E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is because robustness requires discarding of information in order to reduce the sensitivity to outliers. The principal of nonlinear statistical coupling, which is an interpretation of the Tsallis entropy generalization, can be used to quantify this trade-off. The coupled-surprisal,, is a generalization of Shannon surprisal or the logarithmic scoring rule, given a forecast p of a true event by an inferencing algorithm. The coupling parameter 1 q N , where q is the Tsallis entropy index, is the degree of nonlinear coupling between statistical states. Positive (negative) values of nonlinear coupling decrease (increase) the surprisal information metric and thereby biases the risk in favor of decisive (robust) algorithms relative to the Shannon surprisal ( 0 N ). We show that translating the average coupled-surprisal to an effective probability is equivalent to using the generalized mean of the true event probabilities as a scoring rule. The metric is used to assess the robustness, accuracy, and decisiveness of a fusion algorithm. We use a two-parameter fusion algorithm to combine input probabilities from N sources. The generalized mean parameter 'alpha' varies the degree of smoothing and raising to a power N E with ȕ between 0 and 1 provides a model of correlation.
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.Comment: Submitted for presentation at the Machine Intelligence and Bio-inspired Computation: Theory and Applications Conference, SPIE Sensing Technology and Applications, Baltimore, MD, May 8, 201
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