Stochastic complexity of complete bipartite graph-type Boltzmann machines in mean field approximation

Electronics and Communications in Japan (Part III: Fundamental Electronic Science) Pub Date : 2007-04-23 DOI:10.1002/ECJC.20307

Yu Nishiyama, Sumio Watanabe

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Abstract

A variational Bayes method is proposed as an approximation method for implementing Bayesian posterior distribution with moderate computational complexity. Its effectiveness for real problems has been confirmed. The variational Bayes method is a method which generalizes the mean field approximation used in calculating partition functions in statistical physics. In recent years, the mathematical properties of the precision with which it is approximated have been investigated. In this paper, the authors consider the asymptotic stochastic complexity in the case of applying the mean field approximation to complete bipartite graph-type Boltzmann machines and theoretically derive that asymptotic form. Also, based on the results, the authors quantitatively consider the difference between Bayesian posterior distribution and the posterior distribution of the mean field approximation. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(9): 1– 9, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20307

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平均场近似下完全二部图型玻尔兹曼机的随机复杂度

提出了一种变分贝叶斯方法，作为实现贝叶斯后验分布的近似方法，计算复杂度适中。它对实际问题的有效性已得到证实。变分贝叶斯方法是统计物理中用于计算配分函数的平均场近似的一种推广方法。近年来，人们研究了用来逼近它的精度的数学性质。本文考虑了用平均场近似求解完全二部图型玻尔兹曼机的渐近随机复杂度，并从理论上推导了该渐近形式。在此基础上，定量地考虑了贝叶斯后验分布与平均场近似后验分布的区别。©2007 Wiley期刊公司电子工程学报，2009,29 (1):1 - 9;在线发表于Wiley InterScience (www.interscience.wiley.com)。DOI 10.1002 / ecjc.20307

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Electronics and Communications in Japan (Part III: Fundamental Electronic Science)

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