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Spectral Methods for Correlated Topic Models

Arabshahi, Forough and Anandkumar, Animashree (2016) Spectral Methods for Correlated Topic Models. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190401-123319347

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Abstract

In this paper, we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations, by assuming that the hidden topic proportions are drawn from a flexible class of Normalized Infinitely Divisible (NID) distributions. NID distributions are generated through the process of normalizing a family of independent Infinitely Divisible (ID) random variables. The Dirichlet distribution is a special case obtained by normalizing a set of Gamma random variables. We prove that this flexible topic model class can be learned via spectral methods using only moments up to the third order, with (low order) polynomial sample and computational complexity. The proof is based on a key new technique derived here that allows us to diagonalize the moments of the NID distribution through an efficient procedure that requires evaluating only univariate integrals, despite the fact that we are handling high dimensional multivariate moments. In order to assess the performance of our proposed Latent NID topic model, we use two real datasets of articles collected from New York Times and Pubmed. Our experiments yield improved perplexity on both datasets compared with the baseline.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1605.09080arXivDiscussion Paper
Subject Keywords:Latent variable models, spectral methods, tensor decomposition, moment matching, infinitely divisible, Lévy processes
Record Number:CaltechAUTHORS:20190401-123319347
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190401-123319347
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94326
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Apr 2019 22:12
Last Modified:01 Apr 2019 22:12

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