We show that a classifier based on Gaussian mixture models (GMM) can be trained discriminatively to improve accuracy. We describe a training procedure based on the extended Baum-Welch algorithm used in speech recognition. We also compare the accuracy and degree of sparsity of the new discriminative GMM classifier with those of generative GMM classifiers, and of kernel classifiers, such as support vector machines (SVM) and relevance vector machines (RVM).