https://github.com/alisiahkoohi/kl-expansion

Karhunen-Loève expansion for approximation in functions spaces
https://github.com/alisiahkoohi/kl-expansion

eigenfunctions karhunen-loeve stochastic-processes

Last synced: 5 days ago
JSON representation

Karhunen-Loève expansion for approximation in functions spaces

• Host: GitHub
• URL: https://github.com/alisiahkoohi/kl-expansion
• Owner: alisiahkoohi
• License: mit
• Created: 2023-01-30T19:02:31.000Z (almost 2 years ago)
• Default Branch: main
• Last Pushed: 2023-02-16T20:58:44.000Z (almost 2 years ago)
• Last Synced: 2024-10-30T06:05:39.651Z (about 2 months ago)
• Topics: eigenfunctions, karhunen-loeve, stochastic-processes
• Language: Python
• Homepage:
• Size: 625 KB
• Stars: 3
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

        
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:

```bibtex

@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}

}

```

![](plots/toy_example/eigenfunctions.png)

![](plots/toy_example/kl_approximation.png)

## Installation

Run the commands below to install the required packages.

```bash

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.

```bash

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

```

## Questions

Please contact [email protected] for questions.

## Author

Ali Siahkoohi and Lorenzo Baldassari