# Provable Algorithms for Inference in Topic Models

arXiv: https://arxiv.org/abs/1605.08491 · HTML: https://mlsanity.com/paper/1605.08491/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2016.

## Built on by (most cited first, 6 of 6)

- [How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding](https://mlsanity.com/paper/2303.04245/) (2023)
- [Planning in Observable POMDPs in Quasipolynomial Time](https://mlsanity.com/paper/2201.04735/) (2022)
- [Understanding The Robustness of Self-supervised Learning Through Topic Modeling](https://mlsanity.com/paper/2203.03539/) (2022)
- [Likelihood estimation of sparse topic distributions in topic models and its applications to Wasserstein document distance calculations](https://mlsanity.com/paper/2107.05766/) (2021)
- [E-LDA: Toward Interpretable LDA Topic Models with Strong Guarantees in Logarithmic Parallel Time](https://mlsanity.com/paper/2506.07747/) (2025)
- [On-the-Fly Rectification for Robust Large-Vocabulary Topic Inference](https://mlsanity.com/paper/2111.06580/) (2021)

## Abstract (arXiv)

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference has proven to be more challenging. Here we take a first step towards provable inference in topic models. We leverage a property of topic models that enables us to construct simple linear estimators for the unknown topic proportions that have small variance, and consequently can work with short documents. Our estimators also correspond to finding an estimate around which the posterior is well-concentrated. We show lower bounds that for shorter documents it can be information theoretically impossible to find the hidden topics. Finally, we give empirical results that demonstrate that our algorithm works on realistic topic models. It yields good solutions on synthetic data and runs in time comparable to a em single iteration of Gibbs sampling.