1. Hierarchical Relational Models for Document Networks
Jonathan Chang and David Blei
Facebook and Princeton University
The Annals of Applied Statistics, 2010
Presented by Haojun Chen
Images and some text are from the original paper.

2. Introduction
Network data attracted lots of research interests in machine learning and applied statistics.
Previous work focused only for the network structure but ignores the attributes of nodes.
For example, in a citation network of articles, text and abstracts of documents should be used for exploiting the latent structure in the data too.
In this paper, Relational Topic Model (RTM) is developed for network data, which accounts for both links and node attributes.

3. Data Example for RTM

4. Graphical Model for RTM

5. Generative Process for RTM

6. Link Probability Function
Four Link Probability Function:
CDF of Normal distribution
: Hadamard product

7. Model Inference, Estimation and Prediction
Variational inference for and
Maximum likelihood estimate for , and
Prediction
Link prediction from words
Word prediction from links

8. Empirical Results Data summary Three experiments
Evaluating the predictive distribution
Automatic link suggestion
Modeling spatial data

9. Evaluating Predictive Distribution (1/2)
Lower is Better

10. Evaluating Predictive Distribution (2/2)

11. Automatic Link Suggestion (1/3)
Citation suggestion
Suggest citation given the abstract
Cora dataset and number of Topic is set to 10
RTM improves precision over LDA+Regression by 80% in the first 20 documents retrieved from the model

12. Automatic Link Suggestion (2/3)

13. Automatic Link Suggestion (3/3)

14. Modeling Spatial Data (1/4)
Local News Data: 51 documents and each document for one state
Number of Topic is set to 5
Word are ranked by the following score:

15. Modeling Spatial Data (2/4)
Each color depicts a single topic. Each state’s color intensity indicates the magnitude of that topic’s component.
Corresponding words associated with each topic are given in the table.
RTM
LDA

16. Modeling Spatial Data (3/4)
RTM
LDA

17. Modeling Spatial Data (4/4)
RTM
LDA

18. Discussion
Relational Topic Model (RTM) is a hierarchical model of networks and per-node attribute data.
It is demonstrated qualitatively and quantitatively that RTM is effective and useful mechanism for analyzing and using network data.