This library contains a Pytorch implementation of the hyperspherical variational auto-encoder, or S-VAE, as presented in [1](https://arxiv.org/abs/1804.00891). Check also our blogpost (https://nicola-decao.github.io/s-vae).

• Don't use Pytorch? Take a look here for a tensorflow implementation!

• python>=3.6
• pytorch>=0.4.1: https://pytorch.org
• scipy: https://scipy.org
• numpy: https://www.numpy.org

To install, run

$ python setup.py install

• distributions: Pytorch implementation of the von Mises-Fisher and hyperspherical Uniform distributions. Both inherit from torch.distributions.Distribution.
• ops: Low-level operations used for computing the exponentially scaled modified Bessel function of the first kind and its derivative.
• examples: Example code for using the library within a PyTorch project.

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

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

To sample the von Mises-Fisher distribution we follow the rejection sampling procedure as outlined by Ulrich, 1984. This simulation pipeline is visualized below:

Note that as is a scalar, this approach does not suffer from the curse of dimensionality. For the final transformation, , a Householder reflection is utilized.

For questions and comments, feel free to contact Nicola De Cao or Tim Davidson.

MIT

[1] Davidson, T. R., Falorsi, L., De Cao, N., Kipf, T.,
and Tomczak, J. M. (2018). Hyperspherical Variational
Auto-Encoders. 34th Conference on Uncertainty in Artificial Intelligence (UAI-18).

BibTeX format:

@article{s-vae18,
  title={Hyperspherical Variational Auto-Encoders},
  author={Davidson, Tim R. and
          Falorsi, Luca and
          De Cao, Nicola and
          Kipf, Thomas and
          Tomczak, Jakub M.},
  journal={34th Conference on Uncertainty in Artificial Intelligence (UAI-18)},
  year={2018}
}