Lifted Filtering via Exchangeable Decomposition
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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.
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