The Power Spherical distribution

Fork

This fork was made to create a wheel for pypi (in the context of which the setup was also changed/updated to pyproject.toml and poetry) and to introduce good practices in supply chain security, such as sigstore and slsa.

Overview

This library contains a Pytorch implementation of the Power Spherical distribution, as presented in [1](https://arxiv.org/abs/2006.04437).

Dependencies

• python>=3.9
• pytorch>=2.0: https://pytorch.org

Notice that older version could work but they were not tested.

Optional dependency for examples needed for plotting and numerical checks (again older version could work but they were not tested):

• numpy>=1.18.1: https://numpy.org
• matplotlib>=3.1.1: https://matplotlib.org
• quadpy>=0.14.11: https://pypi.org/project/quadpy (a paid license is needed)

Installation

To install, run

pip install power-spherical

Structure

• distributions: Pytorch implementation of the Power Spherical and hyperspherical Uniform distributions. Both inherit from torch.distributions.Distribution.
• examples: Example code for using the library within a PyTorch project.

Usage

Please have a look into the examples. We adapted our implementation to follow the structure of the Pytorch probability distributions.

Here a minimal example that demonstrate differentiable sampling:

import torch
from power_spherical import PowerSpherical
p = PowerSpherical(
      loc=torch.tensor([0., 1.], requires_grad=True),
      scale=torch.tensor(4., requires_grad=True),
    )
p.rsample()

tensor([-0.3820,  0.9242], grad_fn=<SubBackward0>)

and computing KL divergence with the uniform distribution:

from power_spherical import HypersphericalUniform
q = HypersphericalUniform(dim=2)
torch.distributions.kl_divergence(p, q)

tensor(1.2486, grad_fn=<AddBackward0>)

Examples of 2D and 3D plots are show in examples and will generate something similar to these figures below.

Please cite [1] in your work when using this library in your experiments.

Feedback

For questions and comments, feel free to contact Nicola De Cao. For questions according to the package / setup / fork, feel free to contact Andreas Fehlner

License

MIT

Citation

[1] De Cao, N., Aziz, W. (2020). 
The Power Spherical distrbution.
In Proceedings of the 37th International 
Conference on Machine Learning, INNF+.

BibTeX format:

@article{decao2020power,
  title={The Power Spherical distribution},
  author={
    De Cao, Nicola and
    Aziz, Wilker},
  journal={Proceedings of the 37th International Conference on Machine Learning, INNF+},
  year={2020}
}