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June 2007 A correlated topic model of Science
David M. Blei, John D. Lafferty
Ann. Appl. Stat. 1(1): 17-35 (June 2007). DOI: 10.1214/07-AOAS114


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.


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David M. Blei. John D. Lafferty. "A correlated topic model of Science." Ann. Appl. Stat. 1 (1) 17 - 35, June 2007.


Published: June 2007
First available in Project Euclid: 29 June 2007

zbMATH: 1129.62122
MathSciNet: MR2393839
Digital Object Identifier: 10.1214/07-AOAS114

Keywords: approximate posterior inference , hierarchical models , text analysis , variational methods

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.1 • No. 1 • June 2007
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