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Conditional Random Fields, Planted Constraint Satisfaction and Entropy Concentration

机译:条件随机场,种植约束满足和熵集中

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This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted constraint satisfaction problems (CSPs), as well as more general structures motivated by coding and community clustering problems. It is shown that under mild assumptions on the kernel and for sparse random graphs, the conditional entropy of the node variables given the edge variables concentrates around a deterministic threshold. This implies in particular the concentration of the number of solutions in a broad class of planted CSPs, the existence of a threshold function for the disassortative stochastic block model, and the proof of a conjecture on parity check codes. It also establishes new connections among coding, clustering and satisfiability.
机译:本文研究了图上的一类概率模型,其中边缘变量通过固定概率核依赖于入射节点变量。该课程包括植入的约束满足问题(CSP),以及由编码和社区聚类问题引起的更一般的结构。结果表明,在核和稀疏随机图的温和假设下,给定边缘变量的节点变量的条件熵集中在确定性阈值附近。这尤其意味着大量解决方案将被集中在一系列种植的CSP中,存在用于离散随机块模型的阈值函数,以及对奇偶校验码的猜想的证明。它还在编码,聚类和可满足性之间建立了新的联系。

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