Lifted Filtering via Exchangeable Decomposition

TL;DR

This paper introduces a novel Bayesian filtering method using lifted multiset states that efficiently exploits exchangeability and symmetry to reduce inference complexity in dynamic systems.

Contribution

It combines concepts from multiset rewriting, Rao-Blackwellization, and lifted inference to enable exact recursive filtering that adapts to symmetry-breaking observations.

Findings

Achieves exponential reduction in inference complexity for exchangeable systems.

Automatically adapts when symmetry is broken by observations or dynamics.

Provides a unified framework for lifted filtering using multisets.

Abstract

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.