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Sparse Topic Modeling: Computational Efficiency, Near-Optimal Algorithms, and Statistical Inference

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  • Ruijia Wu
  • Linjun Zhang
  • T. Tony Cai

Abstract

Sparse topic modeling under the probabilistic latent semantic indexing (pLSI) model is studied. Novel and computationally fast algorithms for estimation and inference of both the word-topic matrix and the topic-document matrix are proposed and their theoretical properties are investigated. Both minimax upper and lower bounds are established and the results show that the proposed algorithms are rate-optimal, up to a logarithmic factor. Moreover, a refitting algorithm is proposed to establish asymptotic normality and construct valid confidence intervals for the individual entries of the word-topic and topic-document matrices. Simulation studies are carried out to investigate the numerical performance of the proposed algorithms. The results show that the proposed algorithms perform well numerically and are more accurate in a range of simulation settings comparing to the existing literature. In addition, the methods are illustrated through an analysis of the COVID-19 Open Research Dataset (CORD-19).

Suggested Citation

  • Ruijia Wu & Linjun Zhang & T. Tony Cai, 2023. "Sparse Topic Modeling: Computational Efficiency, Near-Optimal Algorithms, and Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1849-1861, July.
    • Handle: RePEc:taf:jnlasa:v:118:y:2023:i:543:p:1849-1861
    DOI: 10.1080/01621459.2021.2018329
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    Cited by:

    1. Laura Battaglia & Timothy Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for Regression with Variables Generated from Unstructured Data," Papers 2402.15585, arXiv.org, revised Mar 2024.

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