Approximations with Reweighted Generalized Belief Propagation
Approximations with Reweighted Generalized Belief Propagation
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发表时间：
2005
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通讯作者：
W. Wiegerinck
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作者：
W. Wiegerinck
在（温赖特等人，2002）给出了任意无向图模型的对数配分函数的一个新的一般上界。这个界限是通过取易处理的分布的凸组合来构造的。到目前为止发表的实验结果集中在树结构分布的组合，导致一个convexified贝特自由能，这是最小化的树重新加权的信念传播算法。这类近似的有利性质之一是，增加近似的复杂性可以保证增加精度。这种保证的缺乏在标准的广义信念传播中是臭名昭著的。我们增加了复杂性的近似分布采取结合树，导致一个convexified菊池自由能，这是最小化的加权广义信念传播。伊辛网格以及完全连接的伊辛模型的实验结果示出的优点和缺点的加权方法在近似推理。
In (Wainwright et al., 2002) a new general class of upper bounds on the log partition function of arbitrary undirected graphical models has been developed. This bound is constructed by taking convex combinations of tractable distributions. The experimental results published so far concentrates on combinations of tree-structured distributions leading to a convexified Bethe free energy, which is minimized by the tree-reweighted belief propagation algorithm. One of the favorable properties of this class of approximations is that increasing the complexity of the approximation is guaranteed to increase the precision. The lack of this guarantee is notorious in standard generalized belief propagation. We increase the complexity of the approximating distributions by taking combinations of junction trees, leading to a convexified Kikuchi free energy, which is minimized by reweighted generalized belief propagation. Experimental results for Ising grids as well as for fully connected Ising models are presented illustrating advantages and disadvantages of the reweighting method in approximate inference.