# On learning parametric-output HMMs

arXiv: https://arxiv.org/abs/1302.6009 · HTML: https://mlsanity.com/paper/1302.6009/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2013.

## Built on by (most cited first, 5 of 5)

- [Learning Hidden Markov Models Using Conditional Samples](https://mlsanity.com/paper/2302.14753/) (2023)
- [Provable Hierarchical Imitation Learning via EM](https://mlsanity.com/paper/2010.03133/) (2020)
- [Model Stealing for Any Low-Rank Language Model](https://mlsanity.com/paper/2411.07536/) (2024)
- [Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm](https://mlsanity.com/paper/2207.00818/) (2022)
- [Representation and De-interleaving of Mixtures of Hidden Markov Processes](https://mlsanity.com/paper/2406.00416/) (2024)

## Abstract (arXiv)

We present a novel approach for learning an HMM whose outputs are distributed according to a parametric family. This is done by em decoupling the learning task into two steps: first estimating the output parameters, and then estimating the hidden states transition probabilities. The first step is accomplished by fitting a mixture model to the output stationary distribution. Given the parameters of this mixture model, the second step is formulated as the solution of an easily solvable convex quadratic program. We provide an error analysis for the estimated transition probabilities and show they are robust to small perturbations in the estimates of the mixture parameters. Finally, we support our analysis with some encouraging empirical results.