# Learning Hidden Markov Models from Pairwise Co-occurrences with Application to Topic Modeling

arXiv: https://arxiv.org/abs/1802.06894 · HTML: https://mlsanity.com/paper/1802.06894/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2018.

## Built on by (most cited first, 4 of 4)

- [Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm](https://mlsanity.com/paper/2207.00818/) (2022)
- [Generating Hidden Markov Models from Process Models Through Nonnegative Tensor Factorization](https://mlsanity.com/paper/2210.01060/) (2022)
- [Approximating Permutations with Neural Network Components for Travelling Photographer Problem](https://mlsanity.com/paper/2205.00242/) (2022)
- [Identifying Latent Actions and Dynamics from Offline Data via Demonstrator Diversity](https://mlsanity.com/paper/2603.17577/) (2026)

## Abstract (arXiv)

We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are often required for identification. The new algorithm is particularly suitable for cases where the available sample size is large enough to accurately estimate second-order output probabilities, but not higher-order ones. We show that if one is only able to obtain a reliable estimate of the pairwise co-occurrence probabilities of the emissions, it is still possible to uniquely identify the HMM if the emission probability is sufficiently scattered. We apply our method to hidden topic Markov modeling, and demonstrate that we can learn topics with higher quality if documents are modeled as observations of HMMs sharing the same emission (topic) probability, compared to the simple but widely used bag-of-words model.