副本对称随机因子图模型的置信传播
Belief Propagation on replica symmetric random factor graph models
摘要：
根据物理学预测，满足特定“静态副本对称”条件的随机因子图模型的自由能可以经由置信传播消息传递方案来计算[Krzakala等人，PNAS 2007]。在这里，我们证明了这一猜想的两个一般类的随机因子图模型，即泊松随机因子图和随机正则因子图。具体而言，我们证明了构造的消息，就像在无环因子图的情况下渐近满足的信念传播方程和自由能密度给出的贝特自由能公式。
英文摘要：
According to physics predictions, the free energy of random factor graph models that satisfy a certain "static replica symmetry" condition can be calculated via the Belief Propagation message passing scheme [Krzakala et al., PNAS 2007]. Here we prove this conjecture for two general classes of random factor graph models, namely Poisson random factor graphs and random regular factor graphs. Specifically, we show that the messages constructed just as in the case of acyclic factor graphs asymptotically satisfy the Belief Propagation equations and that the free energy density is given by the Bethe free energy formula.
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