Estimating a posteriori probability with P-type nodes

P-type nodes are capable of computing the exact a posteriori probability for the multiclass Gaussian problem. A theory that extends to problems where some classes are given by a sum of multiple Gaussian kernels is presented. The corresponding weight solution can actually be achieved through learning since this weight solution is a minima of the mean squared error criterion function. A special type of problem, called the 1/ΣM problem, which demonstrates the capabilities of P-type nodes is presented. The authors show that the P-type node can solve a number of interesting problems, including the I-4i -16I problem, the XOR problem, a multimodal non-Gaussian problem, and a one-class classifier problem