概率图模型中基于多项式回归形式的矩传播方法及其在决策支持系统中的应用
Propagating moments in probabilistic graphical models with polynomial regression forms for decision support systems
AI总结：
本文提出一种基于多项式回归和矩传播的消息传递算法，用于概率图模型中的精确期望效用计算，可扩展应用于能源规划与实时临床决策支持。
摘要：
概率图模型被广泛用于对不确定性下的复杂系统进行建模。传统上，高斯有向图模型因其能够以闭合形式提供条件分布和边缘分布，从而简化推断任务，而被应用于包含连续变量的大型网络分析。高斯性和线性假设通常足够适用，但在处理某些实际应用时可能导致性能不佳。在本文中，我们将图G中的每个变量建模为其父节点的多项式回归，以捕捉各个变量之间的复杂关系，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，仅利用矩在整个网络中传播信息，从而能够精确计算期望效用得分。我们的传播方法具有良好的可扩展性，并能够以有限数量的期望值形式进行推断。我们通过示例以及在实际应用中的演示来说明所提出方法的有效性，这些应用包括能源规划中的决策问题和实时临床决策支持。
英文摘要：
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.
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