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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 cite [1] in your work when using this library in your experiments.
Sampling von Mises-Fisher
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.
[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}
}
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Pytorch implementation of Hyperspherical Variational Auto-Encoders