mlsanityData to 14 Oct 2026

Sequential Estimation of Gaussian Process-based Deep State-Space Models

arXiv 2301.12528 ↗First posted 29 Jan 2023cs.LGcited by 5

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Abstract (arXiv)

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. In these models, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 19 of its 61 references that are in the map. First posted on arXiv 29 Jan 2023.

Builds on

19 of 61 references.

References · 19

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  3. 2019Deep Factors for Forecastingcited by 86
  4. 2015Distributed Gaussian Processescited by 84
  5. 2018Probabilistic Recurrent State-Space Modelscited by 64
  6. 2013Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networkscited by 47
  7. 2014Variational Gaussian Process State-Space Modelscited by 43
  8. 2016Very Deep Convolutional Networks for End-to-End Speech Recognitioncited by 34
  9. 2016Random Feature Expansions for Deep Gaussian Processescited by 32
  10. 2017Identification of Gaussian Process State Space Modelscited by 31
  11. 2020Deep State Space Models for Nonlinear System Identificationcited by 30
  12. 2017Towards End-to-End Speech Recognition with Deep Convolutional Neural Networkscited by 24
7 more
  1. 2015Computationally Efficient Bayesian Learning of Gaussian Process State Space Modelscited by 18
  2. 2016A flexible state space model for learning nonlinear dynamical systemscited by 18
  3. 2018Deep Learning Object Detection Methods for Ecological Camera Trap Datacited by 16
  4. 2018Weakly-Supervised Deep Learning of Heat Transport via Physics Informed Losscited by 15
  5. 2020Deep State-Space Gaussian Processescited by 9
  6. 2020Latent variable modeling with random featurescited by 8
  7. 2020Prediction with Approximated Gaussian Process Dynamical Modelscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 1.

5 papers.

  1. 2023Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inferencecited by 5
  2. 2024Dynamic Online Ensembles of Basis Expansionscited by 5
  3. 2025Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systemscited by 2
  4. 2024Recursive Gaussian Process State Space Modelcited by 0
  5. 2026Simulation-Free Learning of GP-SDEs from Irregular Observationscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Towards Flexibility and Interpretability of Gaussian Process State-Space Model
  2. 2024Learning state and proposal dynamics in state-space models using differentiable particle filters and neural networks
  3. 2023Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models
  4. 2021Traversing Time with Multi-Resolution Gaussian Process State-Space Models
  5. 2022Output-Dependent Gaussian Process State-Space Model
  6. 2024Deep Learning-based Approaches for State Space Models: A Selective Review
  7. 2026Efficient Learning of Deep State Space Models via Importance Smoothing
  8. 2024Deep Continuous-Time State-Space Models for Marked Event Sequences