Gaussian Auto-Encoder

11/12/2018

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by   Jarek Duda, et al.

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Evaluating distance between sample distribution and the wanted one, usually Gaussian, is a difficult task required to train generative Auto-Encoders. After the original Variational Auto-Encoder (VAE) using KL divergence, there was claimed superiority of distances based on Wasserstein metric (WAE, SWAE) and L_2 distance of KDE Gaussian smoothened sample for all 1D projections (CWAE). This article derives formulas for also L_2 distance of KDE Gaussian smoothened sample, but this time directly using multivariate Gaussians, also optimizing position-dependent covariance matrix with mean-field approximation, for application in purely Gaussian Auto-Encoder (GAE).