The spectacular success ofdeep generativemodels calls forquantitativetools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability to measure the quality-diversity trade-off inherent to deep generative modeling. We establish non-asymptotic bounds on the sample complexity of divergence frontiers.

In this appendix we prove Proposition 1 from Section 4. Proposition 1. We next derive two lemmas that will be used in the proofs of our theorems. Hence we select the most under-sampled action if we take!1 in Algorithm 1. Lemma 2. Let s be a state that we visit m times. The proof follows from Lemma 1. The proof is by induction.

On-policy algorithms learn about a particular target policy using data collected by behaving according to the target policy.

In this paper, we aim at bridging this gap and derive various theoretical properties of sliced probability divergences.

In this section, we provide the proofs of the propositions stated in the main text. However, if an'inconsistent' decoder-encoder pair would be used, an encoder with a perturbed mean In the PCA case, the invariant subspace is explicitly known thanks to the linearity. "autoencoding" requires that realizations generated by the decoder are approximately invariant when The algorithm is shown in Algorithm 1. While SE introduced an'external selection mechanism' to generate adversarial examples, the analysis in this appendix shows that the approach could be viewed as a robust Bayesian We can employ a robust Bayesian approach to define a'pessimistic' bound in the sense of selecting With the given tighter bound the algorithm for SE is shown in Algorithm 2. From Equation 18 we This algorithm can be used for post training an already trained V AE. Figure 6 shows the graphical The algorithm is shown in Algorithm 4. We approximate the required expectations by their Monte C.5 SE-A V AE Figure 7 shows the graphical model describing A V AE-SS model. The algorithm is shown in Algorithm 3. We approximate the required expectations by their Monte In this example Section 3.1, we will assume that both the observations Convolutional architectures are stabilized using BatchNorm between each convolutional layer.

The spectacular success of deep generative models calls for quantitative tools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability to measure the quality-diversity trade-off inherent to deep generative modeling.

The spectacular success of deep generative models calls for quantitative tools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability to measure the quality-diversity trade-off inherent to deep generative modeling.

Summary of main contribution (in my view): It is easy to obtain a Monte Carlo estimate of the partition function - while such an estimate is unbiased, the log of the estimate is an underestimate of log-partition function. This means that an estimate for the log-likelihood constructed using this estimate *overestimates* the log-likelihood, which causes many issues in practice because it is not good to think the model is doing better than it actually is. Prior work (notably, RAISE [a]) has developed a way of overestimating the log-partition function and therefore underestimating the log-likelihood. But to my knowledge, there does not exist a way of estimating the log-partition function and the log-likelihood in an unbiased fashion. It works by applying a simple transformation, namely the Fenchel conjugate of -log(t).