The Annals of Applied Statistics

A correlated topic model of Science

David M. Blei and John D. Lafferty

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Abstract

Topic models, such as latent Dirichlet allocation (LDA), can be useful tools for the statistical analysis of document collections and other discrete data. The LDA model assumes that the words of each document arise from a mixture of topics, each of which is a distribution over the vocabulary. A limitation of LDA is the inability to model topic correlation even though, for example, a document about genetics is more likely to also be about disease than X-ray astronomy. This limitation stems from the use of the Dirichlet distribution to model the variability among the topic proportions. In this paper we develop the correlated topic model (CTM), where the topic proportions exhibit correlation via the logistic normal distribution [J. Roy. Statist. Soc. Ser. B 44 (1982) 139–177]. We derive a fast variational inference algorithm for approximate posterior inference in this model, which is complicated by the fact that the logistic normal is not conjugate to the multinomial. We apply the CTM to the articles from Science published from 1990–1999, a data set that comprises 57M words. The CTM gives a better fit of the data than LDA, and we demonstrate its use as an exploratory tool of large document collections.

Article information

Source
Ann. Appl. Stat. Volume 1, Number 1 (2007), 17-35.

Dates
First available in Project Euclid: 29 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1183143727

Digital Object Identifier
doi:10.1214/07-AOAS114

Mathematical Reviews number (MathSciNet)
MR2393839

Zentralblatt MATH identifier
1129.62122

Citation

Blei, David M.; Lafferty, John D. A correlated topic model of Science . Ann. Appl. Stat. 1 (2007), no. 1, 17--35. doi:10.1214/07-AOAS114. http://projecteuclid.org/euclid.aoas/1183143727.


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