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

For Network data, such as social networks of friends, citation networks of documents or hyperlinked networks of web pages, people want to point social network members toward new friends, scientific papers toward relevant citations or web pages toward other related pages. They also want to uncover the hidden community structure. This paper developed a hierarchical model of both network structure and node attributes, based on Latent Dirichlet Allocation.

Methodology

1. For each document $d$:

 (a) Draw topic proportions $\theta _{d}|\alpha \sim Dir(\alpha )$
 (b) For each word $w_{d,n}$:
     i.  Draw assignment $z_{d,n}|\theta _{d}\sim Mult(\theta _{d})$.
     ii. Draw word $w_{d,n}|z_{d,n},\beta _{1:K}\sim Mult(\beta _{z_{d,n}})$.

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

 (a) Draw binary link indicator   
              $y_{d,d'}|z_{d},z_{d'}\sim \psi (.|z_{d},z_{d'},\eta )$
     where $z_{d}=\{z_{d,1},z_{d,2},...,z_{d,n}\}$

Inference, Estimation and Prediction

Prediction

• Link prediction from words

   $p(y_{d,d'}|w_{d},w_{d'})\approx E_{q}[p(y_{d,d'}|{\bar {z_{d}}},{\bar {z_{d'}}})]$

• Words prediction from link

   $p(w_{d,i}|y_{d})\approx E_{q}[p(w_{d,i}|z_{d,i})]$

Data

• Cora: abstracts + citation link
• WebKB: web pages + hyperlinks
• PNAS: abstracts + intra-PNAS citation
• LocalNews: local news of each state in U.S + geographical adjacency

Results

• Evaluating the predictive distribution

• Automatic link suggestion

• Modeling spatial data

Related papers

Airoldi et al, ML2008 AIROLDI, E., BLEI, D., FIENBERG, S. and XING, E. (2008). Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9 1981–2014.

Blei et al, NIPS2007 BLEI, D. M. and MCAULIFFE, J. D. (2007). Supervised topic models. In Neural Information Processsing Systems. Vancouver.

Dietz et al, ICML2007 DIETZ, L., BICKEL, S. and SCHEFFER, T. (2007). Unsupervised prediction of citation influences. In Proc. ICML. Available at http://portal.acm.org/citation.cfm?id=1273526.

Nallapati et al, ACM2008 NALLAPATI, R., AHMED, A., XING, E. P. and COHEN, W. W. (2008). Joint latent topic models for text and citations. In Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 542–550. ACM Press, New York.