Learning Topic Models: Identifiability and Finite-Sample Analysis

TL;DR

This paper introduces a new maximum likelihood estimator for topic models, providing theoretical guarantees on identifiability and finite-sample accuracy under weaker geometric conditions, supported by empirical validation.

Contribution

It proposes a novel MLE based on volume minimization, establishing weaker geometric conditions for identifiability and analyzing finite-sample errors.

Findings

Weaker geometric conditions suffice for topic model identifiability.

Finite-sample error bounds are derived for the proposed estimator.

Empirical results confirm theoretical insights on simulated and real data.

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, lacking in the literature is a formal theoretical investigation of the statistical identifiability and accuracy of latent topic estimation. In this paper, we propose a maximum likelihood estimator (MLE) of latent topics based on a specific integrated likelihood that is naturally connected to the concept, in computational geometry, of volume minimization. Our theory introduces a new set of geometric conditions for topic model identifiability, conditions that are weaker than conventional separability conditions, which typically rely on the existence of pure topic documents or of anchor words. Weaker conditions allow a wider and thus potentially more fruitful investigation. We conduct finite-sample error analysis for the proposed estimator and discuss connections between our results and those of previous investigations. We conclude with empirical studies employing both simulated and real datasets.