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 Liklihood Estimation (PLE) represents a specially suitable method for the estimation of parameters in the model. We propose a new general supervised neural network algorithm, Joint Network and Data Density Estimation (XWDE), that employs PLE to approximate conditional probability density finctions for multi-class classification problems. The logistic regression analysis is generalized to multiple class problems with sofhnm 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 m to the model of data, are imposed resulting in both a jlaible network architecture and distribution modeling. We consider application of JNDDE to channel equalization andpresent simulation results.