Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this inconsistency. We present the first tractable inference algorithm for PDGs with discrete variables, making the asymptotic complexity of PDG inference similar that of the graphical models they generalize. The key components are: (1) the observation that, in many cases, the distribution a PDG specifies can be formulated as a convex optimization problem (with exponential cone constraints), (2) a construction that allows us to express these problems compactly for PDGs of boundeed treewidth, (3) contributions to the theory of PDGs that justify the construction, and (4) an appeal to interior point methods that can solve such problems in polynomial time. We verify the correctness and complexity of our approach, and provide an implementation of it. We then evaluate our implementation, and demonstrate that it outperforms baseline approaches. Our code is available at http://github.com/orichardson/pdg-infer-uai.

翻译：概率依赖图（PDGs）是一类灵活的概率图模型，涵盖贝叶斯网络和因子图。它们还能捕捉不一致的信念，并提供测量这种不一致程度的方法。我们提出了首个针对离散变量PDG的可处理推理算法，使得PDG推理的渐近复杂度与其所泛化的图模型相当。关键组成部分包括：(1) 观察到在许多情况下，PDG指定的分布可表述为凸优化问题（带指数锥约束）；(2) 构建了一种紧凑表达此类问题的方法，适用于有界树宽的PDG；(3) 对PDG理论的贡献，为上述构建提供理论依据；(4) 采用内点法，可在多项式时间内求解此类问题。我们验证了方法的正确性与复杂性，并提供了实现代码。随后我们对实现进行了评估，证明其性能优于基线方法。我们的代码可在 http://github.com/orichardson/pdg-infer-uai 获取。