  Stochastic discriminative EM (sdEM) is an online-EM-type algorithm for
discriminative training of probabilistic generative models belonging to the
exponential family. In this work, we introduce and justify this algorithm as a
stochastic natural gradient descent method, i.e. a method which accounts for
the information geometry in the parameter space of the statistical model. We
show how this learning algorithm can be used to train probabilistic generative
models by minimizing different discriminative loss functions, such as the
negative conditional log-likelihood and the Hinge loss. The resulting models
trained by sdEM are always generative (i.e. they define a joint probability
distribution) and, in consequence, allows to deal with missing data and latent
variables in a principled way either when being learned or when making
predictions. The performance of this method is illustrated by several text
classification problems for which a multinomial naive Bayes and a latent
Dirichlet allocation based classifier are learned using different
discriminative loss functions.
