## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 11, Number 4 (2017), 2298-2331.

### Modeling node incentives in directed networks

#### Abstract

Twitter is a popular medium for individuals to gather information and express opinions on topics of interest to them. By understanding who is interested in what topics, we can gauge the public mood, especially during periods of polarization such as elections. However, while the total volume of tweets may be huge, many people tweet rarely, and tweets are short and often noisy. Hence, directly inferring topics from tweets is both complicated and difficult to scale. Instead, the network structure of Twitter (who tweets at whom, who follows whom) can telegraph the interests of Twitter users. We propose the Producer-Consumer Model (PCM) to link latent topical interests of individuals to the directed structure of the network. A key component of PCM is the modeling of incentives of Twitter users. In particular, for a user to attract more followers and become popular, she must strive to be perceived as an expert on some topic. We use this to reduce the parameter space of PCM, greatly increasing its scalability. We apply PCM to track the evolution of Twitter topics during the Italian Elections of $2013$, and also to interpret those topics using hashtags. A secondary application of PCM to a citation network of machine learning papers is also shown. Extensive simulations and experiments with large real-world datasets demonstrate the accuracy and scalability of PCM.

#### Article information

**Source**

Ann. Appl. Stat., Volume 11, Number 4 (2017), 2298-2331.

**Dates**

Received: May 2016

Revised: May 2017

First available in Project Euclid: 28 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1514430287

**Digital Object Identifier**

doi:10.1214/17-AOAS1079

**Mathematical Reviews number (MathSciNet)**

MR3743298

**Zentralblatt MATH identifier**

1383.62331

**Keywords**

Citation networks social networks stochastic blockmodel

#### Citation

Chakrabarti, Deepayan. Modeling node incentives in directed networks. Ann. Appl. Stat. 11 (2017), no. 4, 2298--2331. doi:10.1214/17-AOAS1079. https://projecteuclid.org/euclid.aoas/1514430287

#### Supplemental materials

- Supplement A: Proofs. We provide the proofs for all propositions and theorems.Digital Object Identifier: doi:10.1214/17-AOAS1079SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.