How does Naïve Bayes relate to log-linear models and exponential discriminative forms?

In log space, Naïve Bayes becomes a linear model over feature counts, closely related to log-linear models like logistic regression.

Taking log of NB posterior yields log P(C) + Σ log P(Xi|C). This is a linear combination of feature functions, placing NB in the family of exponential/log-linear models. Unlike logistic regression, NB models joint distribution P(X, C), whereas log-linear models directly optimize conditional P(C|X).