# Temporal Parallelization of Bayesian Smoothers

## TL;DR

This paper introduces algorithms that enable the parallel processing of Bayesian smoothers over time, significantly reducing computational complexity from linear to logarithmic by leveraging all-prefix-sums operations.

## Contribution

It formulates Bayesian smoothing as all-prefix-sums problems and develops parallel algorithms for filtering and smoothing, especially for linear/Gaussian models.

## Key findings

- Reduces smoothing complexity from linear to logarithmic
- Applies parallel scan algorithms to Bayesian smoothing
- Specializes algorithms for linear/Gaussian models

## Abstract

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.