Shared kernel models for class conditional density estimation

We present probabilistic models which are suitable for class conditional de nsity estimation and can be regarded as shared kernel models where sharing means that each kernel may contribute to the estimation of the conditional densities of all classes. We first propose a model that constitutes an adap tation of the classical radial basis function (RBF) network (with full shar ing of kernels among classes) where the outputs represent class conditional densities. In the opposite direction is the approach of separate mixtures model where the density of each class is estimated using a separate mixture density (no sharing of kernels among classes). We present a general model that allows for the expression of intermediate cases where the degree of ke rnel sharing can be specified through an extra model parameter. This genera l model encompasses both above mentioned models as special cases. In all pr oposed models the training process is treated as a maximum likelihood probl em and expectation-maximization (EM) algorithms have been derived for adjus ting the model parameters.