Radon–Sobolev Variational Auto-Encoders

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