Variational expectation-maximization training for Gaussian networks

This paper introduces variational expectation-maximization (VEM) algorithm for training Gaussian networks. Hyperparameters model distributions of parameters characterizing Gaussian mixture densities. The proposed algorithm employs a hierarchical learning strategy for estimating a set of hyperparameters and the number of Gaussian mixture components. A dual EM algorithm is employed as the initialization stage in the VEM-based learning. In the first stage the EM algorithm is applied on the given data set while the second stage EM is used on distributions of parameters resulted from several runs of the first stage EM. Appropriate maximum log-likelihood estimators are considered for all the parameter distributions involved.