  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%) percent
reduction in (classification, inference) performance.
