# Stochastic Gradient MCMC for Nonlinear State Space Models

arXiv: https://arxiv.org/abs/1901.10568 · HTML: https://mlsanity.com/paper/1901.10568/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Traversing Time with Multi-Resolution Gaussian Process State-Space Models](https://mlsanity.com/paper/2112.03230/) (2021)
- [Accurate Large-sample Uncertainty Quantification using Stochastic Gradient Markov Chain Monte Carlo](https://mlsanity.com/paper/2606.00293/) (2026)
- [Dynestyx: A Probabilistic Programming Library for Dynamical Systems](https://mlsanity.com/paper/2606.16985/) (2026)

## Abstract (arXiv)

State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with time, as in the linear case, but particle filters additionally suffer from increasing particle degeneracy with longer series. Stochastic gradient MCMC methods have been developed to scale Bayesian inference for finite-state hidden Markov models and linear SSMs using buffered stochastic gradient estimates to account for temporal dependencies. We extend these stochastic gradient estimators to nonlinear SSMs using particle methods. We present error bounds that account for both buffering error and particle error in the case of nonlinear SSMs that are log-concave in the latent process. We evaluate our proposed particle buffered stochastic gradient using stochastic gradient MCMC for inference on both long sequential synthetic and minute-resolution financial returns data, demonstrating the importance of this class of methods.