  We deal with Bayesian generative and discriminative classifiers. Given a
model distribution $p(x, y)$, with the observation $y$ and the target $x$, one
computes generative classifiers by firstly considering $p(x, y)$ and then using
the Bayes rule to calculate $p(x | y)$. A discriminative model is directly
given by $p(x | y)$, which is used to compute discriminative classifiers.
However, recent works showed that the Bayesian Maximum Posterior classifier
defined from the Naive Bayes (NB) or Hidden Markov Chain (HMC), both generative
models, can also match the discriminative classifier definition. Thus, there
are situations in which dividing classifiers into "generative" and
"discriminative" is somewhat misleading. Indeed, such a distinction is rather
related to the way of computing classifiers, not to the classifiers themselves.
We present a general theoretical result specifying how a generative classifier
induced from a generative model can also be computed in a discriminative way
from the same model. Examples of NB and HMC are found again as particular
cases, and we apply the general result to two original extensions of NB, and
two extensions of HMC, one of which being original. Finally, we shortly
illustrate the interest of the new discriminative way of computing classifiers
in the Natural Language Processing (NLP) framework.
