No human celebrating a first birthday is as verbose, knowledgeable, or prone to fabrication as ChatGPT, which is blowing out its first candle as I type these words. Of course, OpenAI's game-changing large language model was precocious at birth, tumbling into civilization's ongoing conversation like an uninvited guest busting into a dinner party and instantly commanding the room. The chatbot astonished everyone who prompted it with fully realized, if not always completely factual, responses to almost any possible query. Suddenly, the world had access to a Magic 8 Ball with a PhD in every discipline. In almost no time, 100 million people became regular users, delighted and terrified to realize that humans had suddenly lost their monopoly on discourse.

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.