Karhunen-Loève expansion

Python implementation of the Karhunen-Loève expansion, with parallelism over the evaluation of the eigenfunctions, for approximating stochastic processes via a set of eigenfunctions. This is useful for separating the space-time components of stochastic processes from their stochastic components. The implementation is based on the following paper:

@inproceedings{
phillips2022spectral,
title={Spectral Diffusion Processes},
author={Angus Phillips and Thomas Seror and Michael John Hutchinson 
    and Valentin De Bortoli and Arnaud Doucet and Emile Mathieu},
booktitle={NeurIPS 2022 Workshop on Score-Based Methods},
year={2022},
url={https://openreview.net/forum?id=bOmLb2i0W_h}
}

Installation

Run the commands below to install the required packages.

git clone https://github.com/alisiahkoohi/kl-expansion
cd kl-expansion/
conda env create -f environment.yml
conda activate klexp
pip install -e .

After the above steps, you can run the example scripts by just activating the environment, i.e., conda activate klexp, the following times.

Usage

To run the example scripts, you can use the following commands.

python scripts/kl-expansion-toy-example.py --x_range [-10,10] --M 20 --num_workers 8

Questions

Please contact alisk@rice.edu for questions.

Author

Ali Siahkoohi and Lorenzo Baldassari