ModelSelectionforBayesianAutoencoders: SupplementaryMaterial

In this section, we review some key results on the Wasserstein distance. Wpp Rπ(t,θi),Rρ(t,θi), (4) where the approximation comes from using Monte-Carlo integration by samplingθi uniformly in SD 1 [2]. M,M is the number of points used to approximate the integral. Calculating the Wasserstein distance with the empirical distribution function is computationally attractive. To do that, we first sortxms in an ascending order, such thatxi[m] xi[m+1], where i[m]istheindexofthesortedxms. Hamiltonian Monte Carlo (HMC)[24]isahighly-efficient MarkovChain Monte Carlo (MCMC) method used to generate samples from the posteriorw p(w|y).