The second order mean field approximation of graphical models and its application to Bayesian inference

马尔可夫随机场(MRF)及其判别形式在生物分析和实际应用中都是有用的。在生物学分析中，关于神经元相关性的争论仍在继续，其中需要分析在刺激S的条件下神经元反应r的概率P(r|S)，这可以用MRF来建模。在这一背景下，通过对联合概率P(r，S)进行吉布斯分布建模，证明了参数模型在相关性分析中的重要性。已有几种近似方法被用来计算MRF、CRF的状态概率，包括信任传播，这些方法在一般情况下不适用于MRF。平均场近似(MRF)是目前已知的唯一一种普遍适用的近似技术。为了提高平均场近似的精度，人们提出了几种先进的技术。因为我们获得的精度越高，我们进入的方程就越复杂，it…更难知道有效的训练程序。本研究的成果是改进了平均场近似，减少了测试和学习时间，并展示了变分相量平均场模型(VPMF)用于目标识别的有效学习方案。实验结果表明，尽管我们使用的训练数据量要小得多，但我们的学习方案的测试性能与支持向量机相当，而且检测时间和训练时间都比基于支持向量机的人脸检测要小得多。我们还得到了群体编码在神经网络中的相关性比只使用平均发射速率更强的结论。对VPMF的逼近精度、局部极小值和人脸识别问题进行了性能评估。较少

Markov random field (MRF) and its discriminative version have been shown useful for both biological analysis and practical applications. In biological analysis, the debate on neuronal correlations is now continuing in which the analysis of the probability P( r| s) of the neuronal response r conditional on a stimulus s is required, which could be modeled with MRF. In this context the importance of a parametric model for analyzing correlations by modeling joint probability P(r, s) is shown using Gibbs distribution.Several approximation techniques have been proposed for computing state probabilities of MRFs, CRFs, including belief propagation, which is not applicable for MRFs in a general situation. Mean field approximation (MRF) is known as only the generally applicable approximation technique at present.To improve the accuracy of the mean-field approximation several advanced techniques have been proposed. Since the better accuracy we attain, the more intricate equations we get into, it … More becomes hard to know the efficient training procedure. In fact the training procedure is known only for the naive mean-field approximation (NMF), which is not so sufficient for the approximation accuracy.The achievement of this research is to have refined the mean field approximation to alleviate both the testing and learning time, and to have shown the efficient learning scheme for object recognition with the variational phasor mean field model (VPMF). The striking result is that our learning scheme shows comparable testing performance with SVM, despite using much smaller size of training data, and in addition the detection time and the training time are much smaller than SVM based face detection.Performance evaluation of VPMF is given for approximation accuracy, the local minima, and a face recognition problems. We have also attained the conclusion that the correlation of population coding in neural networks is more powerful than just using only the mean firing rate.Performance evaluation of VPMF is given for approximation accuracy, the local minima, and a face recognition problems. Less