fastgps 1.1

Fast Gaussian processes regression in O(n log n)

fastgps: Fast Gaussian Process Regression in Python

Installation

pip install fastgps

Overview

Gaussian process (GP) regression on $n$ data points typically require $\mathcal{O}(n^3)$ computations and $\mathcal{O}(n^2)$ storage. Fast GPs only require $\mathcal{O}(n \log n)$ computations and $\mathcal{O}(n)$ storage by forcing nice structure into the $n \times n$ Gram matrix of pairwise kernel evaluations. Fast GPs require

• Control over the design of experiments, i.e., sampling at fixed locations which we will choose to be quasi-random (low-discrepancy) sequences, and
• Using special kernel forms that are practically performant but generally uncommon, e.g., one cannot use common kernels such as the Squared Exponential, Matern, or Rational Quadratic. We will use (digitally)-shift invariant kernels.

Scope

fastgps currently support two flavors:

1. Pairing rank-1 integration lattices with shift-invariant (SI) kernels creates circulant Gram matrices that are diagonalizable by Fast Fourier Transforms (FFTs). SI kernels are periodic and arbitrarily smooth.
2. Pairing digital sequences (e.g. Sobol' sequences) with digitally-shift-invariant (DSI) kernels creates Gram matrices diagonalizable by Fast Walsh-Hadamard Transforms (FWHTs). DSI kernels are discontinuous, yet versions exist for which the corresponding Reproducing Kernel Hilbert Space (RKHSs) contains arbitrarily smooth functions.

Features

A reference standard GP implementation is available alongside the fast GP implementations. All GP methods support:

• GPU computations as fastgps is built on the PyTorch stack.
• Batching of both outputs (for functions with tensor outputs) and parameters (with flexibly shareable parameters among batched outputs).
• Multi-Task GPs with product kernels and generalized fast multi-task GPs.
• Derivative Information of arbitrarily high order.
• Bayesian Cubature for approximating integrals or expectations.
• Flexible kernel parameterizations from the QMCPy package.
• Efficient variance projections for determining if and where to sample next.

Resources

The fastgps documentation contains a detailed package reference documenting classes including thorough doctests. A number of example notebooks are also rendered into the documentation from fastgps/docs/examples/. We recommend reading Aleksei Sorokin's slides on Fast GPs which he presented at MCM 2025 Chicago.

Citation

If you find the fastgps package helpful in your work, please consider citing the following papers

@phdthesis{sorokin.thesis,
  title               = {Algorithms and scientific software for quasi-{M}onte {C}arlo, fast {G}aussian process regression, and scientific machine learning},
  author              = {Aleksei G. Sorokin},
  year                = {2025},
  school              = {Illinois Institute of Technology},
  journal             = {ArXiv preprint},
  volume              = {abs/2511.21915},
  url                 = {https://arxiv.org/abs/2511.21915},
}

@inproceedings{sorokin.fastgps_probnum25,
  title               = {Fast {G}aussian process regression for high dimensional functions with derivative information},
  author              = {Sorokin, Aleksei G. and Robbe, Pieterjan and Hickernell, Fred J.},
  year                = {2025},
  booktitle           = {Proceedings of the First International Conference on Probabilistic Numerics},
  publisher           = {{PMLR}},
  series              = {Proceedings of Machine Learning Research},
  volume              = {271},
  pages               = {35--49},
  url                 = {https://proceedings.mlr.press/v271/sorokin25a.html},
  editor              = {Kanagawa, Motonobu and Cockayne, Jon and Gessner, Alexandra and Hennig, Philipp},
  pdf                 = {https://raw.githubusercontent.com/mlresearch/v271/main/assets/sorokin25a/sorokin25a.pdf},
}

@article{sorokin.FastBayesianMLQMC,
  title               = {Fast {B}ayesian multilevel quasi-{M}onte {C}arlo},
  author              = {Aleksei G. Sorokin and Pieterjan Robbe and Gianluca  Geraci and Michael S. Eldred and Fred J. Hickernell},
  year                = {2025},
  journal             = {ArXiv preprint},
  volume              = {abs/2510.24604},
  url                 = {https://arxiv.org/abs/2510.24604},
}