# Learning Topic Models: Identifiability and Finite-Sample Analysis

arXiv: https://arxiv.org/abs/2110.04232 · HTML: https://mlsanity.com/paper/2110.04232/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 8 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Probabilistic Latent Semantic Analysis](https://mlsanity.com/paper/1301.6705/) (2013)
- [State Aggregation Learning from Markov Transition Data](https://mlsanity.com/paper/1811.02619/) (2018)
- [Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm](https://mlsanity.com/paper/1611.05010/) (2016)
- [Non-negative Matrix Factorization via Archetypal Analysis](https://mlsanity.com/paper/1705.02994/) (2017)
- [Poisson Random Fields for Dynamic Feature Models](https://mlsanity.com/paper/1611.07460/) (2016)
- [A provable SVD-based algorithm for learning topics in dominant admixture corpus](https://mlsanity.com/paper/1410.6991/) (2014)
- [Intersecting Faces: Non-negative Matrix Factorization With New Guarantees](https://mlsanity.com/paper/1507.02189/) (2015)
- [Sparse Partially Collapsed MCMC for Parallel Inference in Topic Models](https://mlsanity.com/paper/1506.03784/) (2015)
- [P'olya Urn Latent Dirichlet Allocation: a doubly sparse massively parallel sampler](https://mlsanity.com/paper/1704.03581/) (2017)
- [Convergence Rates of Latent Topic Models Under Relaxed Identifiability Conditions](https://mlsanity.com/paper/1710.11070/) (2017)
- [Minimum Volume Topic Modeling](https://mlsanity.com/paper/1904.02064/) (2019)
- [Geometric Dirichlet Means algorithm for topic inference](https://mlsanity.com/paper/1610.09034/) (2016)

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

- [Unsupervised Learning under Latent Label Shift](https://mlsanity.com/paper/2207.13179/) (2022)
- [Deep Discrete Encoders: Identifiable Deep Generative Models for Rich Data with Discrete Latent Layers](https://mlsanity.com/paper/2501.01414/) (2025)

## Abstract (arXiv)

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.