# Butterfly resampling: asymptotics for particle filters with constrained interactions

arXiv: https://arxiv.org/abs/1411.5876 · HTML: https://mlsanity.com/paper/1411.5876/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2014.

## Built on by (most cited first, 1 of 1)

- [Efficient Learning of Deep State Space Models via Importance Smoothing](https://mlsanity.com/paper/2605.21108/) (2026)

## Abstract (arXiv)

We generalize the elementary mechanism of sampling with replacement N times from a weighted population of size N, by introducing auxiliary variables and constraints on conditional independence characterised by modular congruence relations. Motivated by considerations of parallelism, a convergence study reveals how sparsity of the mechanism's conditional independence graph is related to fluctuation properties of particle filters which use it for resampling, in some cases exhibiting exotic scaling behaviour. The proofs involve detailed combinatorial analysis of conditional independence graphs.