贝叶斯与概率图模型（PGM）

作者

Simonzhou

发布于

2025年2月28日

修改于

2025年4月28日

1 概率图模型（Probabilistic Graphical Models）

概率图模型是一种结合概率论与图论的理论框架，用于表示和分析复杂系统中的不确定性及概率关系。

1.1 常见类型

贝叶斯网络
马尔科夫随机场（MRF)
隐马尔科夫模型（HMM)

1.2 用R来展示概率图模型

1.2.1 使用R程序包`gRain`。

安装：

install.packages("gRain")

加载：

library("gRbase")

首先定义一个带有变量的A、B、C、D、E的简单无向图

graph <- ug("A:B:E + C:E:D")
class(graph)

[1] "igraph"

安装可视化程序包，使用流行的Rgraphviz

Rgraphviz是 Bioconductor 生态系统的一部分，所以可以通过 Bioconductor 来安装它。首先要确保已经安装了BiocManager，若未安装，可使用以下代码进行安装：

if (!require("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

安装好BiocManager之后，使用它来安装Rgraphviz：

BiocManager::install("Rgraphviz")

载入并使用：

library("Rgraphviz")
plot(graph)

定义有向图：

dag <- dag("A + B:A + C:B + D:B + E:C:D")
dag

IGRAPH 28898ca DN-- 1 0 -- 
+ attr: name (v/c)
+ edges from 28898ca (vertex names):

plot(dag)

1.3 报错

报错：无法正确显示图形

原因：Rgraphviz 没有被正确的安装。

需要从 bioconductor 中安装：

> install.packages("Rgraphviz")
Installing package into 'C:/Users/asus/AppData/Local/R/win-library/4.4'
(as 'lib' is unspecified)
Warning message:
package 'Rgraphviz' is not available for this version of R

A version of this package for your version of R might be available elsewhere,
see the ideas at
https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages

当使用 bidconductor 源来安装 Rgraphviz ，首先安装 BiocManager ：

> if (!require("BiocManager", quietly = TRUE))
+     install.packages("BiocManager")
Installing package into 'C:/Users/asus/AppData/Local/R/win-library/4.4'
(as 'lib' is unspecified)
trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/BiocManager_1.30.25.zip'
Content type 'application/zip' length 506482 bytes (494 KB)
downloaded 494 KB

package 'BiocManager' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
        C:\Users\asus\AppData\Local\Temp\RtmpSCcZNG\downloaded_packages

然后使用 BiocManager 安装 Rgraphviz ，需要安装的配套程序包很多，需要几分钟，但是这里出现了报错。

> BiocManager::install("Rgraphviz")
'getOption("repos")' replaces Bioconductor standard repositories, see
'help("repositories", package = "BiocManager")' for details.
Replacement repositories:
    CRAN: https://mirrors.sustech.edu.cn/CRAN
Bioconductor version 3.20 (BiocManager 1.30.25), R 4.4.2 (2024-10-31 ucrt)
Installing package(s) 'BiocVersion', 'Rgraphviz'
also installing the dependencies 'BiocGenerics', 'graph'

trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/BiocGenerics_0.52.0.zip'
libpng warning: iCCP: known incorrect sRGB profile
libpng warning: iCCP: known incorrect sRGB profile
Content type 'application/zip' length 639558 bytes (624 KB)
downloaded 624 KB

trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/graph_1.84.1.zip'
Content type 'application/zip' length 2173761 bytes (2.1 MB)
downloaded 2.1 MB

trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/BiocVersion_3.20.0.zip'
Content type 'application/zip' length 8386 bytes
downloaded 8386 bytes

trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/Rgraphviz_2.50.0.zip'
Content type 'application/zip' length 1457153 bytes (1.4 MB)
downloaded 1.4 MB

package 'BiocGenerics' successfully unpacked and MD5 sums checked
package 'graph' successfully unpacked and MD5 sums checked
package 'BiocVersion' successfully unpacked and MD5 sums checked
package 'Rgraphviz' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
        C:\Users\asus\AppData\Local\Temp\RtmpSCcZNG\downloaded_packages
Installation paths not writeable, unable to update packages
  path: C:/Program Files/R/R-4.4.2/library
  packages:
    class, cli, cluster, curl, data.table, foreign, glue, jsonlite, KernSmooth,
    lintr, MASS, Matrix, nlme, nnet, processx, ps, purrr, R.utils, R6, renv,
    reticulate, rlang, rpart, sessioninfo, spatial, survival, tinytex, xfun,
    xml2, zoo
Old packages: 'httpgd', 'readxl', 'unigd'
apdate all/some/none? [a/s/n]:
trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/httpgd_2.0.3.zip'
Content type 'application/zip' length 874316 bytes (853 KB)
downloaded 853 KB

trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/readxl_1.4.4.zip' 
Content type 'application/zip' length 750422 bytes (732 KB)
downloaded 732 KB

trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/unigd_0.1.3.zip'
Content type 'application/zip' length 5591347 bytes (5.3 MB)
downloaded 5.3 MB

package 'httpgd' successfully unpacked and MD5 sums checked
package 'readxl' successfully unpacked and MD5 sums checked
Warning: cannot remove prior installation of package 'readxl'
Warning: restored 'readxl'
package 'unigd' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
        C:\Users\asus\AppData\Local\Temp\RtmpSCcZNG\downloaded_packages
Warning message:
In file.copy(savedcopy, lib, recursive = TRUE) :
  problem copying C:\Users\asus\AppData\Local\R\win-library\4.4\00LOCK\readxl\libs\x64\readxl.dll to C:\Users\asus\AppData\Local\R\win-library\4.4\readxl\libs\x64\readxl.dll: Permission denied

主要问题是没有写入权限，这可能和在 vscode 中安装有关，因此，换到 R 的终端中进行安装（注意，可能需要使用管理员权限），但是仍然免不了一系列的包冲突问题，需要根据提示选择操作：

使用管理员身份运行 R 。
选择合适的源来下载。

处理有冲突的包（卸载），或者重新创建一个 env 。

 # 删除 readxl 包
 readxl_path <- system.file(package = "readxl")
 if (!is.na(readxl_path)) {
 unlink(readxl_path, recursive = TRUE)
 }
 # 删除 cli 包
 cli_path <- system.file(package = "cli")
 if (!is.na(cli_path)) {
 unlink(cli_path, recursive = TRUE)
 }
 # 再次尝试安装 Rgraphviz
 BiocManager::install("Rgraphviz")

强制更新，忽略冲突

有些包的版本已经是最新的，但安装过程仍然提示需要更新，你可以使用 force = TRUE 参数强制重新安装。

BiocManager::install("Rgraphviz", force = TRUE)

具体信息如下：

> BiocManager::install("Rgraphviz")
'getOption("repos")' replaces Bioconductor standard repositories, see
'help("repositories", package = "BiocManager")' for details.
Replacement repositories:
    CRAN: https://mirrors.nju.edu.cn/CRAN
Bioconductor version 3.20 (BiocManager 1.30.25), R 4.4.2 (2024-10-31 ucrt)
Warning message:
package(s) not installed when version(s) same as or greater than current; use
  `force = TRUE` to re-install: 'Rgraphviz' 
> BiocManager::install("Rgraphviz", force = TRUE)
'getOption("repos")' replaces Bioconductor standard repositories, see
'help("repositories", package = "BiocManager")' for details.
Replacement repositories:
    CRAN: https://mirrors.nju.edu.cn/CRAN
Bioconductor version 3.20 (BiocManager 1.30.25), R 4.4.2 (2024-10-31 ucrt)
Installing package(s) 'Rgraphviz'
trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/Rgraphviz_2.50.0.zip'
Content type 'application/zip' length 1457153 bytes (1.4 MB)
downloaded 1.4 MB

package ‘Rgraphviz’ successfully unpacked and MD5 sums checked

The downloaded binary packages are in
        C:\Users\asus\AppData\Local\Temp\Rtmp2j7SlA\downloaded_packages

1.4 灯泡机的简单概率图模型

首先，为每一个节点定义取值：

machine_val <- c("working", "broken")
light_bulb_val <- c("good", "bad")

为两个随机变量定义百分比数值：

machine_val <- c(99,1)
light_bulb_val <- c(99,1,60,40)

使用 gRain 定义随机变量：

library(gRain)
M <- cptable(~machine, values = machine_prob,
            levels = machine_val)
L <- cptable(~light_bulb | machine,
            values = light_bulb_prob,
            levels = light_bulb_val)

这里的 cptable 表示条件概率表¹：它是离散型随机变量概率分布的内存表示²。

1.4.1 构建新的概率图模型

plist <- compileCPT(list(M,L))
plist

输出结果如上，这里可以清楚地看到之前定义的概率分布

2025.04.05 再次尝试复现程序，失败，暂时停止概率图R程序的复现工作。

end.

脚注

条件概率表（Conditional Probability Table, CPT），是一种表格形式的数据结构，用来描述离散型随机变量之间的概率关系。通常用于表示一个变量（或一组变量）的概率分布，可能依赖于其他变量（条件变量）。↩︎
“内存表示”指的是在计算机程序中，这种概率分布被组织和存储为一种数据结构（例如表格、数组或矩阵），以便程序可以高效地访问和操作这些概率值。具体来说，cptable 函数会根据你提供的参数（如 values 和 levels）生成一个对象，这个对象在内存中以某种形式存储了变量的概率分布。↩︎

--- title: "贝叶斯与概率图模型（PGM）" author: "Simonzhou" date: "2025-02-28" date-modified: "today" #format: # html: # 输出格式为 HTML # self-contained: true # 生成独立的 HTML 文件 # pdf: # 可选：如果需要 PDF 输出 # default execute: echo: true # 在输出中显示代码 eval: true # 执行代码 warning: false # 隐藏警告信息 message: false # 隐藏消息 --- # 概率图模型（Probabilistic Graphical Models）概率图模型是一种结合概率论与图论的理论框架，用于表示和分析复杂系统中的不确定性及概率关系。 ## 常见类型 - 贝叶斯网络 - 马尔科夫随机场（MRF) - 隐马尔科夫模型（HMM) ## 用R来展示概率图模型 ### 使用R程序包`gRain`。安装： ```{r,eval = FALSE} install.packages("gRain") ``` 加载： ```{r} library("gRbase") ``` 首先定义一个带有变量的A、B、C、D、E的简单无向图 ```{r} graph <- ug("A:B:E + C:E:D") class(graph) ``` 安装可视化程序包，使用流行的`Rgraphviz` `Rgraphviz`是 Bioconductor 生态系统的一部分，所以可以通过 Bioconductor 来安装它。首先要确保已经安装了`BiocManager`，若未安装，可使用以下代码进行安装： ```{r, eval = FALSE} if (!require("BiocManager", quietly = TRUE)) install.packages("BiocManager") ``` 安装好`BiocManager`之后，使用它来安装`Rgraphviz`： ```{r, eval = FALSE} BiocManager::install("Rgraphviz") ``` 载入并使用： ```{r} library("Rgraphviz") plot(graph) ``` 定义有向图： ```{r} dag <- dag("A + B:A + C:B + D:B + E:C:D") dag plot(dag) ``` ## 报错报错：无法正确显示图形原因：`Rgraphviz` 没有被正确的安装。需要从 `bioconductor` 中安装： ```{bash,eval = FALSE} > install.packages("Rgraphviz") Installing package into 'C:/Users/asus/AppData/Local/R/win-library/4.4' (as 'lib' is unspecified) Warning message: package 'Rgraphviz' is not available for this version of R A version of this package for your version of R might be available elsewhere, see the ideas at https://cran.r-project.org/doc/manuals/r-patched/R-admin.html#Installing-packages ``` 当使用 `bidconductor` 源来安装 `Rgraphviz` ，首先安装 `BiocManager` ： ```{bash, eval = FALSE} > if (!require("BiocManager", quietly = TRUE)) + install.packages("BiocManager") Installing package into 'C:/Users/asus/AppData/Local/R/win-library/4.4' (as 'lib' is unspecified) trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/BiocManager_1.30.25.zip' Content type 'application/zip' length 506482 bytes (494 KB) downloaded 494 KB package 'BiocManager' successfully unpacked and MD5 sums checked The downloaded binary packages are in C:\Users\asus\AppData\Local\Temp\RtmpSCcZNG\downloaded_packages ``` 然后使用 `BiocManager` 安装 `Rgraphviz` ，需要安装的配套程序包很多，需要几分钟，但是这里出现了报错。 ```{bash, eval = FALSE} > BiocManager::install("Rgraphviz") 'getOption("repos")' replaces Bioconductor standard repositories, see 'help("repositories", package = "BiocManager")' for details. Replacement repositories: CRAN: https://mirrors.sustech.edu.cn/CRAN Bioconductor version 3.20 (BiocManager 1.30.25), R 4.4.2 (2024-10-31 ucrt) Installing package(s) 'BiocVersion', 'Rgraphviz' also installing the dependencies 'BiocGenerics', 'graph' trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/BiocGenerics_0.52.0.zip' libpng warning: iCCP: known incorrect sRGB profile libpng warning: iCCP: known incorrect sRGB profile Content type 'application/zip' length 639558 bytes (624 KB) downloaded 624 KB trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/graph_1.84.1.zip' Content type 'application/zip' length 2173761 bytes (2.1 MB) downloaded 2.1 MB trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/BiocVersion_3.20.0.zip' Content type 'application/zip' length 8386 bytes downloaded 8386 bytes trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/Rgraphviz_2.50.0.zip' Content type 'application/zip' length 1457153 bytes (1.4 MB) downloaded 1.4 MB package 'BiocGenerics' successfully unpacked and MD5 sums checked package 'graph' successfully unpacked and MD5 sums checked package 'BiocVersion' successfully unpacked and MD5 sums checked package 'Rgraphviz' successfully unpacked and MD5 sums checked The downloaded binary packages are in C:\Users\asus\AppData\Local\Temp\RtmpSCcZNG\downloaded_packages Installation paths not writeable, unable to update packages path: C:/Program Files/R/R-4.4.2/library packages: class, cli, cluster, curl, data.table, foreign, glue, jsonlite, KernSmooth, lintr, MASS, Matrix, nlme, nnet, processx, ps, purrr, R.utils, R6, renv, reticulate, rlang, rpart, sessioninfo, spatial, survival, tinytex, xfun, xml2, zoo Old packages: 'httpgd', 'readxl', 'unigd' apdate all/some/none? [a/s/n]: trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/httpgd_2.0.3.zip' Content type 'application/zip' length 874316 bytes (853 KB) downloaded 853 KB trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/readxl_1.4.4.zip' Content type 'application/zip' length 750422 bytes (732 KB) downloaded 732 KB trying URL 'https://mirrors.sustech.edu.cn/CRAN/bin/windows/contrib/4.4/unigd_0.1.3.zip' Content type 'application/zip' length 5591347 bytes (5.3 MB) downloaded 5.3 MB package 'httpgd' successfully unpacked and MD5 sums checked package 'readxl' successfully unpacked and MD5 sums checked Warning: cannot remove prior installation of package 'readxl' Warning: restored 'readxl' package 'unigd' successfully unpacked and MD5 sums checked The downloaded binary packages are in C:\Users\asus\AppData\Local\Temp\RtmpSCcZNG\downloaded_packages Warning message: In file.copy(savedcopy, lib, recursive = TRUE) : problem copying C:\Users\asus\AppData\Local\R\win-library\4.4\00LOCK\readxl\libs\x64\readxl.dll to C:\Users\asus\AppData\Local\R\win-library\4.4\readxl\libs\x64\readxl.dll: Permission denied ``` 主要问题是没有写入权限，这可能和在 vscode 中安装有关，因此，换到 R 的终端中进行安装（注意，可能需要使用管理员权限），但是仍然免不了一系列的包冲突问题，需要根据提示选择操作： 1. 使用管理员身份运行 R 。 2. 选择合适的源来下载。 3. 处理有冲突的包（卸载），或者重新创建一个 env 。 ```{r, eval = FALSE} # 删除 readxl 包 readxl_path <- system.file(package = "readxl") if (!is.na(readxl_path)) { unlink(readxl_path, recursive = TRUE) } # 删除 cli 包 cli_path <- system.file(package = "cli") if (!is.na(cli_path)) { unlink(cli_path, recursive = TRUE) } # 再次尝试安装 Rgraphviz BiocManager::install("Rgraphviz") ``` 4. 强制更新，忽略冲突有些包的版本已经是最新的，但安装过程仍然提示需要更新，你可以使用 `force = TRUE` 参数强制重新安装。 ```{r, eval = FALSE} BiocManager::install("Rgraphviz", force = TRUE) ``` 5. 具体信息如下： ```{r, eval = FALSE} > BiocManager::install("Rgraphviz") 'getOption("repos")' replaces Bioconductor standard repositories, see 'help("repositories", package = "BiocManager")' for details. Replacement repositories: CRAN: https://mirrors.nju.edu.cn/CRAN Bioconductor version 3.20 (BiocManager 1.30.25), R 4.4.2 (2024-10-31 ucrt) Warning message: package(s) not installed when version(s) same as or greater than current; use `force = TRUE` to re-install: 'Rgraphviz' > BiocManager::install("Rgraphviz", force = TRUE) 'getOption("repos")' replaces Bioconductor standard repositories, see 'help("repositories", package = "BiocManager")' for details. Replacement repositories: CRAN: https://mirrors.nju.edu.cn/CRAN Bioconductor version 3.20 (BiocManager 1.30.25), R 4.4.2 (2024-10-31 ucrt) Installing package(s) 'Rgraphviz' trying URL 'https://bioconductor.org/packages/3.20/bioc/bin/windows/contrib/4.4/Rgraphviz_2.50.0.zip' Content type 'application/zip' length 1457153 bytes (1.4 MB) downloaded 1.4 MB package ‘Rgraphviz’ successfully unpacked and MD5 sums checked The downloaded binary packages are in C:\Users\asus\AppData\Local\Temp\Rtmp2j7SlA\downloaded_packages ``` ## 灯泡机的简单概率图模型首先，为每一个节点定义取值： ```{r,eval = FALSE} machine_val <- c("working", "broken") light_bulb_val <- c("good", "bad") ``` 为两个随机变量定义百分比数值： ```{r,eval = FALSE} machine_val <- c(99,1) light_bulb_val <- c(99,1,60,40) ``` 使用 gRain 定义随机变量： ```{r,eval=FALSE} library(gRain) M <- cptable(~machine, values = machine_prob, levels = machine_val) L <- cptable(~light_bulb | machine, values = light_bulb_prob, levels = light_bulb_val) ``` 这里的 `cptable` 表示条件概率表[^1]：它是离散型随机变量概率分布的内存表示[^2]。 [^1]: 条件概率表（Conditional Probability Table, CPT），是一种表格形式的数据结构，用来描述离散型随机变量之间的概率关系。通常用于表示一个变量（或一组变量）的概率分布，可能依赖于其他变量（条件变量）。 [^2]: “内存表示”指的是在计算机程序中，这种概率分布被组织和存储为一种数据结构（例如表格、数组或矩阵），以便程序可以高效地访问和操作这些概率值。具体来说，`cptable` 函数会根据你提供的参数（如 `values` 和 `levels`）生成一个对象，这个对象在内存中以某种形式存储了变量的概率分布。 ### 构建新的概率图模型 ```{r,eval=FALSE} plist <- compileCPT(list(M,L)) plist ``` 输出结果如上，这里可以清楚地看到之前定义的概率分布 2025.04.05 再次尝试复现程序，失败，暂时停止概率图R程序的复现工作。 end.