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… 

Figures from this paper

Parallel Iterated Extended and Sigma-Point Kalman Smoothers
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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.
Bayesian machine learning analysis
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
TLDR
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.
...
1
2
...

References

SHOWING 1-10 OF 35 REFERENCES
Parallelizable sparse inverse formulation Gaussian processes (SpInGP)
We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the
Iterated Posterior Linearization Smoother
TLDR
The iterated posterior linearization smoother (IPLS) is proposed, which is an iterated algorithm that performs SLR of the nonlinear functions with respect to the current posterior approximation and is demonstrated to outperform conventional Gaussian nonlinear smoothers in two numerical examples.
Iterative Filtering and Smoothing in Nonlinear and Non-Gaussian Systems Using Conditional Moments
TLDR
This letter presents the development of novel iterated filters and smoothers that only require specification of the conditional moments of the dynamic and measurement models and demonstrates the merits of the proposed algorithms in simulations of the stochastic Ricker map.
Spatio-Temporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing
TLDR
Methods for converting spatio-temporal Gaussian process regression and classification problems into infinite-dimensional state space models and the use of machine learning models in signal processing becomes computationally feasible, and it opens the possibility to combine machine learning techniques with signal processing methods.
Parallel Prefix (Scan) Algorithms for MPI
TLDR
The doubly-pipelined algorithm is more than a factor two faster than the straight-forward binomial-tree algorithm found in many MPI implementations, and due to its small constant factors the simple, linear pipeline algorithm is preferable for systems with a moderate number of processors.
Parallel Implementation of a Kalman Filter for Constituent Data Assimilation
Abstract A Kalman filter for the assimilation of long-lived atmospheric chemical constituents was developed for two-dimensional transport models on isentropic surfaces over the globe. Since the
Bayesian Filtering and Smoothing
  • S. Särkkä
  • Computer Science
    Institute of Mathematical Statistics textbooks
  • 2013
TLDR
This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework and learns what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.
Efficient Parallel Implementation of State Estimation Algorithms on Multicore Platforms
TLDR
This article investigated how two of the most popular and powerful state estimation algorithms, the Kalman filter and the particle filter, can be efficiently implemented in parallel on a multicore architecture and found that linear speedup, in the number of cores used, can indeed be achieved without loss of accuracy, for bothstate estimation algorithms.
Bayesian Filtering and Smoothing
TLDR
This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework, learning what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.
Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering
TLDR
Methods for converting spatiotemporal Gaussian process regression problems into infinite-dimensional state-space models are presented and the use of machine-learning models in signal processing becomes computationally feasible, and it opens the possibility to combine machine- learning techniques with signal processing methods.
...
1
2
3
4
...