Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide conditional and marginal distributions in closed form simplifying the inferential task. The Gaussianity and linearity assumptions are often adequate, yet can lead to poor performance when dealing with some practical applications. In this paper, we model each variable in graph G as a polynomial regression of its parents to capture complex relationships between individual variables and with a utility function of polynomial form. We develop a message-passing algorithm to propagate information throughout the network solely using moments which enables the expected utility scores to be calculated exactly. Our propagation method scales up well and enables to perform inference in terms of a finite number of expectations. We illustrate how the proposed methodology works with examples and in an application to decision problems in energy planning and for real-time clinical decision support.

翻译：概率图模型被广泛用于建模不确定性下的复杂系统。传统上，高斯有向图模型因其能以闭式形式提供条件分布与边缘分布、简化推断任务，而被应用于连续变量大型网络的分析。高斯性与线性假设通常足够有效，但在处理某些实际应用时可能导致性能不佳。本文提出将图G中的每个变量建模为其父节点的多项式回归，以捕捉变量间复杂的关联关系，并采用多项式形式的效用函数。我们开发了一种消息传递算法，仅利用矩在网络中传播信息，从而能够精确计算期望效用得分。所提出的传播方法具有良好的可扩展性，并能基于有限个期望值执行推断。我们通过示例以及在能源规划决策问题和实时临床决策支持中的应用，阐明了所提方法的工作原理。