Yasuda Muneki, Kataoka Shun, Tanaka Kazuyuki
Graduate School of Science and Engineering, Yamagata University, Japan. CREST, JST (Yamagata University).
Graduate School of Information Sciences, Tohoku University, Japan. CREST, JST (Tohoku University).
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042120. doi: 10.1103/PhysRevE.92.042120. Epub 2015 Oct 8.
Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pairwise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.
循环信念传播（LBP）等同于统计力学中的贝叶斯近似，是一种基于消息传递的推理方法，广泛用于分析基于马尔可夫随机场（MRF）的系统。在本文中，我们提出了一种基于消息传递的方法，通过使用复制簇变分方法来解析评估随机场中LBP的淬火平均值。所提出的解析方法适用于具有彼此不同分布的随机场的一般成对MRF，并且可以给出随机场上贝叶斯自由能的淬火平均值，这与数值结果一致。其计算成本的阶数与标准LBP的计算成本阶数相当。在本文的后半部分，我们描述了所提出方法在贝叶斯图像恢复中的应用，我们观察到我们的理论结果与自然图像的数值结果非常吻合。
