A Junction Tree Propagation Algorithm for Bayesian Networks with Second-Order Uncertainties

Maurizio Borsotto, Weihong Zhang, Emir Kapanci, A. Pfeffer, C. Crick
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引用次数: 13

Abstract

Bayesian networks (BNs) have been widely used as a model for knowledge representation and probabilistic inferences. However, the single probability representation of conditional dependencies has been proven to be over-constrained in realistic applications. Many efforts have proposed to represent the dependencies using probability intervals instead of single probabilities. In this paper, we move one step further and adopt a probability distribution schema. This results in a higher order representation of uncertainties in a BN. We formulate probabilistic inferences in this context and then propose a mean/covariance propagation algorithm based on the well-known junction tree propagation for standard BNs. For algorithm validation, we develop a two-layered Markov likelihood weighting approach that handles high-order uncertainties and provides "ground-truth" solutions to inferences, albeit very slowly. Our experiments show that the mean/covariance propagation algorithm can efficiently produce high-quality solutions that compare favorably to results obtained through painstaking sampling
二阶不确定贝叶斯网络的连接树传播算法
贝叶斯网络(BNs)作为一种知识表示和概率推理模型已被广泛应用。然而,在实际应用中,条件依赖关系的单概率表示已被证明是过度约束的。许多人已经提出用概率间隔代替单一概率来表示依赖关系。在本文中,我们更进一步,采用概率分布模式。这导致了BN中不确定性的高阶表示。在此背景下,我们制定了概率推断,然后提出了一种基于众所周知的标准bn的连接树传播的均值/协方差传播算法。对于算法验证,我们开发了一种双层马尔可夫似然加权方法,该方法处理高阶不确定性,并为推理提供“基本事实”解决方案,尽管速度很慢。我们的实验表明,均值/协方差传播算法可以有效地产生高质量的解决方案,与辛苦采样获得的结果相比,效果更好
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