mlsanityData to 7 Oct 2026

Sampling-Free Probabilistic Deep State-Space Models

arXiv 2309.08256 ↗First posted 15 Sep 2023cs.LG stat.MLcited by 2

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Abstract (arXiv)

Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM) generalizes this framework to dynamical systems of unknown parametric form, where the transition and emission models are described by neural networks with uncertain weights. In this work, we propose the first deterministic inference algorithm for models of this type. Our framework allows efficient approximations for training and testing. We demonstrate in our experiments that our new method can be employed for a variety of tasks and enjoys a superior balance between predictive performance and computational budget.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 23 of its 48 references that are in the map. First posted on arXiv 15 Sep 2023.

Builds on

23 of 48 references.

References · 23

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
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  12. 2018Probabilistic Recurrent State-Space Modelscited by 64
11 more
  1. 2016Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networkscited by 49
  2. 2020Bayesian Neural Ordinary Differential Equationscited by 44
  3. 2015Black box variational inference for state space modelscited by 31
  4. 2019Overcoming Mean-Field Approximations in Recurrent Gaussian Process Modelscited by 20
  5. 2022Latent Neural ODEs with Sparse Bayesian Multiple Shootingcited by 17
  6. 2020Learning Partially Known Stochastic Dynamics with Empirical PAC Bayescited by 15
  7. 2021Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Modelscited by 14
  8. 2021Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equationcited by 14
  9. 2020Beyond the Mean-Field: Structured Deep Gaussian Processes Improve the Predictive Uncertaintiescited by 5
  10. 2020A Deterministic Approximation to Neural SDEscited by 5
  11. 2023Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systemscited by 5

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Cited by year

Citing papers per year: 2023: 1; 2024: 1.

2 papers.

  1. 2023Exact nonlinear state estimationcited by 4
  2. 2024Motion Forecasting via Model-Based Risk Minimizationcited by 4

Similar, not cited

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  1. 2021Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty
  2. 2024HiPPO-Prophecy: State-Space Models can Provably Learn Dynamical Systems in Context
  3. 2024Deep Learning-based Approaches for State Space Models: A Selective Review
  4. 2026Efficient Learning of Deep State Space Models via Importance Smoothing
  5. 2023Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification
  6. 2026Truncated Neural Likelihood Estimation for Simulation-Based Inference in State-Space Models
  7. 2026Latent Matters: Learning Deep State-Space Models
  8. 2023Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems