A Hybrid System for Probability Estimation in Multiclass Problems Combining SVMs and Neural Networks
In this paper, a new algorithm, the Joint Network and Data Density Estimation (XKDDE), is proposed to estimate the 'a posteriori' probabilities of the targets with neural networks in multiple classes problem. It is based on the estimation of conditional dens@ functions for each class with some restrictions or constraints imposed by the classifier structure and the use B a y a rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the Generalized Sofhnm Perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.