Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing
Accuracy of the Bethe approximation for hyperparameter estimation in probabilistic image processing
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DOI：
10.1088/0305-4470/37/36/007
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发表时间：
2004-09
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影响因子：
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通讯作者：
Kazuyuki Tanaka;Hayaru Shouno;M. Okada;D. Titterington
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文献类型：
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作者：
Kazuyuki Tanaka;Hayaru Shouno;M. Okada;D. Titterington
研究了概率图像处理中基于贝叶斯统计和极大似然估计的超参数估计的统计-力学近似的准确性。统计科学中的超参数对应于统计力学背景下的相互作用或外部场。本文确定了概率模型中的超参数，以使边际似然最大化。提出了一种实用的基于高斯图形模型和贝特近似的灰度级图像恢复算法。该算法对应于人工智能中的循环信念传播。当我们使用贝特近似时，我们检验了超参数估计的准确性。众所周知，在贝叶斯公式中采用高斯图模型作为先验概率模型，可以解析地规定一种实用的概率图像处理算法。因此，在数值研究中，我们能够将通过平均场近似获得的结果与基于精确计算的结果进行比较。
We investigate the accuracy of statistical-mechanical approximations for the estimation of hyperparameters from observable data in probabilistic image processing, which is based on Bayesian statistics and maximum likelihood estimation. Hyperparameters in statistical science correspond to interactions or external fields in the statistical-mechanics context. In this paper, hyperparameters in the probabilistic model are determined so as to maximize a marginal likelihood. A practical algorithm is described for grey-level image restoration based on a Gaussian graphical model and the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We examine the accuracy of hyperparameter estimation when we use the Bethe approximation. It is well known that a practical algorithm for probabilistic image processing can be prescribed analytically when a Gaussian graphical model is adopted as a prior probabilistic model in Bayes' formula. We are therefore able to compare, in a numerical study, results obtained through mean-field-type approximations with those based on exact calculation.