Neural network design has utilized flexible nonlinear processes which can mimic biological systems, but has suffered
from a lack of traceability in the resulting network. Graphical probabilistic models ground network design in
probabilistic reasoning, but the restrictions reduce the expressive capability of each node making network designs
complex. The ability to model coupled random variables using the calculus of nonextensive statistical mechanics
provides a neural node design incorporating nonlinear coupling between input states while maintaining the rigor of
probabilistic reasoning. A generalization of Bayes rule using the coupled product enables a single node to model
correlation between hundreds of random variables. A coupled Markov random field is designed for the inferencing and
classification of UCI’s MLR ‘Multiple Features Data Set’ such that thousands of linear correlation parameters can be
replaced with a single coupling parameter with just a (3%, 4%) reduction in (classification, inference) performance.
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