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The Discrete Infinite Logistic Normal Distribution

Author(s): Paisley, John; Wang, Chong; Blei, David M

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Abstract: We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN generalizes the hierarchical Dirichlet process (HDP) to model correlation structure between the weights of the atoms at the group level. We derive a representation of DILN as a normalized collection of gamma-distributed random variables and study its statistical properties. We derive a variational inference algorithm for approximate posterior inference. We apply DILN to topic modeling of documents and study its empirical performance on four corpora, comparing performance with the HDP and the correlated topic model (CTM). To compute with large-scale data, we develop a stochastic variational inference algorithm for DILN and compare with similar algorithms for HDP and latent Dirichlet allocation (LDA) on a collection of 350,000 articles from Nature.
Publication Date: 2012
Citation: Paisley, John, Chong Wang, and David Blei. "The Discrete Infinite Logistic Normal Distribution." Bayesian Analysis 7, no. 4 (2012): pp. 997-1034. doi:10.1214/12-BA734.
DOI: doi:10.1214/12-BA734
ISSN: 1936-0975
EISSN: 1931-6690
Pages: 997 - 1034
Type of Material: Journal Article
Journal/Proceeding Title: Bayesian Analysis
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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