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The combination of the re-parameterization trick with the use of variationalauto-encoders has caused a sensation in Bayesian deep learning, allowing thetraining of realistic generative models of images and has considerablyincreased our ability to use scalable latent variable models. There-parameterization trick is necessary for models in which no analyticalvariational bound is available and allows noisy gradients to be computed forarbitrary models. However, for certain standard output layers of a neuralnetwork, analytical bounds are available and the variational auto-encoder maybe used both without the re-parameterization trick or the need for any MonteCarlo approximation. In this work, we show that using Jaakola and Jordan bound,we can produce a binary classification layer that allows a Bayesian outputlayer to be trained, using the standard stochastic gradient descent algorithm.We further demonstrate that a latent variable model utilizing the Bouchardbound for multi-class classification allows for fast training of a fullyprobabilistic latent factor model, even when the number of classes is verylarge.

Reconsidering Analytical Variational Bounds for Output Layers of Deep Networks