Chang and Blei, AOAS2010

Citation

J. Chang and D. Blei. Hierarchical relational models for document networks. Annals of Applied Statistics, 4(1):124–150, 2010

Online version

D.Blei's papers

Motivation

• Network data

 - social networks of friends
 - citation networks of documents
 - hyperlinked networks of web pages

• “Predictive Models”

 - point social network members toward new friends
 - point scientific papers toward relevant citations
 - point web pages toward other related pages

• “Descriptive statistics”

 - uncover the hidden community structure

Methodology

1. For each document $d$:

 (a) Draw topic proportions $\theta _{d}|\alpha \approx Dir(\alpha )$

 (b) For each word $w_{d,n}$:

     i.  Draw assignment $z_{d,n}|\theta _{d}\approx Mult(\theta _{d})$.

     ii. Draw word $w_{d,n}|z_{d,n},\beta _{1:K}\approx Mult(\beta _{z_{d,n}})$.

2. For each pair of documents $d$,$d'$:

 (a) Draw binary link indicator
   
              $y_{d,d'}|z_{d},z_{d'}\approx \psi (.|z_{d},z_{d'},\eta )$

     where $z_{d}=\{z_{d,1},z_{d,2},...,z_{d,n}\}$