Multiclass logistic regression is also referred to as multinomial regression.
Multinomial Naive Bayes is designed for text classification. It's a lot faster than plain Naive Bayes.
also known as maximum entropy classifiers ?
The symmetric form:
<MATH> \begin{array}{rrrl} Pr(Y = k|X) & = & \frac{\displaystyle e^{\displaystyle B_{0k} + B_{1k} . X_1 + \dots + B_{ik} . X_i }}{\displaystyle \sum^K_{l=1} e^{\displaystyle B_{0l} + B_{1l} . X_1 + \dots + B_{il} . X_i }} \\ \end{array} </MATH>
package glmnet