V ariational methods are extremely popular in the analysis of network data.

In this section, we review some key results on the Wasserstein distance. The formulation in Eq. 6 is obtained by employing We use a single multi layer perceptron (MLP) layer with normalized output as the h function. Calculating the Wasserstein distance with the empirical distribution function is computationally attractive. Metropolis steps to accommodate numerical errors stemming from the integration. F .1 Experimental environment In our experiments, we use 4 workstations, which have the following specifications: GPU: NVIDIA Tesla P100 PCIe 16 GB.

We develop a novel method for carrying out model selection for Bayesian autoen-coders (BAEs) by means of prior hyper-parameter optimization.

Repeated subsampling to reduce cost has the same issues that it does in MCMC.

Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often a sum over likelihood terms or potentials - is expensive to evaluate.

For many applications, variables in the data can be gathered into semantically meaningful groups, where useful insights are at group level. For example, in finance, one may be interested in how a financial situation influences different industries (i.e.

Sampling from a continuous distribution in high dimensions is a fundamental problem in algorithm design. As sampling serves as a key subroutine in a variety of tasks in machine learning [AdFDJ03], statistical methods [RC99], and scientific computing [Liu01], it is an important undertaking to understand the complexity of sampling from families of distributions arising in applications. The more restricted problem of sampling from a particular family of distributions, which we call "well-conditioned distributions," has garnered a substantial amount of recent research effort from the algorithmic learning and statistics communities. This specific family is interesting for a number of reasons. First of all, it is practically relevant: Bayesian methods have found increasing use in machine learning applications [Bar12], and many distributions arising from these methods are well-conditioned, such as multivariate Gaussians, mixture models with small separation, and densities arising from Bayesian logistic regression with a Gaussian prior [DCWY18].

While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs.