Bayesian Probabilistic Neural Network (BPNN)
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The purpose of this chapter is to introduce a different way of implementing Bayes theorem using a distributed, parallel algorithm first introduced by Specht (1990), which he named the probabilistic neural network (PNN). We have discussed in Chap. 6 the difficulties in constructing Bayesian networks using both the data-driven and expert-driven approaches. A significant advantage of the Bayesian PNN (BPNN) is that the node edge architecture is theoretically predetermined by the Parzen (1962)-Cacoullos (1966) theoretical formulation.
It develops the mathematical formulation for the PNN.
It demonstrates that the normal PNN can be configured as an optimal Bayesian classifier (BPNN).
It shows how Parzen’s theorem maps into Cacoullos’s theorem.
It provides an illustrative toy example, showing a BPNN analysis for two classes and nine samples (four benign and five malignant) for a twofold cross-validation analysis.
It shows how to develop the optimal standard or variance sigma value for the Gaussian density function (a significant problem) and discusses PNN training methods.
It provides a BPNN application to the Alzheimer’s speech data.
KeywordsBayesian probabilistic neural network Kernel probability estimation Alternative kernel functions Alzheimer’s speech data
Area under the ROC curve
Bayesian probabilistic neural network
Generalized regression neural network
probability density function
Probabilistic neural network
Receiver operator characteristic
Support vector machine
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