  In Bayesian machine learning, the posterior distribution is typically
computationally intractable, hence variational inference is often required. In
this approach, an evidence lower bound on the log likelihood of data is
maximized during training. Variational Autoencoders (VAE) are one important
example where variational inference is utilized. In this tutorial, we derive
the variational lower bound loss function of the standard variational
autoencoder. We do so in the instance of a gaussian latent prior and gaussian
approximate posterior, under which assumptions the Kullback-Leibler term in the
variational lower bound has a closed form solution. We derive essentially
everything we use along the way; everything from Bayes' theorem to the
Kullback-Leibler divergence.
