functional_autoencoders: Autoencoders in Function Space

This is the official code repository accompanying the paper:

Autoencoders in Function Space

Justin Bunker, Mark Girolami, Hefin Lambley, Andrew M. Stuart and T. J. Sullivan (2025). Journal of Machine Learning Research 26(165):1–54.

Full text at JMLR — arXiv:2408.01362.

The functional_autoencoders module contains implementations of

1. Functional Variational Autoencoder (FVAE), an extension of variational autoencoders (VAEs) to functional data; and
2. Functional Autoencoder (FAE), a regularised nonprobabilistic autoencoder for functional data.

Quickstart

If you want to install the functional_autoencoders package (e.g., to use in your own projects and notebooks): clone the repository and install the package using pip with

git clone https://github.com/htlambley/functional_autoencoders
cd functional_autoencoders
pip install .

You can then import the functional_autoencoders package in your own scripts and notebooks. To get started, why not follow one of our quickstart notebooks: head to the getting started notebook (quickstart/0_Geting_Started.ipynb) for an introduction to functional_autoencoders, and a guide on when to use each model. Alternatively, you can go straight to

• an introduction to FVAE (quickstart/1_FVAE.ipynb); or
• an introduction to FAE (quickstart/2_FAE.ipynb)

depending on your interests, where you'll learn how to reproduce some of the results in the paper. You can also learn how to use FVAE and FAE with your own data (quickstart/3_Custom_Datasets.ipynb) and custom encoder/decoder architectures (quickstart/4_Custom_Architectures.ipynb).

Reproducing results in the paper

If you want to reproduce the results from the paper without installing the functional_autoencoders package: clone the repository, install the dependencies, and run the main experimental script with

git clone https://github.com/htlambley/functional_autoencoders
cd functional_autoencoders
pip install -r requirements.txt
python experiments/main_run.py

Citation

You can cite the paper with the following BibTeX/BibLaTeX entry:

@article{BunkerGirolamiLambleyStuartSullivan2025,
    author = {Bunker, Justin and Girolami, Mark and Lambley, Hefin and Stuart, Andrew M. and Sullivan, T. J.},
    title = {Autoencoders in Function Space},
    journal = {Journal of Machine Learning Research},
    pages = {1--54}, 
    volume = {26},
    number = {165},
    year = {2025},
    url = {http://jmlr.org/papers/v26/25-0035.html},
}

Questions, comments, and suggestions for the code repository are welcome through the issue tracker on GitHub or via email to

• Justin Bunker ([email protected]); and
• Hefin Lambley ([email protected]).