# Finite state space non parametric Hidden Markov Models are in general identifiable

arXiv: https://arxiv.org/abs/1306.4657 · HTML: https://mlsanity.com/paper/1306.4657/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2013.

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

- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Tight Bounds on the Hardness of Learning Simple Nonparametric Mixtures](https://mlsanity.com/paper/2203.15150/) (2022)

## Abstract (arXiv)

In this paper, we prove that finite state space non parametric hidden Markov models are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions are linearly independent. We then propose several non parametric likelihood based estimation methods, which we apply to models used in applications. We finally show on examples that the use of non parametric modeling and estimation may improve the classification performances.