mlsanityData to 14 Oct 2026

Free-Form Variational Inference for Gaussian Process State-Space Models

arXiv 2302.09921 ↗First posted 20 Feb 2023cs.LG stat.MLcited by 7

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Abstract (arXiv)

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 25 of its 51 references that are in the map. First posted on arXiv 20 Feb 2023.

Builds on

25 of 51 references.

References · 25

  1. 2013Gaussian Processes for Big Datacited by 383
  2. 2014Stochastic Gradient Hamiltonian Monte Carlocited by 343
  3. 2015Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)cited by 177
  4. 2017Doubly Stochastic Variational Inference for Deep Gaussian Processescited by 143
  5. 2020Efficiently Sampling Functions from Gaussian Process Posteriorscited by 127
  6. 2016Variational Fourier features for Gaussian processescited by 85
  7. 2016Understanding Probabilistic Sparse Gaussian Process Approximationscited by 68
  8. 2018Probabilistic Recurrent State-Space Modelscited by 64
  9. 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
  10. 2018Learning unknown ODE models with Gaussian processescited by 54
  11. 2015MCMC for Variationally Sparse Gaussian Processescited by 44
  12. 2014Variational Gaussian Process State-Space Modelscited by 43
13 more
  1. 2016Random Feature Expansions for Deep Gaussian Processescited by 32
  2. 2018Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlocited by 32
  3. 2017Identification of Gaussian Process State Space Modelscited by 31
  4. 2019Learning interpretable continuous-time models of latent stochastic dynamical systemscited by 30
  5. 2013Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMCcited by 24
  6. 2021SigGPDE: Scaling Sparse Gaussian Processes on Sequential Datacited by 22
  7. 2019Overcoming Mean-Field Approximations in Recurrent Gaussian Process Modelscited by 21
  8. 2015Computationally Efficient Bayesian Learning of Gaussian Process State Space Modelscited by 18
  9. 2019Implicit Posterior Variational Inference for Deep Gaussian Processescited by 17
  10. 2021Variational multiple shooting for Bayesian ODEs with Gaussian processescited by 15
  11. 2018State Space Gaussian Processes with Non-Gaussian Likelihoodcited by 12
  12. 2020Variational Orthogonal Featurescited by 9
  13. 2018Efficient Inference in Multi-task Cox Process Modelscited by 5

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Cited by year

Citing papers per year: 2023: 2; 2024: 2; 2025: 3.

7 papers.

  1. 2025Koopman-Equivariant Gaussian Processescited by 6
  2. 2023Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inferencecited by 5
  3. 2024FedSI: Federated Subnetwork Inference for Efficient Uncertainty Quantificationcited by 4
  4. 2023Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Modelscited by 3
  5. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  6. 2025Interpretable neural network system identification method for two families of second-order systems based on characteristic curvescited by 2
  7. 2024Recursive Gaussian Process State Space Modelcited by 0