贝叶斯学习中的线性联合先验

计算机工程与应用 ›› 2012, Vol. 48 ›› Issue (1): 33-35.

贝叶斯学习中的线性联合先验

胡振宇1，2，林士敏3

1.清华大学信息科学与技术国家实验室，北京 100084
2.启明星辰核心研究院，北京 100193
3.广西师范大学计算机科学与信息工程学院，广西桂林 541004

收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2012-01-01 发布日期:2012-01-01

Linear opinion pool prior for Bayesian learning

HU Zhenyu1，2, LIN Shimin3

1.National Lab of Information Science and Technology, Tsinghua University, Beijing 100084, China
2.Venus Institute of Core Technical Research, Beijing 100193, China
3.Faculty of Computer Science & Information Engineering, Guangxi Normal University, Guilin, Guangxi 541004, China

Received:1900-01-01 Revised:1900-01-01 Online:2012-01-01 Published:2012-01-01

摘要/Abstract

摘要： 提出了贝叶斯学习中先验分布选取的一个新技术。该技术将若干个可能的先验进行加权平均，形成一个以权重为参数的线性联合先验，并通过选取权重参数得到一个最合适先验的一个近似。证明了线性联合先验的似然与其组合参数的似然的等价性，并提出了用极大似然或矩估计的方法来确定权重参数的值，从而得到一个最合适的线性联合先验。提出的线性联合先验及确定方法，使得可以利用样本数据对已知先验进行校正，导出未被发现的更合理的先验，从而使贝叶斯学习更为有效。

关键词: 贝叶斯学习, 先验分布, 线性联合先验, 极大似然估计, 矩估计

Abstract: This paper brings forward a new technique for prior choosing in Bayesian learning, in which several priors are averaged in weight to form the Linear Opinion Pool（LOP）, and then compound parameters are chosen to get an approximation of suitable prior. This paper also proves the equivalency between the likelihood of LOP prior and the likelihood of the compound parameters, and offers a method of MLE or moment to determine the compound parameters, therefore a suitable LOP prior is determined. In this way one can use sample data to correct known prior, derive undiscovered and reasonable prior, therefore can make Bayesian learning more effective.

Key words: Bayesian learning, prior distribution, linear opinion pool, Maximum Likelihood Eestimation（MLE）, method of moment

胡振宇1，2，林士敏3. 贝叶斯学习中的线性联合先验[J]. 计算机工程与应用, 2012, 48(1): 33-35.

HU Zhenyu1，2, LIN Shimin3. Linear opinion pool prior for Bayesian learning[J]. Computer Engineering and Applications, 2012, 48(1): 33-35.

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