Fantasia Impromptu: Multinomial Naive Bayes

12/01/2011

This book from Stanford is really a great material to learn through the bayes model. Should have found that earlier
http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html
Material from of probabilistic inference:
http://www.cs.cmu.edu/~lewicki/cp-s08/Bayesian-inference.pdf

There is an interesting meetup tonight talking about recommendation using topic modeling..Unfortunately I just don't have time to go. Another newly released paper is going to be presented!!! Really want to go.
http://www.cs.princeton.edu/~chongw/papers/WangBlei2011.pdf

different types of multinomial distribution

Multinomial
parameters:	$n > 0$ number of trials (integer) $p_1, \ldots, p_k$ event probabilities ( $Σ p i = 1$ )
support:	$X_i \in \{0,\dots,n\}$ $\Sigma X_i = n\!$
pmf:	$\frac{n!}{x_1!\cdots x_k!} p_1^{x_1} \cdots p_k^{x_k}$
mean:	$E {X i} = n p i$
variance:	$\textstyle{\mathrm{Var}}(X_i) = n p_i (1-p_i)$ $\textstyle {\mathrm{Cov}}(X_i,X_j) = - n p_i p_j~~(i\neq j)$
mgf:	$\biggl( \sum_{i=1}^k p_i e^{t_i} \biggr)^n$
pgf:	$\biggl( \sum_{i=1}^k p_i z_i \biggr)^n\text{ for }(z_1,\ldots,z_k)\in\mathbb{C}^k$

Ten years ago, I was longing for traveling far from home

Ten years after, I am eager for going back home

Fantasia Impromptu