Parallel Gaussian process with kernel approximation in CUDA
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 Kuli\'c (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.
- Stable evaluation of gaussian radial basis function interpolants. SIAM Journal on Scientific Computing 34, A737–A762.
- Gpytorch: Blackbox matrix-matrix gaussian process inference with gpu acceleration. arXiv:1809.11165.
- GPy, since 2012. GPy: A gaussian process framework in python. http://github.com/SheffieldML/GPy.
- Fast approximate multioutput gaussian processes. IEEE Intelligent Systems 37, 56–69. doi:10.1109/MIS.2022.3169036.
- On sparse variational methods and the kullback-leibler divergence between stochastic processes, in: Gretton, A., Robert, C.C. (Eds.), Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR, Cadiz, Spain. pp. 231–239. URL: https://proceedings.mlr.press/v51/matthews16.html.
- Eigengp: Gaussian process models with adaptive eigenfunctions, in: Proceedings of the 24th International Conference on Artificial Intelligence, AAAI Press. p. 3763–3769.
- Gpjax: A gaussian process framework in jax. Journal of Open Source Software 7, 4455. URL: https://doi.org/10.21105/joss.04455, doi:10.21105/joss.04455.
- A unifying view of sparse approximate gaussian process regression. The Journal of Machine Learning Research 6, 1939–1959.
- Sparse gaussian processes using pseudo-inputs. Advances in neural information processing systems 18.
- Mercer’s Theorem on General Domains: On the Interaction between Measures, Kernels, and RKHSs. Constructive Approximation 35, 363–417. URL: https://doi.org/10.1007/s00365-012-9153-3, doi:10.1007/s00365-012-9153-3.
- Variational learning of inducing variables in sparse gaussian processes, in: Artificial intelligence and statistics, PMLR. pp. 567–574.
- A framework for interdomain and multioutput Gaussian processes. arXiv:2003.01115 URL: https://arxiv.org/abs/2003.01115.
- Using the nyström method to speed up kernel machines, in: Proceedings of the 13th International Conference on Neural Information Processing Systems, MIT Press, Cambridge, MA, USA. p. 661–667.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.