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贝叶斯方法

Bayesian Methods
课程网址: http://videolectures.net/acai05_borgelt_bm/  
主讲教师: Christian Borgelt
开课单位: 欧洲软计算中心
开课时间: 2007-02-25
课程语种: 英语
中文简介:
在过去的十年中,概率图形模型——特别是贝叶斯网络和马尔可夫网络——作为一种工具变得非常流行,用于构造有关感兴趣领域的不确定知识,以及用于构建基于知识的系统,从而能够对该领域进行合理和有效的推断。图形模型的核心思想是,用于描述感兴趣领域的属性之间通常存在某种独立关系。在大多数不确定性计算中,特别是在概率论中,这些独立关系的结构非常类似于图中节点连接性的性质。因此,它试图通过一个图来捕获独立关系,其中每个节点表示一个属性,每个边表示属性之间的直接依赖关系。此外,如果图只捕获有效的独立性,它规定了如何将属性张成的(通常是高维的)空间上的概率分布分解为一组较小的(边际的或条件的)分布。这种分解可以用来推导证据传播方法,从而在不确定条件下进行合理有效的推理。本课程从图形化模型的对应关系出发,简要介绍图形化模型的核心思想,并强调独立与分解之间的关系。此外,还讨论了模型构造和证据传播的基础,重点介绍了连接树的传播。这堂课的主要内容是从数据中学习图形模型,其中包括定量学习(参数估计)以及更复杂的定性或结构学习(模型选择)。讲座以对示例应用程序的简要讨论结束。
课程简介: In the last decade probabilistic graphical models - in particular Bayes networks and Markov networks - became very popular as tools for structuring uncertain knowledge about a domain of interest and for building knowledge-based systems that allow sound and efficient inferences about this domain. The core idea of graphical models is that usually certain independence relations hold between the attributes that are used to describe a domain of interest. In most uncertainty calculi -- and in particular in probability theory -- the structure of these independence relations is very similar to properties concerning the connectivity of nodes in a graph. As a consequence, it is tried to capture the independence relations by a graph, in which each node represents an attribute and each edge a direct dependence between attributes. In addition, provided that the graph captures only valid independences, it prescribes how a probability distribution on the (usually high-dimensional) space that is spanned by the attributes can be decomposed into a set of smaller (marginal or conditional) distributions. This decomposition can be exploited to derive evidence propagation methods and thus enables sound and efficient reasoning under uncertainty. The lecture gives a brief introduction into the core ideas underlying graphical models, starting from their relational counterparts and highlighting the relation between independence and decomposition. Furthermore, the basics of model construction and evidence propagation are discussed, with an emphasis on join/junction tree propagation. A substantial part of the lecture is then devoted to learning graphical models from data, in which quantitative learning (parameter estimation) as well as the more complex qualitative or structural learning (model selection) are studied. The lecture closes with a brief discussion of example applications.
关 键 词: 贝叶斯方法; 概率图形模型; 连接树
课程来源: 视频讲座网
最后编审: 2019-10-31:lxf
阅读次数: 71