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Temporal Parallelization of Bayesian Smoothers

arXiv 1905.13002 ↗First posted 30 May 2019stat.CO cs.DC math.DScited by 33

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Abstract (arXiv)

This paper presents algorithms for temporal parallelization of Bayesian smoothers. We define the elements and the operators to pose these problems as the solutions to all-prefix-sums operations for which efficient parallel scan-algorithms are available. We present the temporal parallelization of the general Bayesian filtering and smoothing equations and specialize them to linear/Gaussian models. The advantage of the proposed algorithms is that they reduce the linear complexity of standard smoothing algorithms with respect to time to logarithmic.

Key facts. Cited by 33 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 May 2019.

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Citing papers per year: 2021: 6; 2022: 3; 2023: 5; 2024: 8; 2025: 5; 2026: 6.

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  1. 2022Simplified State Space Layers for Sequence Modelingcited by 788
  2. 2024Towards Scalable and Stable Parallelization of Nonlinear RNNscited by 38
  3. 2021Spatio-Temporal Variational Gaussian Processescited by 32
  4. 2021Reactive Message Passing for Scalable Bayesian Inferencecited by 16
  5. 2022Markovian Gaussian Process Variational Autoencoderscited by 16
  6. 2024Computation-Aware Kalman Filtering and Smoothingcited by 12
  7. 2023Revisiting Structured Variational Autoencoderscited by 11
  8. 2024Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Seriescited by 10
  9. 2024KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertaintycited by 9
  10. 2025Robust and Conjugate Spatio-Temporal Gaussian Processescited by 9
  11. 2026Kalman Linear Attention: Parallel Bayesian Filtering For Efficient Language Modelling and State Trackingcited by 8
  12. 2021Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processescited by 7
21 more
  1. 2024Physics-Informed Variational State-Space Gaussian Processescited by 7
  2. 2021Temporal Parallelization of Inference in Hidden Markov Modelscited by 5
  3. 2024Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observabilitycited by 5
  4. 2025SING: SDE Inference via Natural Gradientscited by 5
  5. 2024Learning Time-Varying Multi-Region Brain Communications via Scalable Markovian Gaussian Processescited by 4
  6. 2025A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systemscited by 4
  7. 2023Parallel-in-Time Probabilistic Numerical ODE Solverscited by 3
  8. 2021State-space deep Gaussian processes with applicationscited by 2
  9. 2022De-Sequentialized Monte Carlo: a parallel-in-time particle smoothercited by 2
  10. 2023Unbiased Learning of Deep Generative Models with Structured Discrete Representationscited by 2
  11. 2023SynJax: Structured Probability Distributions for JAXcited by 2
  12. 2024Numerically Robust Fixed-Point Smoothing Without State Augmentationcited by 2
  13. 2025Context-Selective State Space Models: Feedback is All You Needcited by 2
  14. 2021Temporal Gaussian Process Regression in Logarithmic Timecited by 1
  15. 2023Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systemscited by 0
  16. 2025The two filter formula reconsidered: Smoothing in partially observed Gauss--Markov models without information parametrizationcited by 0
  17. 2026Integrative neurocybernetic modeling in the era of large-scale neurosciencecited by 0
  18. 2026Efficient Learning of Deep State Space Models via Importance Smoothingcited by 0
  19. 2026Surgical Kinematics from Monocular Video with Learned Articulated Motion Constraintscited by 0
  20. 2026Voltic: Distinguishing Volatility from Stochasticity in Recurrent Memorycited by 0
  21. 2026Scan-Parallel Variational Inference for event-driven Latent Jump Modelscited by 0