# Parallelising Particle Filters with Butterfly Interactions

## TL;DR

This paper proposes a constrained parallel particle filter method using butterfly interactions to reduce communication costs in parallel computing environments while maintaining stability and consistency.

## Contribution

It introduces a novel constrained interaction scheme for particle filters that decreases communication overhead in parallel implementations without sacrificing long-term stability.

## Key findings

- Reduced communication costs demonstrated in numerical experiments
- Method maintains stability despite interaction constraints
- Potential for improved parallel particle filter implementations

## Abstract

Bootstrap particle filter (BPF) is the corner stone of many popular algorithms used for solving inference problems involving time series that are observed through noisy measurements in a non-linear and non-Gaussian context. The long term stability of BPF arises from particle interactions which in the context of modern parallel computing systems typically means that particle information needs to be communicated between processing elements, which makes parallel implementation of BPF nontrivial. In this paper we show that it is possible to constrain the interactions in a way which, under some assumptions, enables the reduction of the cost of communicating the particle information while still preserving the consistency and the long term stability of the BPF. Numerical experiments demonstrate that although the imposed constraints introduce additional error, the proposed method shows potential to be the method of choice in certain settings.