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

• 成果类型: Article
• 署名作者: Wu, Ruijia; Zhang, Linjun; Cai, T. Tony
• 署名单位: University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2018329
• 发表日期: 2023
• 页码: 1849-1861
• 关键词: confidence-intervals; least-squares; Consistency

摘要

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).