估计随机多面体体积相关性质的加权置信传播算法
A weighted belief-propagation algorithm to estimate volume-related properties of random polytopes
摘要：
在这项工作中，我们引入了一种新的加权消息传递算法的基础上的空腔方法来估计随机多面体的体积相关的属性，这些属性是相关的各种研究领域，从代谢网络，神经网络，压缩传感。不同于通常的方法，包括近似的实值腔边缘分布的几个参数，我们提出了一个算法，忠实地代表整个边缘分布。我们解释了各种替代方案，以实现算法和基准的理论研究结果，显示具体的应用随机多面体。与我们的方法得到的结果被发现是在非常好的协议与打了就跑算法，已知产生均匀的采样所产生的估计。
英文摘要：
In this work we introduce a novel weighted message-passing algorithm based on the cavity method to estimate volume-related properties of random polytopes, properties which are relevant in various research fields ranging from metabolic networks, to neural networks, to compressed sensing. Unlike the usual approach consisting in approximating the real-valued cavity marginal distributions by a few parameters, we propose an algorithm to faithfully represent the entire marginal distribution. We explain various alternatives to implement the algorithm and benchmark the theoretical findings by showing concrete applications to random polytopes. The results obtained with our approach are found to be in very good agreement with the estimates produced by the Hit-and-Run algorithm, known to produce uniform sampling.
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