How to use TFIDF vectors with multinomial naive bayes?
When predicting the most likely class, the factorial terms are present in the probability calculation for every class, so they can essentially be ignored in the calculation. This leaves word probabilities which are raised to fractional powers, which are easily calculated. See this paper for a more detailed explanation: http://www.cs.waikato.ac.nz/ml/publications/2004/kibriya_et_al_cr.pdf.