Belief propagation, robust reconstruction and optimal recovery of block models
Belief propagation, robust reconstruction and optimal recovery of block models
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DOI：
10.1214/15-aap1145
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发表时间：
2013-09
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影响因子：
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通讯作者：
Elchanan Mossel;Joe Neeman;A. Sly
中科院分区：
文献类型：
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作者：
Elchanan Mossel;Joe Neeman;A. Sly
我们考虑了分别为间隔和内部内部边缘概率和连接概率a = n和b = n重建具有两个块的稀疏对称块模型的问题。最近显示，只有（a b）2> 2（a + b），就可以做一个比随机猜测更好的猜测。使用一种信念传播的变体，我们给出了一种重建算法，从某种意义上说，如果（a b）2> c（a + b）对于某些常数C，则我们的算法最大化了正确标记的节点的分数。在此过程中，我们证明了关于常规和泊松树的Ising模型的强大重建的独立兴趣结果。
We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a=n and b=n for inter- and intra-block edge probabilities respectively. It was recently shown that one can do better than a random guess if and only if (a b) 2 > 2(a + b). Using a variant of Belief Propagation, we give a reconstruction algorithm that is optimal in the sense that if (a b) 2 > C(a + b) for some constant C then our algorithm maximizes the fraction of the nodes labelled correctly. Along the way we prove some results of independent interest regarding robust reconstruction for the Ising model on regular and Poisson trees.