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变分贝叶斯的全局解析解

Global Analytic Solution for Variational Bayesian
课程网址: http://videolectures.net/nips2010_nakajima_gas/  
主讲教师: Shinichi Nakajima
开课单位: 尼康公司
开课时间: 2011-03-25
课程语种: 英语
中文简介:
近年来,作为经典奇异值分解的替代方法,贝叶斯矩阵因式分解方法得到了广泛的研究。本文证明,尽管优化问题是非凸的,但通过求解一个四次方程,可以解析地计算变分贝叶斯(VB)MF的全局最优解。这比流行的基于迭代条件模式的VBMF算法有很大优势,因为它只能在迭代后找到局部最优解。我们进一步证明,经验vbmf(超参数也从数据中学习)的全局最优解也可以通过分析计算得到。我们通过实验说明了我们的结果的有用性。
课程简介: Bayesian methods of matrix factorization (MF) have been actively explored recently as promising alternatives to classical singular value decomposition. In this paper, we show that, despite the fact that the optimization problem is non-convex, the global optimal solution of variational Bayesian (VB) MF can be computed analytically by solving a quartic equation. This is highly advantageous over a popular VBMF algorithm based on iterated conditional modes since it can only find a local optimal solution after iterations. We further show that the global optimal solution of empirical VBMF (hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments.
关 键 词: 计算机科学; 机器学习; 贝叶斯学习
课程来源: 视频讲座网
最后编审: 2020-06-06:zyk
阅读次数: 86