Midterm Report Nitin Yandong Ming Yanbo

Team members

Nitin Agarwal

Yandong Liu

Yanbo Xu

Ming Sun

Gibbs Sampling for Collaboration Influence Model

We want $P(Z,X,R|W)$, the posterior distribution of topic Z, (author, collaborator) pair X and which favor of collaboration over influence R given the words W in the corpus:

$P(Z,X,R|W)={\frac {P(Z,X,R,W)}{\sum _{Z,X,R}P(Z,X,R,W)}}$

We begin by calculating $P(W|Z,X,R)$:

$P(W|Z,X,R)=P(W|Z)=\prod _{z=1}^{T}({\frac {\Gamma (\sum _{v=1}^{V}\beta _{v})}{\prod _{v=1}^{V}\Gamma (\beta _{v})}}({\frac {\prod _{v=1}^{V}\Gamma (n_{z}^{w_{v}}+\beta _{v})}{\Gamma (\sum _{v=1}^{V}\beta _{v}+\sum _{v=1}^{V}n_{z}^{w_{v}})}}))$

then,

$P(Z,X,R)=()()$