混合贝叶斯网络中时间约束近似推理的高斯混合约简
Gaussian Mixture Reduction for Time-Constrained Approximate Inference in Hybrid Bayesian Networks
摘要：
混合贝叶斯网络（HBN）包含离散和连续变量，在许多应用领域（例如，图像理解、数据融合、医疗诊断、欺诈检测）。本文研究了HBN的一个重要子类--条件高斯网络（CG）中的推理问题，其中所有连续随机变量都具有高斯分布，并且连续随机变量的所有子节点都必须是连续的。CG网络中的推理即使对于特殊情况的结构也可能是NP难的，例如poly-tree，其中离散贝叶斯网络中的推理可以在多项式时间内执行。因此，需要近似推理。在近似推理中，经常需要在精度和求解时间之间进行权衡。本文提出了一种扩展的混合消息传递推理算法一般CG网络和算法，以优化其准确性给定的计算时间的限制。扩展算法使用高斯混合减少，以防止高斯混合成分的数量呈指数增长。权衡算法执行预处理，以找到扩展算法的最佳运行时设置。四个CG网络的实验结果与现有算法的扩展算法的性能进行比较，并显示这些CG网络的最佳设置。
英文摘要：
Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., image understanding, data fusion, medical diagnosis, fraud detection). This paper concerns inference in an important subclass of HBNs, the conditional Gaussian (CG) networks, in which all continuous random variables have Gaussian distributions and all children of continuous random variables must be continuous. Inference in CG networks can be NP-hard even for special-case structures, such as poly-trees, where inference in discrete Bayesian networks can be performed in polynomial time. Therefore, approximate inference is required. In approximate inference, it is often necessary to trade off accuracy against solution time. This paper presents an extension to the Hybrid Message Passing inference algorithm for general CG networks and an algorithm for optimizing its accuracy given a bound on computation time. The extended algorithm uses Gaussian mixture reduction to prevent an exponential increase in the number of Gaussian mixture components. The trade-off algorithm performs pre-processing to find optimal run-time settings for the extended algorithm. Experimental results for four CG networks compare performance of the extended algorithm with existing algorithms and show the optimal settings for these CG networks.
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