Bayesian Analysis of Dynamic Linear Topic Models

TL;DR

This paper introduces an advanced dynamic topic model that incorporates covariates, polynomial trends, and periodicity, utilizing a novel MCMC inference method with Polya-Gamma augmentation for large text corpora.

Contribution

It extends the Dynamic Topic Model by explicitly modeling document-level proportions with covariates and temporal structures, and develops a fast, parallelizable inference algorithm.

Findings

Sharing information across documents improves estimation accuracy.

Modeling polynomial and periodic trends enhances future topic prevalence predictions.

The proposed inference method is efficient and scalable for large datasets.

Abstract

In dynamic topic modeling, the proportional contribution of a topic to a document depends on the temporal dynamics of that topic's overall prevalence in the corpus. We extend the Dynamic Topic Model of Blei and Lafferty (2006) by explicitly modeling document level topic proportions with covariates and dynamic structure that includes polynomial trends and periodicity. A Markov Chain Monte Carlo (MCMC) algorithm that utilizes Polya-Gamma data augmentation is developed for posterior inference. Conditional independencies in the model and sampling are made explicit, and our MCMC algorithm is parallelized where possible to allow for inference in large corpora. To address computational bottlenecks associated with Polya-Gamma sampling, we appeal to the Central Limit Theorem to develop a Gaussian approximation to the Polya-Gamma random variable. This approximation is fast and reliable for parameter values relevant in the text mining domain. Our model and inference algorithm are validated with multiple simulation examples, and we consider the application of modeling trends in PubMed abstracts. We demonstrate that sharing information across documents is critical for accurately estimating document-specific topic proportions. We also show that explicitly modeling polynomial and periodic behavior improves our ability to predict topic prevalence at future time points.