  Maximum entropy approach to classification is very well studied in applied
statistics and machine learning and almost all the methods that exists in
literature are discriminative in nature. In this paper, we introduce a maximum
entropy classification method with feature selection for large dimensional data
such as text datasets that is generative in nature. To tackle the curse of
dimensionality of large data sets, we employ conditional independence
assumption (Naive Bayes) and we perform feature selection simultaneously, by
enforcing a `maximum discrimination' between estimated class conditional
densities. For two class problems, in the proposed method, we use Jeffreys
($J$) divergence to discriminate the class conditional densities. To extend our
method to the multi-class case, we propose a completely new approach by
considering a multi-distribution divergence: we replace Jeffreys divergence by
Jensen-Shannon ($JS$) divergence to discriminate conditional densities of
multiple classes. In order to reduce computational complexity, we employ a
modified Jensen-Shannon divergence ($JS_{GM}$), based on AM-GM inequality. We
show that the resulting divergence is a natural generalization of Jeffreys
divergence to a multiple distributions case. As far as the theoretical
justifications are concerned we show that when one intends to select the best
features in a generative maximum entropy approach, maximum discrimination using
$J-$divergence emerges naturally in binary classification. Performance and
comparative study of the proposed algorithms have been demonstrated on large
dimensional text and gene expression datasets that show our methods scale up
very well with large dimensional datasets.
