Here we describe CGS in more details. Eqn. 10 we obtain: null null Expression under the last integral in Eqn. 13 is tractable, thanks to the conjugacy of the Normal-inverse-Wishart prior to the Gaussian likelihood. Finally, posterior predictive density (10) can be written as a mixture of multivariate Student's CIFAR experiments used the standard train/test split. Results for architectures not included in Section 4 are summarized in Fig. C.1. Table C.1: CNN architectures used in experiments (Section 4).

Top-10 rejected images in the MNIST testing set found by two methods.

Neural Information Processing Systems http://nips.cc/

Ensembles of geophysical models improve prediction accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotem-porally varying model weights and bias, while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware predictions without sacrificing interpretability.

We thank the reviewers for the valuable comments and discussions. Please find our clarifications below. IC model [11,43,45], which also learns unknown edge probability parameters. It is interesting that the reviewer brought up the frequentist versus Bayesian view on OIM-LT. LT model and our work is a frequentist approach for the online setting.

Submodular and supermodular functions have found wide applicability in machine learning, capturing notions such as diversity and regularity, respectively. These notions have deep consequences for optimization, and the problem of (approximately) optimizing submodular functions has received much attention. However, beyond optimization, these notions allow specifying expressive probabilistic models that can be used to quantify predictive uncertainty via marginal inference. Prominent, well-studied special cases include Ising models and determinan-tal point processes, but the general class of log-submodular and log-supermodular models is much richer and little studied. In this paper, we investigate the use of Markov chain Monte Carlo sampling to perform approximate inference in general log-submodular and log-supermodular models. In particular, we consider a simple Gibbs sampling procedure, and establish two sufficient conditions, the first guaranteeing polynomial-time, and the second fast ( O ( n log n)) mixing. We also evaluate the efficiency of the Gibbs sampler on three examples of such models, and compare against a recently proposed variational approach.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Previous work has shown that even in the infinite width limit, when NNs become GPs, there is no GP posterior interpretation to a deep ensemble trained with squared error loss.