GPflowSampling

Companion code for Efficiently Sampling Functions from Gaussian Process Posteriors and Pathwise Conditioning of Gaussian processes.

Overview

Software provided here revolves around Matheron's update rule

<a href="https://www.codecogs.com/eqnedit.php?latex=\large&space;(f&space;\mid&space;\mathbf{y})(\cdot)&space;=&space;f(\cdot)&space;&plus;&space;k(\cdot,&space;\mathbf{X})\mathbf{K}^{-1}\big(\mathbf{y}&space;-&space;f(\mathbf{X})\big)," target="_blank"><img src="https://latex.codecogs.com/svg.latex?\large&space;(f&space;\mid&space;\mathbf{y})(\cdot)&space;=&space;f(\cdot)&space;&plus;&space;k(\cdot,&space;\mathbf{X})\mathbf{K}^{-1}\big(\mathbf{y}&space;-&space;f(\mathbf{X})\big)," title="matherons_update_rule" /></a>

which allows us to represent a GP posterior as the sum of a prior random function and a data-driven update term. Thinking about conditioning at the level of random function (rather than marginal distributions) enables us to accurately sample GP posteriors in linear time.

Please see examples for tutorials and (hopefully) illustrative use cases.

Installation

git clone git@github.com:j-wilson/GPflowSampling.git
cd GPflowSampling
pip install -e .

To install the dependencies needed to run examples, use pip install -e .[examples].

Citing Us

If our work helps you in a way that you feel warrants reference, please cite the following paper:

@inproceedings{wilson2020efficiently,
    title={Efficiently sampling functions from Gaussian process posteriors},
    author={James T. Wilson
            and Viacheslav Borovitskiy
            and Alexander Terenin
            and Peter Mostowsky
            and Marc Peter Deisenroth},
    booktitle={International Conference on Machine Learning},
    year={2020},
    url={https://arxiv.org/abs/2002.09309}
}