Conic Scan-and-Cover algorithms for nonparametric topic modeling

TL;DR

This paper introduces novel conic scan-and-cover algorithms for nonparametric topic modeling that accurately estimate topics without prior knowledge of their number, leveraging geometric properties of the topic simplex.

Contribution

The paper presents a new geometric approach for nonparametric topic modeling, providing algorithms that are both fast and statistically consistent, unlike existing methods requiring the number of topics.

Findings

Algorithms achieve accuracy comparable to Gibbs sampling.

Methods are among the fastest in the state of the art.

Statistical consistency is theoretically established.

Abstract

We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex hull of vertices representing the latent topics. Our algorithms are shown in practice to have accuracy comparable to a Gibbs sampler in terms of topic estimation, which requires the number of topics be given. Moreover, they are one of the fastest among several state of the art parametric techniques. Statistical consistency of our estimator is established under some conditions.