# Convergence Rates of Latent Topic Models Under Relaxed Identifiability Conditions

arXiv: https://arxiv.org/abs/1710.11070 · HTML: https://mlsanity.com/paper/1710.11070/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

## Built on by (most cited first, 2 of 2)

- [Learning Topic Models: Identifiability and Finite-Sample Analysis](https://mlsanity.com/paper/2110.04232/) (2021)
- [Parameter Estimation in DAGs from Incomplete Data via Optimal Transport](https://mlsanity.com/paper/2305.15927/) (2023)

## Abstract (arXiv)

In this paper we study the frequentist convergence rate for the Latent Dirichlet Allocation (Blei et al., 2003) topic models. We show that the maximum likelihood estimator converges to one of the finitely many equivalent parameters in Wasserstein's distance metric at a rate of n-1/4 without assuming separability or non-degeneracy of the underlying topics and/or the existence of more than three words per document, thus generalizing the previous works of Anandkumar et al. (2012, 2014) from an information-theoretical perspective. We also show that the n-1/4 convergence rate is optimal in the worst case.