directional density
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2020 ◽  
Vol 34 (04) ◽  
pp. 5298-5305
Author(s):  
Changyong Oh ◽  
Kamil Adamczewski ◽  
Mijung Park

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.


2007 ◽  
Vol 97 (10) ◽  
pp. 1315-1324 ◽  
Author(s):  
S. Soubeyrand ◽  
J. Enjalbert ◽  
A. Sanchez ◽  
I. Sache

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).


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