Taming Reasoning in Temporal Probabilistic Relational Models

Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal approximate merging (T AMe), which incorporates (i) clustering for grouping submodels as well as (ii) statistical significance checks to test the fitness of the clustering outcome. In exchange for faster runtimes, T AMe introduces a bounded error that becomes negligible over time. Empirical results show that T AMe significantly improves the runtime performance of inference, while keeping errors small. Introduction Temporal probabilistic relational models express relations between objects, modelling uncertainty as well as temporal aspects. Within one time step, a temporal model is considered static. Performing inference on such models requires algorithms to efficiently handle the temporal aspect to be able to efficiently answer queries. Reasoning in lifted representations has a complexity polynomial in domain sizes. But, models dissolve into ground instances through evidence, which no longer permits reasoning in polynomial time, making query answering infeasible for any reasoning algorithm, exact or approximate. Thus, a key challenge during inference in temporal models is to restore a lifted, i.e., non-grounded, representation. Therefore, we formulate and study the problem of keeping reasoning polynomial (KRP) in temporal models to tame the effect of evidence for efficient query answering. First-order probabilistic inference leverages the relational aspect of a static model, using representatives for groups of indistinguishable, known objects, also known as lifting (Poole 2003). Poole (2003) presents parametric factor graphs as relational models and proposes lifted variable elimination (L VE) as an exact inference algorithm on relational models.