mlsanityData to 14 Oct 2026

Identification of Gaussian Process State Space Models

arXiv 1705.10888 ↗First posted 30 May 2017stat.MLcited by 31

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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.

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

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Citing papers per year: 2021: 7; 2022: 7; 2023: 8; 2024: 6; 2025: 2; 2026: 1.

31 papers.

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  1. 2021Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecastingcited by 29
  2. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  3. 2021SSDNet: State Space Decomposition Neural Network for Time Series Forecastingcited by 15
  4. 2022On Uncertainty in Deep State Space Models for Model-Based Reinforcement Learningcited by 13
  5. 2021Safe Chance Constrained Reinforcement Learning for Batch Process Controlcited by 11
  6. 2024Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systemscited by 11
  7. 2024VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantificationcited by 9
  8. 2024KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertaintycited by 9
  9. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  10. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  11. 2022Output-Dependent Gaussian Process State-Space Modelcited by 6
  12. 2025Koopman-Equivariant Gaussian Processescited by 6
19 more
  1. 2023Towards Flexibility and Interpretability of Gaussian Process State-Space Modelcited by 5
  2. 2023Sequential Estimation of Gaussian Process-based Deep State-Space Modelscited by 5
  3. 2023Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inferencecited by 5
  4. 2021On the Stochastic Stability of Deep Markov Modelscited by 4
  5. 2023Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Modelscited by 3
  6. 2023Out of Distribution Detection via Domain-Informed Gaussian Process State Space Modelscited by 3
  7. 2021Active Learning in Gaussian Process State Space Modelcited by 2
  8. 2023The Bayesian Context Trees State Space Model for time series modelling and forecastingcited by 2
  9. 2023Multi-Response Heteroscedastic Gaussian Process Models and Their Inferencecited by 2
  10. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  11. 2022Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learningcited by 1
  12. 2022Dynamic Bayesian Learning for Spatiotemporal Mechanistic Modelscited by 1
  13. 2022Variational Inference for Model-Free and Model-Based Reinforcement Learningcited by 1
  14. 2024Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processescited by 1
  15. 2021Traversing Time with Multi-Resolution Gaussian Process State-Space Modelscited by 0
  16. 2022Time Series Prediction by Multi-task GPR with Spatiotemporal Information Transformationcited by 0
  17. 2024Online Algorithm for Node Feature Forecasting in Temporal Graphscited by 0
  18. 2024Recursive Gaussian Process State Space Modelcited by 0
  19. 2026Simulation-Free Learning of GP-SDEs from Irregular Observationscited by 0