Maximum a posteriori decision and evaluation of class probabilities by Boltzmann perceptron classifiers

It is shown that neural network architectures may offer a valuable alternative to the Bayesian classifier. With neural networks, the a posteriori probabilities are computed with no a priori assumptions about the probability distribution functions (PDFs) that generate the data. Rather than assuming certain types of PDFs for the input data, the neural classifier uses a general type of input-output mapping which is then designed to optimally comply with a given set of examples called the training set. It is demonstrated that the a posteriori class probabilities can be efficiently computed by a deterministic feedforward network which is called the Boltzmann perceptron classifier (BPC). Maximum a posteriori (MAP) classifiers are also constructed as a special case of the BPC. Structural relationships between the BPC and a conventional multilayer perceptron (MLP) are given, and it is demonstrated that rather intricate boundaries between classes can be formed even with a relatively modest number of network units. Simulation results show that the BPC is comparable in performance to a Bayesian classifier