On the Minima of Bethe Free Energy in Gaussian Distributions
On the Minima of Bethe Free Energy in Gaussian Distributions
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DOI：
10.1007/978-3-540-69731-2_101
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发表时间：
2006-06
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影响因子：
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通讯作者：
Yu Nishiyama;Sumio Watanabe
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文献类型：
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作者：
Yu Nishiyama;Sumio Watanabe
置信度传播(BP)是计算高维概率分布的边际概率的有效方法。众所周知，循环信任传播(LBP)不能计算精确的边缘概率，也不能保证收敛。已知LBP的固定点符合Bethe自由能的极值。因此，我们通过最小化Bethe自由能来分析不动点。在本文中，我们考虑了高斯分布中的Bethe自由能，并解析地阐明了某些特殊情况下LBP的极值，等价地，不动点。分析结果给出了LBP收敛的必要条件和决定高斯分布LBP精度的参数。在分析结果的基础上，我们对LBP进行了数值实验，并与解析解进行了比较。
Belief propagation (BP) is effective for computing marginal probabilities of a high dimensional probability distribution. Loopy belief propagation (LBP) is known not to compute precise marginal probabilities and not to guarantee its convergence. The fixed points of LBP are known to accord with the extrema of Bethe free energy. Hence, the fixed points are analyzed by minimizing the Bethe free energy.In this paper, we consider the Bethe free energy in Gaussian distributions and analytically clarify the extrema, equivalently, the fixed points of LBP for some particular cases. The analytical results tell us a necessary condition for LBP convergence and the quantities which determine the accuracy of LBP in Gaussian distributions. Based on the analytical results, we perform numerical experiments of LBP and compare the results with analytical solutions.