Radon Sobolev Variational Autoencoders

# Radon Sobolev Variational Auto-Encoders

**arXiv ID:** 1911.13135
**Authors:** Gabriel Turinici
**Published:** 2019-11-29T15:02:28Z
**Abstract:**
The quality of generative models (such as Generative adversarial networks and Variational Auto-Encoders) depends heavily on the choice of a good probability distance. However some popular metrics like the Wasserstein or the Sliced Wasserstein distances, the Jensen-Shannon divergence, the Kullback-Leibler divergence, lack convenient properties such as (geodesic) convexity, fast evaluation and so on. To address these shortcomings, we introduce a class of distances that have built-in convexity. We investigate the relationship with some known paradigms (sliced distances - a synonym for Radon distances -, reproducing kernel Hilbert spaces, energy distances). The distances are shown to possess fast implementations and are included in an adapted Variational Auto-Encoder termed Radon Sobolev Variational Auto-Encoder (RS-VAE) which produces high quality results on standard generative datasets.
  Keywords: Variational Auto-Encoder; Generative model; Sobolev spaces; Radon Sobolev Variational Auto-Encoder;

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## References

- [arXiv:1911.13135](http://arxiv.org/abs/1911.13135v3)