Gaussian interconnection networks have been introduced as a useful alternative to the classical toroidal networks, and in this paper this concept is generalized to higher dimensions. We also explore many important properties of this new topology, including distance distribution and the decomposition of higher dimensional Gaussian networks into edge-disjoint tori and Hamiltonian cycles. In addition, an optimal shortest path routing algorithm and a one-to-all broadcast algorithm for higher dimensional Gaussian networks are given. Simulation results show that the routing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus network of the same node-degree and the same number of nodes.

Dependency networks are a compelling alternative to Bayesian networks for learning joint probability distributions from data and using them to compute probabilities. A dependency network consists of a set of conditional probability distributions, each representing the probability of a single variable given its Markov blanket. Running Gibbs sampling with these conditional distributions produces a joint distribution that can be used to answer queries, but suffers from the traditional slowness of sampling-based inference. In this paper, we observe that the mean field update equation can be applied to dependency networks, even though the conditional probability distributions may be inconsistent with each other. In experiments with learning and inference on 12 datasets, we demonstrate that mean field inference in dependency networks offers similar accuracy to Gibbs sampling but with orders of magnitude improvements in speed. Compared to Bayesian networks learned on the same data, dependency networks offer higher accuracy at greater amounts of evidence. Furthermore, mean field inference is consistently more accurate in dependency networks than in Bayesian networks learned on the same data.