We analyze belief propagation on patch potential models – these are attractive models with varying local potentials – obtain all of the possibly many fixed points, and gather novel insights into belief propagation’s properties. In particular, we observe and theoretically explain several regions in the parameter space that behave fundamentally different. We specify and elaborate on one specific region that, despite the existence of multiple fixed points, is relatively well behaved and provides insights into the relationship between the accuracy of the marginals and the partition function. We demonstrate the inexistence of a principle relationship between both quantities and provide sufficient conditions for a fixed point to be optimal with respect to approximating both the marginals and the partition function.

中文翻译：

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信念传播：准确的边际或准确的分区函数——区别在哪里？

我们分析了对补丁潜在模型的信念传播——这些是具有不同局部潜力的有吸引力的模型——获得所有可能的许多固定点，并收集对信念传播特性的新见解。特别是，我们观察并在理论上解释了参数空间中表现根本不同的几个区域。我们指定并详细说明了一个特定区域，尽管存在多个固定点，但该区域表现相对较好，并提供了对边缘精度与分区函数之间关系的见解。我们证明了两个数量之间不存在主要关系，并为固定点在逼近边际和分配函数方面达到最佳状态提供了充分条件。