# Computationally Efficient Bayesian Learning of Gaussian Process State Space Models

arXiv: https://arxiv.org/abs/1506.02267 · HTML: https://mlsanity.com/paper/1506.02267/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2015.

## Built on by (most cited first, 18 of 18)

- [Structure-preserving Gaussian Process Dynamics](https://mlsanity.com/paper/2102.01606/) (2021)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [Training Bayesian Neural Networks with Sparse Subspace Variational Inference](https://mlsanity.com/paper/2402.11025/) (2024)
- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference](https://mlsanity.com/paper/2312.05910/) (2023)
- [Probabilistic Robust Linear Quadratic Regulators with Gaussian Processes](https://mlsanity.com/paper/2105.07668/) (2021)
- [Learning Nonparametric Volterra Kernels with Gaussian Processes](https://mlsanity.com/paper/2106.05582/) (2021)
- [Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models](https://mlsanity.com/paper/2309.06655/) (2023)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements](https://mlsanity.com/paper/2407.07368/) (2024)
- [Canonical Bayesian Linear System Identification](https://mlsanity.com/paper/2507.11535/) (2025)
- [Bayesian Inference and Learning in Nonlinear Dynamical Systems: A Framework for Incorporating Explicit and Implicit Prior Knowledge](https://mlsanity.com/paper/2508.15345/) (2025)
- [Exploiting Hankel-Toeplitz Structures for Fast Computation of Kernel Precision Matrices](https://mlsanity.com/paper/2408.02346/) (2024)
- [Adaptive Basis Function Selection for Computationally Efficient Predictions](https://mlsanity.com/paper/2408.07480/) (2024)
- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)
- [Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models](https://mlsanity.com/paper/2511.06407/) (2025)
- [A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements](https://mlsanity.com/paper/2606.31137/) (2026)
- [A Factor Graph Approach to Scalable Multi-Output Gaussian Process Regression](https://mlsanity.com/paper/2608.11917/) (2026)

## Abstract (arXiv)

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.