论文标题
对概率图形模型推断的严格解释
Rigorous Explanation of Inference on Probabilistic Graphical Models
论文作者
论文摘要
概率图形模型，例如马尔可夫随机场（MRF），在随机变量之间利用依赖性，以建模丰富的关节概率分布家族。复杂的推理算法（例如信仰传播（BP））可以有效地计算边缘后代。尽管如此，对于重要的人类决策而言，仍然很难解释推理结果。没有现有的方法将推理结果严格归因于图形模型的影响因素。 Shapley值提供了一个公理框架，但是在一般图形模型上进行天真的计算甚至近似值是具有挑战性的，并且研究较少。我们建议GraphShapley以原则上的方式集成Shapley值，MRF的结构以及BP推断的迭代性质的可分解性，以进行快速Shapley值计算，即1）系统地列举了对解释变量的Shapley值的重要贡献； 2）逐步计算贡献而无需从划痕开始。从理论上讲，我们对GraphShapley进行了描述，涉及独立性，同等贡献和添加性。在九个图上，我们证明了GraphShapley提供了明智而实用的解释。
Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Sophisticated inference algorithms, such as belief propagation (BP), can effectively compute the marginal posteriors. Nonetheless, it is still difficult to interpret the inference outcomes for important human decision making. There is no existing method to rigorously attribute the inference outcomes to the contributing factors of the graphical models. Shapley values provide an axiomatic framework, but naively computing or even approximating the values on general graphical models is challenging and less studied. We propose GraphShapley to integrate the decomposability of Shapley values, the structure of MRFs, and the iterative nature of BP inference in a principled way for fast Shapley value computation, that 1) systematically enumerates the important contributions to the Shapley values of the explaining variables without duplicate; 2) incrementally compute the contributions without starting from scratches. We theoretically characterize GraphShapley regarding independence, equal contribution, and additivity. On nine graphs, we demonstrate that GraphShapley provides sensible and practical explanations.
