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Variational Gaussian Process State-Space Models

arXiv 1406.4905 ↗First posted 18 Jun 2014cs.LG cs.RO cs.SYcited by 43

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Abstract (arXiv)

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo. We also present stochastic variational inference and online learning approaches for fast learning with long time series.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2014.

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Citing papers per year: 2021: 11; 2022: 4; 2023: 13; 2024: 5; 2025: 5; 2026: 5.

43 papers.

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  1. 2021A Framework for Machine Learning of Model Error in Dynamical Systemscited by 37
  2. 2023Deep networks for system identification: a Surveycited by 35
  3. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  4. 2021Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equationcited by 14
  5. 2024Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systemscited by 11
  6. 2021Structure-preserving Gaussian Process Dynamicscited by 9
  7. 2021Inferring the Structure of Ordinary Differential Equationscited by 7
  8. 2023Free-Form Variational Inference for Gaussian Process State-Space Modelscited by 7
  9. 2022Output-Dependent Gaussian Process State-Space Modelcited by 6
  10. 2025Koopman-Equivariant Gaussian Processescited by 6
  11. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 6
  12. 2022Recurrent Neural Networks and Universal Approximation of Bayesian Filterscited by 5
31 more
  1. 2023Sequential Estimation of Gaussian Process-based Deep State-Space Modelscited by 5
  2. 2023Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trainscited by 5
  3. 2023Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inferencecited by 5
  4. 2021Probabilistic Robust Linear Quadratic Regulators with Gaussian Processescited by 4
  5. 2023Towards Flexibility and Interpretability of Gaussian Process State-Space Modelcited by 4
  6. 2023Variational sparse inverse Cholesky approximation for latent Gaussian processes via double Kullback-Leibler minimizationcited by 4
  7. 2023Variational Nonlinear Kalman Filtering with Unknown Process Noise Covariancecited by 3
  8. 2023Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Modelscited by 3
  9. 2023Out of Distribution Detection via Domain-Informed Gaussian Process State Space Modelscited by 3
  10. 2021Keep it Simple: Data-efficient Learning for Controlling Complex Systems with Simple Modelscited by 2
  11. 2021Active Learning in Gaussian Process State Space Modelcited by 2
  12. 2022Conditional Approximate Normalizing Flows for Joint Multi-Step Probabilistic Forecasting with Application to Electricity Demandcited by 2
  13. 2023The Bayesian Context Trees State Space Model for time series modelling and forecastingcited by 2
  14. 2023Multi-Response Heteroscedastic Gaussian Process Models and Their Inferencecited by 2
  15. 2024Hybrid Data-Driven SSM for Interpretable and Label-Free mmWave Channel Predictioncited by 2
  16. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  17. 2021Forecasting COVID-19 Counts At A Single Hospital: A Hierarchical Bayesian Approachcited by 1
  18. 2021Deep Probabilistic Time Series Forecasting using Augmented Recurrent Input for Dynamic Systemscited by 1
  19. 2021Likelihood-Free Inference in State-Space Models with Unknown Dynamicscited by 1
  20. 2022Continual Learning of Multi-modal Dynamics with External Memorycited by 1
  21. 2024Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processescited by 1
  22. 2024Least Squares and Marginal Log-Likelihood Model Predictive Control using Normalizing Flowscited by 1
  23. 2026A Predictive View on Streaming Hidden Markov Modelscited by 1
  24. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  25. 2023A projected nonlinear state-space model for forecasting time series signalscited by 0
  26. 2024Recursive Gaussian Process State Space Modelcited by 0
  27. 2025Bayesian Nonparametric Dynamical Clustering of Time Seriescited by 0
  28. 2025pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurementscited by 0
  29. 2026Dynestyx: A Probabilistic Programming Library for Dynamical Systemscited by 0
  30. 2026PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilationcited by 0
  31. 2026Simulation-Free Learning of GP-SDEs from Irregular Observationscited by 0