Estimates of constrained multi-class a posteriori probabilities in time series problems with neural networks

In time series problems, where time ordering is a crucial issue, the use of partial likelihood estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a general supervised neural network algorithm, joint network and data density estimation (JNDDE), that employs PLE to approximate conditional probability density functions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with a softmax regression neural network used to model the a posteriori probabilities such that they are approximated by the network outputs. Constraints to the network architecture, as well as to the model of data, are imposed, resulting in both a flexible network architecture and distribution modeling. We consider application of JNDDE to channel equalization and present simulation results