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狄利克雷过程和非参数贝叶斯建模

Dirichlet Processes and Nonparametric Bayesian Modelling
课程网址: http://videolectures.net/mlss06au_tresp_dpnbm/  
主讲教师: Volker Tresp
开课单位: 西门子公司
开课时间: 2007-02-25
课程语种: 英语
中文简介:
贝叶斯建模是一种原则性的方法,用于在给定先验知识和给出可用证据的情况下更新假设的信念程度。使用贝叶斯规则将先验知识和证据结合起来以获得后验假设。在机器学习感兴趣的大多数情况下,先验知识被公式化为参数的先验分布,并且证据对应于观察到的数据。通过应用贝叶斯公式,我们可以对新数据进行推理。观察到足够的数据后,后验参数分布越来越集中,先验分布的影响减小。在一些假设下(特别是似然模型是正确的并且真实参数具有正的先验概率),后验分布收敛于位于真实参数的点分布。贝叶斯建模中的挑战首先是找到合适的特定应用统计模型,其次是(近似地)求解所得的推理方程。
课程简介: Bayesian modeling is a principled approach to updating the degree of belief in a hypothesis given prior knowledge and given available evidence. Both prior knowledge and evidence are combined using Bayes' rule to obtain the a posterior hypothesis. In most cases of interest to machine learning, the prior knowledge is formulated as a prior distribution over parameters and the evidence corresponds to the observed data. By applying Bayes' formula we can perform inference about new data. Having observed sufficient data, the a posteriori parameter distribution is increasingly concentrated and the influence of the prior distribution diminishes. Under some assumptions (in particular that the likelihood model is correct and that the true parameters have positive a priori probability), the a posteriori distribution converges to a point distribution located at the true parameters. The challenges in Bayesian modeling are, first, to find suitable application specific statistical models and, second, to (approximately) solve the resulting inference equations.
关 键 词: 贝叶斯建模; 先验知识; 后验参数; 特定应用统计模型
课程来源: 视频讲座网
最后编审: 2019-07-16:cjy
阅读次数: 98