贝叶斯网络模型的例子详解,贝叶斯网络三种基本模型

笔者近期在学习贝叶斯网络模型相关知识的时候，分别使用了Matlab、python、R、Netica、GeNIe、unbbayes等。这些软件各有千秋，但是R语言必须安利给大家，希望大家指正。

R语言
R是用于统计分析、绘图的语言和操作环境。R是属于GNU系统的一个自由、免费、源代码开放的软件，它是一个用于统计计算和统计制图的优秀工具。
那么为什么特别推荐R呢？
图美、上手快、效率高

安装R语言

R语言也是要安装的，不安装怎么用呢？目前按照操作习惯可以划分为两种：R Console和R stuido。

R Console

下载地址为：https://cran.r-project.org，进入以后根据自己的电脑版本对号入座，此处不再赘述。安装完成后如图。

R stuido

下载地址： http://www.rstudio.com/ide,老规矩还是对号入座，可以发现有Desktop和Server两个版本，我们选择Desktop。这个笔者并没有安装，所以就不在这分享了。

贝叶斯网络模型包

bnlearn is an R package for learning the graphical structure of Bayesian networks, estimate their parameters and perform some useful inference. It was first released in 2007, it has been been under continuous development for more than 10 years (and still going strong). To get started and install the latest development snapshot type.

安装bnlearn包

二者选其一即可，安装的过程中会提示选择服务器，随便选择一个服务器即可。

install.packages("bnlearn") install.packages("https://www.bnlearn.com/releases/bnlearn_latest.tar.gz") 导入bnlearn包 library("bnlearn")bn.boot

如果返回下图证明导入成功。

创建贝叶斯网络模型 空网络 e = empty.graph(LETTERS[1:6])class(e)e

第一个语句代表建立一个贝叶斯网络，第二个语句是查看变量内容，第三个语句是查看变量类型。

非空网络 cptA = matrix(c(0.4, 0.6), ncol = 2, dimnames = list(NULL, c("LOW", "HIGH")))cptB = matrix(c(0.8, 0.2), ncol = 2, dimnames = list(NULL, c("GOOD", "BAD")))cptC = c(0.5, 0.5, 0.4, 0.6, 0.3, 0.7, 0.2, 0.8)dim(cptC) = c(2, 2, 2)dimnames(cptC) = list("C" = c("TRUE", "FALSE"), "A" = c("LOW", "HIGH"),"B" = c("GOOD", "BAD"))net = model2network("[A][B][C|A:B]")dfit = custom.fit(net, dist = list(A = cptA, B = cptB, C = cptC))dfit

打印模型与参数

参数学习 data(learning.test)pdag = iamb(learning.test)score(set.arc(pdag, from = "A", to = "B"), learning.test)score(set.arc(pdag, from = "B", to = "A"), learning.test)fit = bn.fit(dag, learning.test)

学习结果如下

Bayesian network parameters Parameters of node A (multinomial distribution)Conditional probability table: a b c0.334 0.334 0.332 Parameters of node B (multinomial distribution)Conditional probability table: AB a b c a 0.8561 0.4449 0.1149 b 0.0252 0.2210 0.0945 c 0.1187 0.3341 0.7906 Parameters of node C (multinomial distribution)Conditional probability table: a b c0.7434 0.2048 0.0518 Parameters of node D (multinomial distribution)Conditional probability table:, , C = a AD a b c a 0.8008 0.0925 0.1053 b 0.0902 0.8021 0.1117 c 0.1089 0.1054 0.7830, , C = b AD a b c a 0.1808 0.8830 0.2470 b 0.1328 0.0702 0.4939 c 0.6864 0.0468 0.2591, , C = c AD a b c a 0.4286 0.3412 0.1333 b 0.2024 0.3882 0.4444 c 0.3690 0.2706 0.4222 Parameters of node E (multinomial distribution)Conditional probability table:, , F = a BE a b c a 0.8052 0.2059 0.1194 b 0.0974 0.1797 0.1145 c 0.0974 0.6144 0.7661, , F = b BE a b c a 0.4005 0.3168 0.2376 b 0.4903 0.3664 0.5067 c 0.1092 0.3168 0.2557 Parameters of node F (multinomial distribution)Conditional probability table: a b0.502 0.498 结构学习 data(learning.test)data(gaussian.test)learn.net = empty.graph(names(learning.test))modelstring(learn.net) = "[A][C][F][B|A][D|A:C][E|B:F]"gauss.net = empty.graph(names(gaussian.test))modelstring(gauss.net) = "[A][B][E][G][C|A:B][D|B][F|A:D:E:G]"score(learn.net, learning.test)score(gauss.net, gaussian.test)score(learn.net, learning.test, type = "bic")score(learn.net, learning.test, type = "aic")score(learn.net, learning.test, type = "bde")

以上分别使用bic、aic、bde评分标准进行结构打分。

参考文献

[1] https://www.bnlearn.com/examples/
[2] zjdyj, kddyc. 贝叶斯网络结构学习综述[J]. 计算机应用研究, 2015(3).
[3] Scutari M . Bayesian network models for incomplete and dynamic data[J]. Stata Neerlandica, 2020(7).
[4] Scutari M , Vitolo C , Tucker A . Learning Bayesian networks from big data with greedy search: computational complexity and efficient implementation[J]. Stats and Computing, 2019, 29(5):1095-1108.
[5] Scutari M . Dirichlet Bayesian Network Scores and the Maximum Relative Entropy Principle[J]. Behaviormetrika, 2018(11):337-362.