# Stochastic Gradient MCMC Methods for Hidden Markov Models

arXiv: https://arxiv.org/abs/1706.04632 · HTML: https://mlsanity.com/paper/1706.04632/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2017.

## Built on by (most cited first, 8 of 8)

- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [Structured Stochastic Gradient MCMC](https://mlsanity.com/paper/2107.09028/) (2021)
- [Uncertainty-Aware Deep Neural Representations for Visual Analysis of Vector Field Data](https://mlsanity.com/paper/2407.16119/) (2024)
- [Uncertainty-Informed Volume Visualization using Implicit Neural Representation](https://mlsanity.com/paper/2408.06018/) (2024)
- [Visual Analysis of Prediction Uncertainty in Neural Networks for Deep Image Synthesis](https://mlsanity.com/paper/2406.18545/) (2024)
- [Scalable Monte Carlo for Bayesian Learning](https://mlsanity.com/paper/2407.12751/) (2024)
- [Improving the stability of the covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling](https://mlsanity.com/paper/2512.24515/) (2025)
- [Dynestyx: A Probabilistic Programming Library for Dynamical Systems](https://mlsanity.com/paper/2606.16985/) (2026)

## Abstract (arXiv)

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this setting: The latent discrete states, and needing to break dependencies when considering minibatches. We consider a marginal likelihood representation of the HMM and propose an algorithm that harnesses the inherent memory decay of the process. We demonstrate the effectiveness of our algorithm on synthetic experiments and an ion channel recording data, with runtimes significantly outperforming batch MCMC.