# Lifted Filtering via Exchangeable Decomposition

arXiv: https://arxiv.org/abs/1801.10495 · HTML: https://mlsanity.com/paper/1801.10495/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Exchangeability-Aware Sum-Product Networks](https://mlsanity.com/paper/2110.05165/) (2021)
- [Activity Recognition in Assembly Tasks by Bayesian Filtering in Multi-Hypergraphs](https://mlsanity.com/paper/2202.00332/) (2022)

## Abstract (arXiv)

We present a model for exact recursive Bayesian filtering based on lifted multiset states. Combining multisets with lifting makes it possible to simultaneously exploit multiple strategies for reducing inference complexity when compared to list-based grounded state representations. The core idea is to borrow the concept of Maximally Parallel Multiset Rewriting Systems and to enhance it by concepts from Rao-Blackwellization and Lifted Inference, giving a representation of state distributions that enables efficient inference. In worlds where the random variables that define the system state are exchangeable -- where the identity of entities does not matter -- it automatically uses a representation that abstracts from ordering (achieving an exponential reduction in complexity) -- and it automatically adapts when observations or system dynamics destroy exchangeability by breaking symmetry.