paper contains 9 sections, 18 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical background
  3. Gaussian process regression
  4. Gaussian process regression with a decomposed kernel
  5. Kernel decomposition
  6. Implementation details
  7. Results and discussion
  8. Conclusion
  9. Computational details

Figures (1)

  • Figure 1: Execution times when varying the number of dimensions $p$ and eigenvalues $n$