Radial and Directional Posteriors for Bayesian Deep Learning

We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The dependencies learned via the directional density provide better modeling performance compared to the widely-used Gaussian mean-field-type variational family. In addition, the strength of input and output neurons learned via our posterior provides a structured way to compress neural networks. Indeed, experiments show that our variational family improves predictive performance and yields compressed networks simultaneously.

Anisotropy, in Density and in Distance, of the Dispersal of Yellow Rust of Wheat: Experiments in Large Field Plots and Estimation

Long-distance dispersal of spores generally presents anisotropy. This anisotropy can appear in the mean number of spores deposited along a given direction (anisotropy in density) and in the mean distance that a spore travels in a given direction (anisotropy in distance). Specific experiments together with a statistical methodology are proposed to study this effect. The experiments are based on the use of a point source of a traceable inoculum and susceptible trap plots in large resistant field plots. The anisotropy is characterized by two functions: a directional density function and a mean distance function which are related with the anisotropies in density and distance, respectively. A nonparametric approach is developed to estimate these functions and to help in choosing a parametric model. Then, the parametric model is estimated. In two field experiments, migrations up to 175 and 225 m from the source were detected, with ≈25% of the trap plots infected. Whatever the experiment, the two estimated anisotropies presented different shapes (i.e., the number of spores dispersed in a given direction was not proportional to the mean distance travelled by these spores).