概率图模型(一):贝叶斯网络

本文概述了斯坦福大学概率图模型课程中关于贝叶斯网络的内容,包括其定义(有向无环图DAG,条件概率分布CPD),概率影响的流动,如V结构和d-separation,条件独立的概念以及I-map和朴素贝叶斯模型的原理。

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这部分文章主要是总结斯坦福大学的概率图模型课程(coursera链接
Graohical Model主要分为两种:
贝叶斯网络(Bayesian Network)和马尔科夫随机场(Markov Network)
概率图理论共分为三个部分:
概率图模型表示理论、概率图模型推理理论和概率图模型学习理论。

贝叶斯网络基础

Semantics & Factorization

首先用一个学生成绩的例子引出了贝叶斯网络的定义

贝叶斯网络是一个有向无环图(directed acyclic graph, DAG)G,其中节点表示的是随机变量 X1,...,Xn ;对每一个节点 Xi 有一个条件概率分布(conditional probility distribution, CPD) P(Xi|ParG(Xi)) ,其中 Pa

Bayesian model selection is a fundamental part of the Bayesian statistical modeling process. In principle, the Bayesian analysis is straightforward. Specifying the data sampling and prior distributions, a joint probability distribution is used to express the relationships between all the unknowns and the data information. Bayesian inference is implemented based on the posterior distribution, the conditional probability distribution of the unknowns given the data information. The results from the Bayesian posterior inference are then used for the decision making, forecasting, stochastic structure explorations and many other problems. However, the quality of these solutions usually depends on the quality of the constructed Bayesian models. This crucial issue has been realized by researchers and practitioners. Therefore, the Bayesian model selection problems have been extensively investigated. The Bayesian inference on a statistical model was previously complex. It is now possible to implement the various types of the Bayesian inference thanks to advances in computing technology and the use of new sampling methods, including Markov chain Monte Carlo (MCMC). Such developments together with the availability of statistical software have facilitated a rapid growth in the utilization of Bayesian statistical modeling through the computer simulations. Nonetheless, model selection is central to all Bayesian statistical modeling. There is a growing need for evaluating the Bayesian models constructed by the simulation methods.
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