On Lifting the Gibbs Sampling Algorithm

Statistical relational learning models combine the power of first-order logic, the de facto tool for handling relational structure, with that of probabilistic graphical models, the de facto tool for handling uncertainty. Lifted probabilistic inference algorithms for them have been the subject of much recent research. The main idea in these algorithms is to improve the speed, accuracy and scalability of existing graphical models' inference algorithms by exploiting symmetry in the first-order representation. In this paper, we consider blocked Gibbs sampling, an advanced variation of the classic Gibbs sampling algorithm and lift it to the first-order level. We propose to achieve this by partitioning the first-order atoms in the relational model into a set of disjoint clusters such that exact lifted inference is polynomial in each cluster given an assignment to all other atoms not in the cluster. We propose an approach for constructing such clusters and determining their complexity and show how it can be used to trade accuracy with computational complexity in a principled manner. Our experimental evaluation shows that lifted Gibbs sampling is superior to the propositional algorithm in terms of accuracy and convergence.