Lifted Filtering via Exchangeable Decomposition

We present a model for 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-Blackwellisation 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.