# Temporal Parallelization of Bayesian Smoothers

@article{Srkk2021TemporalPO, title={Temporal Parallelization of Bayesian Smoothers}, author={Simo S{\"a}rkk{\"a} and {\'A}ngel F. Garc{\'i}a-Fern{\'a}ndez}, journal={IEEE Transactions on Automatic Control}, year={2021}, volume={66}, pages={299-306} }

This article 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…

## 14 Citations

Parallel Iterated Extended and Sigma-Point Kalman Smoothers

- Computer ScienceICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2021

This paper presents a set of parallel formulas that replace the existing sequential ones in order to achieve lower time (span) complexity and demonstrates the efficiency of the proposed methods over their sequential counterparts.

Temporal Parallelization of Inference in Hidden Markov Models

- Computer ScienceIEEE Transactions on Signal Processing
- 2021

This paper proposes parallel backward-forward type of filtering and smoothing algorithm as well as parallel Viterbi-type maximum-aposteriori (MAP) algorithm for parallelization of inference in hidden Markov models (HMMs).

Temporal Gaussian Process Regression in Logarithmic Time

- Computer Science, Mathematics
- 2021

A novel parallelization method for temporal Gaussian process (GP) regression problems that reduces the linear computational complexity of the temporal GP regression problems into logarithmic span complexity when run on parallel hardware such as a graphics processing unit (GPU).

Gaussian Process Regression in Logarithmic Time

- Computer Science, MathematicsArXiv
- 2021

A novel parallelization method for temporal Gaussian process (GP) regression problems that is able to reduce the linear computational complexity of the Kalman filter and smoother solutions to the GP regression problems into logarithmic span complexity, which transforms intologarithm time complexity when implemented in parallel hardware such as a graphics processing unit (GPU).

Temporal Parallelisation of Dynamic Programming and Linear Quadratic Control

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2022

This paper derives the elements and associative operators to be able to use parallel scans to solve problems with logarithmic time complexity rather than linear time complexity to solve dynamic programming problems with finite state and control spaces.

Spatio-Temporal Variational Gaussian Processes

- Computer ScienceNeurIPS
- 2021

A sparse approximation is derived that constructs a state-space model over a reduced set of spatial inducing points, and it is shown that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties.

Combining Pseudo-Point and State Space Approximations for Sum-Separable Gaussian Processes

- Computer ScienceUAI
- 2021

This work shows that there is a simple and elegant way to combine pseudo-point methods with the state space GP approximation framework to get the best of both worlds, and demonstrates empirically that the combined approach is more scalable and applicable to a greater range of spatio-temporal problems than either method on its own.

Generalized pseudo Bayesian algorithms for tracking of multiple model underwater maneuvering target

- Engineering, Computer Science
- 2020

Bayesian machine learning analysis

- Physics
- 2022

Multi-wavelength single-molecule fluorescence colocalization (CoSMoS) methods 7 allow elucidation of complex biochemical reaction mechanisms. However, analysis of CoSMoS 8 data is intrinsically…

A Structured Observation Distribution for Generative Biological Sequence Prediction and Forecasting

- Computer Science, BiologyICML
- 2021

It is shown empirically that models that use the MuE as an observation distribution outperform comparable methods across a variety of datasets, and applied to a novel problem for generative probabilistic sequence models: forecasting pathogen evolution.

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