Don't Fear Optimality: Sampling for Probabilistic-Logic Sequence Models

One of the current challenges in artificial intelligence is modeling dynamic environments that change due to the actions or activities undertaken by people or agents. The task of inferring hidden states, e.g. the activities or intentions of people, based on observations is called filtering. Standard probabilistic models such as Dynamic Bayesian Networks are able to solve this task efficiently using approximative methods such as particle filters. However, these models do not support logical or relational representations. The key contribution of this paper is the upgrade of a particle filter algorithm for use with a probabilistic logical representation through the definition of a proposal distribution. The performance of the algorithm depends largely on how well this distribution fits the target distribution. We adopt the idea of logical compilation into Binary Decision Diagrams for sampling. This allows us to use the optimal proposal distribution which is normally prohibitively slow.