# Identification of Gaussian Process State Space Models

arXiv: https://arxiv.org/abs/1705.10888 · HTML: https://mlsanity.com/paper/1705.10888/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2017.

## Built on by (most cited first, 30 of 31)

- [Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2102.00397/) (2021)
- [Variational multiple shooting for Bayesian ODEs with Gaussian processes](https://mlsanity.com/paper/2106.10905/) (2021)
- [SSDNet: State Space Decomposition Neural Network for Time Series Forecasting](https://mlsanity.com/paper/2112.10251/) (2021)
- [On Uncertainty in Deep State Space Models for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2210.09256/) (2022)
- [Safe Chance Constrained Reinforcement Learning for Batch Process Control](https://mlsanity.com/paper/2104.11706/) (2021)
- [Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems](https://mlsanity.com/paper/2408.03330/) (2024)
- [VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification](https://mlsanity.com/paper/2405.20905/) (2024)
- [KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertainty](https://mlsanity.com/paper/2406.15131/) (2024)
- [Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs](https://mlsanity.com/paper/2205.12550/) (2022)
- [Free-Form Variational Inference for Gaussian Process State-Space Models](https://mlsanity.com/paper/2302.09921/) (2023)
- [Output-Dependent Gaussian Process State-Space Model](https://mlsanity.com/paper/2212.07608/) (2022)
- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [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)
- [On the Stochastic Stability of Deep Markov Models](https://mlsanity.com/paper/2111.04601/) (2021)
- [Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models](https://mlsanity.com/paper/2309.01074/) (2023)
- [Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models](https://mlsanity.com/paper/2309.06655/) (2023)
- [Active Learning in Gaussian Process State Space Model](https://mlsanity.com/paper/2108.00819/) (2021)
- [The Bayesian Context Trees State Space Model for time series modelling and forecasting](https://mlsanity.com/paper/2308.00913/) (2023)
- [Multi-Response Heteroscedastic Gaussian Process Models and Their Inference](https://mlsanity.com/paper/2308.15370/) (2023)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning](https://mlsanity.com/paper/2205.15703/) (2022)
- [Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models](https://mlsanity.com/paper/2208.06528/) (2022)
- [Variational Inference for Model-Free and Model-Based Reinforcement Learning](https://mlsanity.com/paper/2209.01693/) (2022)
- [Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes](https://mlsanity.com/paper/2405.10581/) (2024)
- [Traversing Time with Multi-Resolution Gaussian Process State-Space Models](https://mlsanity.com/paper/2112.03230/) (2021)
- [Time Series Prediction by Multi-task GPR with Spatiotemporal Information Transformation](https://mlsanity.com/paper/2204.12085/) (2022)
- [Online Algorithm for Node Feature Forecasting in Temporal Graphs](https://mlsanity.com/paper/2401.16800/) (2024)
- [Recursive Gaussian Process State Space Model](https://mlsanity.com/paper/2411.14679/) (2024)

## Abstract (arXiv)

The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in GPSSMs has not been satisfactorily addressed yet: system identification, i.e., learning the model. To address this challenge, we impose a structured Gaussian variational posterior distribution over the latent states, which is parameterised by a recognition model in the form of a bi-directional recurrent neural network. Inference with this structure allows us to recover a posterior smoothed over sequences of data. We provide a practical algorithm for efficiently computing a lower bound on the marginal likelihood using the reparameterisation trick. This further allows for the use of arbitrary kernels within the GPSSM. We demonstrate that the learnt GPSSM can efficiently generate plausible future trajectories of the identified system after only observing a small number of episodes from the true system.