Importantly, this template captures constrained problems via indicator functions.

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.

The goal in statistical learning is to learn hypotheses that generalize well, which is typically formalized by seeking to minimize the expected risk associated with a given loss function.

Belanger & McCallum (2016) and Gygli et al. (2017) have shown that energy In this work, we propose Structured Energy As Loss (SEAL) to take advantage of the expressivity of energy networks without incurring the high inference cost. This raises a question: Can energy networks be used in a way that is as expressive as SPENs, as efficient at inference as feedforward approaches, and also easy to train?

We revisit the problem of learning mixtures of spherical Gaussians.