Learning Topic Models: Identifiability and Finite-Sample Analysis

• URL: http://arxiv.org/abs/2110.04232v1
• Date: Fri, 8 Oct 2021 16:35:42 GMT
• Title: Learning Topic Models: Identifiability and Finite-Sample Analysis
• Authors: Yinyin Chen, Shishuang He, Yun Yang and Feng Liang
• Abstract summary: We propose a maximum likelihood estimator (MLE) of latent topics based on a specific integrated likelihood. We conclude with empirical studies on both simulated and real datasets.
• Score: 6.181048261489101
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topic models provide a useful text-mining tool for learning, extracting and discovering latent structures in large text corpora. Although a plethora of methods have been proposed for topic modeling, a formal theoretical investigation on the statistical identifiability and accuracy of latent topic estimation is lacking in the literature. In this paper, we propose a maximum likelihood estimator (MLE) of latent topics based on a specific integrated likelihood, which is naturally connected to the concept of volume minimization in computational geometry. Theoretically, we introduce a new set of geometric conditions for topic model identifiability, which are weaker than conventional separability conditions relying on the existence of anchor words or pure topic documents. We conduct finite-sample error analysis for the proposed estimator and discuss the connection of our results with existing ones. We conclude with empirical studies on both simulated and real datasets.

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