Lifted Marginal Filtering for Asymmetric Models by Clustering-Based Merging

Recently, Lifted Marginal Filtering (LiMa) has been proposed, an efficient exact Bayesian filtering algorithm for stochastic systems consisting of multiple, (inter-)acting entities where the system dynamics is represented by a multiset rewriting system (MRS). The core idea is to represent distributions over multisets more efficiently than by complete enumeration, by exploiting exchangeability that naturally arises due to the MRS dynamics. However, due to system dynamics or observations of individuals, symmetry can break over time, requiring to resort to the original, much larger representation. In this paper, we propose a method to retain the lifted representation in LiMa. The method identifies groups of lifted multiset states that describe a sufficiently similar distribution of ground multiset states for affording a representation by a single lifted state. Technically, we propose a novel distance measure for lifted states that does not require to completely ground the distribution first, and show how such a single representative for a group of lifted states can be computed. We show empirically that the error induced by this approach is significantly smaller than by limiting the representational complexity conventionally by sampling.