Scalable Explanation of Inferences on Large Graphs

Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference outcomes. Different from deep or high dimensional parametric models, the lack of interpretability in graphical models is due to the cyclic and long-range dependencies and the byzantine inference procedures. Prior works did not tackle cycles and make the inferences interpretable. We formulate the explanation of probabilistic inferences as a constrained cross-entropy minimization problem to find simple subgraphs that faithfully approximate the inferences. We prove that the optimization is NP-hard, while the objective is not monotonic and submodular to guarantee efficient greedy approximation. We propose a beam search algorithm to find trees to enhance the explanation interpretability and diversity. To allow efficient search on large and dense graphs without hurting faithfulness, we further propose parallelization and a pruning strategy. We demonstrate superior performance on four networks from distinct applications, comparing favorably to other explanation methods, including LIME.