A Spectral Algorithm for Latent Dirichlet Allocation

author: Daniel Hsu, Microsoft Research New England, Microsoft Research
published: Jan. 14, 2013,   recorded: December 2012,   views: 298
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Description

Topic modeling is a generalization of clustering that posits that observations (words in a document) are generated by \emph{multiple} latent factors (topics), as opposed to just one. This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic-word distributions when only words are observed, and the topics are hidden. This work provides a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of topic models, including Latent Dirichlet Allocation (LDA). For LDA, the procedure correctly recovers both the topic-word distributions and the parameters of the Dirichlet prior over the topic mixtures, using only trigram statistics (\emph{i.e.}, third order moments, which may be estimated with documents containing just three words). The method, called Excess Correlation Analysis, is based on a spectral decomposition of low-order moments via two singular value decompositions (SVDs). Moreover, the algorithm is scalable, since the SVDs are carried out only on k×k matrices, where k is the number of latent factors (topics) and is typically much smaller than the dimension of the observation (word) space.

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