# Stochastic Variational Inference for Hidden Markov Models

arXiv: https://arxiv.org/abs/1411.1670 · HTML: https://mlsanity.com/paper/1411.1670/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2014.

## Built on by (most cited first, 12 of 12)

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- [Discovering group dynamics in coordinated time series via hierarchical recurrent switching-state models](https://mlsanity.com/paper/2401.14973/) (2024)
- [A New Algorithm for Hidden Markov Models Learning Problem](https://mlsanity.com/paper/2102.07112/) (2021)
- [Scalable nonparametric Bayesian learning for heterogeneous and dynamic velocity fields](https://mlsanity.com/paper/2102.07695/) (2021)
- [Time Series Clustering with General State Space Models via Stochastic Variational Inference](https://mlsanity.com/paper/2407.00429/) (2024)
- [Fast Gibbs Sampling on Bayesian Hidden Markov Model with Missing Observations](https://mlsanity.com/paper/2601.01442/) (2026)
- [Anchored Variational Inference for Personalized Sequential Latent-State Models](https://mlsanity.com/paper/2604.23454/) (2026)
- [Dynestyx: A Probabilistic Programming Library for Dynamical Systems](https://mlsanity.com/paper/2606.16985/) (2026)

## Abstract (arXiv)

Variational inference algorithms have proven successful for Bayesian analysis in large data settings, with recent advances using stochastic variational inference (SVI). However, such methods have largely been studied in independent or exchangeable data settings. We develop an SVI algorithm to learn the parameters of hidden Markov models (HMMs) in a time-dependent data setting. The challenge in applying stochastic optimization in this setting arises from dependencies in the chain, which must be broken to consider minibatches of observations. We propose an algorithm that harnesses the memory decay of the chain to adaptively bound errors arising from edge effects. We demonstrate the effectiveness of our algorithm on synthetic experiments and a large genomics dataset where a batch algorithm is computationally infeasible.