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Moved page from wikipedia:en:Graphical model (history)
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{{More footnotes|date=May 2017}}
A '''graphical model''' or '''probabilistic graphical model''' ('''PGM''') or '''structured probabilistic model''' is a [[probabilistic model]] for which a [[Graph (discrete mathematics)|graph]] expresses the [[conditional dependence]] structure between [[random variable]]s. They are commonly used in [[probability theory]], [[statistics]]—particularly [[Bayesian statistics]]—and [[machine learning]].
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
图模型或概率图模型(PGM)或结构化概率模型是一种用图表示随机变量之间条件依赖结构的概率模型。它们通常用于概率论、统计学---- 尤其是贝叶斯统计学---- 和机器学习。
[[File:Graph model.svg|thumb|right|alt=An example of a graphical model.| An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent.]]
An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent.
一个图形模型的例子。每个箭头表示一个依赖项。在这个例子中: d 依赖于 a、 b 和 c; c 依赖于 b 和 d; 而 a 和 b 各自独立。
==Types of graphical models==
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or [[Factor graph|factorized]] representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, [[Bayesian network]]s and [[Markov random field]]s. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
一般来说，概率图模型使用基于图的表示作为对多维空间上的分布进行编码的基础，而图是一组独立分布的紧凑或分解表示。分布的图形表示常用的两个分支，即贝叶斯网络和马尔可夫随机场。这两个族都包含因子分解和独立性的性质，但是它们在它们可以编码的独立性集合和它们所诱导的分布的因子分解上有所不同。 09{ cite book
|author=Koller, D.
|author=Koller, D.
作者 Koller，d。
|author2=Friedman, N.
|author2=Friedman, N.
弗里德曼，n。
|title=Probabilistic Graphical Models
|title=Probabilistic Graphical Models
| 题目概率图形模型
|url=http://pgm.stanford.edu/
|url=http://pgm.stanford.edu/
Http://pgm.stanford.edu/
|publisher=MIT Press
|publisher=MIT Press
出版商: MIT 出版社
|location=Massachusetts
|location=Massachusetts
马萨诸塞州 | 地点
|year=2009
|year=2009
2009年
|pages=1208
|pages=1208
第1208页
|isbn=978-0-262-01319-2
|isbn=978-0-262-01319-2
[国际标准图书编号978-0-262-01319-2]
|doi=
|doi=
不会吧
|accessdate=
|accessdate=
访问日期
|author2-link=Nir Friedman
|author2-link=Nir Friedman
| author2-link Nir Friedman
|author-link=Daphne Koller
|author-link=Daphne Koller
作者链接 Daphne Koller
|archive-url=https://web.archive.org/web/20140427083249/http://pgm.stanford.edu/
|archive-url=https://web.archive.org/web/20140427083249/http://pgm.stanford.edu/
| 档案-网址 https://web.archive.org/web/20140427083249/http://pgm.stanford.edu/
|archive-date=2014-04-27
|archive-date=2014-04-27
| 档案-日期2014-04-27
|url-status=dead
|url-status=dead
状态死机
}}</ref>
}}</ref>
{} / ref
===Bayesian network===
{{main|Bayesian network}}
If the network structure of the model is a [[directed acyclic graph]], the model represents a factorization of the joint [[probability]] of all random variables. More precisely, if the events are <math>X_1,\ldots,X_n</math> then the joint probability satisfies
If the network structure of the model is a directed acyclic graph, the model represents a factorization of the joint probability of all random variables. More precisely, if the events are <math>X_1,\ldots,X_n</math> then the joint probability satisfies
如果模型的网络结构是有向无环图，则模型表示所有随机变量的联合概率的因子分解。更确切地说，如果事件是数学 x1， ldots，xn / math，那么联合概率满足
:<math>P[X_1,\ldots,X_n]=\prod_{i=1}^nP[X_i|\text{pa}(X_i)]</math>
<math>P[X_1,\ldots,X_n]=\prod_{i=1}^nP[X_i|\text{pa}(X_i)]</math>
数学 p [ x1， ldots，xn ] prod { i 1} nP [ xi | text { pa }(xi)] / math
where <math>\text{pa}(X_i)</math> is the set of parents of node <math>X_i</math> (nodes with edges directed towards <math>X_i</math>). In other words, the [[joint distribution]] factors into a product of conditional distributions. For example, the graphical model in the Figure shown above (which is actually not a directed acyclic graph, but an [[ancestral graph]]) consists of the random variables <math>A, B, C, D</math>
where <math>\text{pa}(X_i)</math> is the set of parents of node <math>X_i</math> (nodes with edges directed towards <math>X_i</math>). In other words, the joint distribution factors into a product of conditional distributions. For example, the graphical model in the Figure shown above (which is actually not a directed acyclic graph, but an ancestral graph) consists of the random variables <math>A, B, C, D</math>
其中 math text { pa }(xi) / math 是节点 math x i / math 的父节点集(边指向 math x i / math 的节点)。换句话说，联合分布因子成为条件分布的乘积。例如，上面图中的图形模型(实际上不是有向无环图，而是祖先的图形)由随机变量数学 a，b，c，d / math 组成
with a joint probability density that factors as
with a joint probability density that factors as
联合概率密度
:<math>P[A,B,C,D] = P[A]\cdot P[B]\cdot P[C,D|A,B]</math>
<math>P[A,B,C,D] = P[A]\cdot P[B]\cdot P[C,D|A,B]</math>
数学[ a，b，c，d ] p [ a ] cdot p [ b ] cdot p [ c，d | a，b ] / 数学
Any two nodes are [[Conditional independence|conditionally independent]] given the values of their parents. In general, any two sets of nodes are conditionally independent given a third set if a criterion called [[d-separation|''d''-separation]] holds in the graph. Local independences and global independences are equivalent in Bayesian networks.
Any two nodes are conditionally independent given the values of their parents. In general, any two sets of nodes are conditionally independent given a third set if a criterion called d-separation holds in the graph. Local independences and global independences are equivalent in Bayesian networks.
任何两个节点都是根据其父节点的值条件独立的。一般来说，如果一个称为 d- 分离的准则在图中成立，那么给定第三个集合的任意两组节点都是条件独立的。贝叶斯网络中的局部独立性和全局独立性是等价的。
This type of graphical model is known as a directed graphical model, [[Bayesian network]], or belief network. Classic machine learning models like [[hidden Markov models]], [[neural networks]] and newer models such as [[variable-order Markov model]]s can be considered special cases of Bayesian networks.
This type of graphical model is known as a directed graphical model, Bayesian network, or belief network. Classic machine learning models like hidden Markov models, neural networks and newer models such as variable-order Markov models can be considered special cases of Bayesian networks.
这种类型的图形模型被称为有向图形模型、贝氏网路或信念网络。经典的机器学习模型如隐马尔可夫模型、神经网络和新的模型如可变阶马尔可夫模型都可以看作是贝叶斯网络的特殊情况。
===Other types===
*[[Naive Bayes classifier]] where we use a tree with a single root
*[[Dependency network (graphical model)|Dependency network]] where cycles are allowed
*Tree-augmented classifier or '''TAN model'''
*A [[factor graph]] is an undirected [[bipartite graph]] connecting variables and factors. Each factor represents a function over the variables it is connected to. This is a helpful representation for understanding and implementing [[belief propagation]].
* A [[clique tree]] or junction tree is a [[tree (graph theory)|tree]] of [[clique (graph theory)|cliques]], used in the [[junction tree algorithm]].
* A [[chain graph]] is a graph which may have both directed and undirected edges, but without any directed cycles (i.e. if we start at any vertex and move along the graph respecting the directions of any arrows, we cannot return to the vertex we started from if we have passed an arrow). Both directed acyclic graphs and undirected graphs are special cases of chain graphs, which can therefore provide a way of unifying and generalizing Bayesian and Markov networks.<ref>{{cite journal|last=Frydenberg|first=Morten|year=1990|title=The Chain Graph Markov Property|journal=[[Scandinavian Journal of Statistics]]|volume=17|issue=4|pages=333–353|mr=1096723|jstor=4616181 }}
</ref>
</ref>
/ 参考
* An [[ancestral graph]] is a further extension, having directed, bidirected and undirected edges.<ref>{{cite journal
|first1=Thomas |last1=Richardson |first2=Peter |last2=Spirtes
|first1=Thomas |last1=Richardson |first2=Peter |last2=Spirtes
1 Thomas | last 1 Richardson | first2 Peter | last 2 Spirtes
|title=Ancestral graph Markov models
|title=Ancestral graph Markov models
| 标题祖先图马尔科夫模型
|journal=[[Annals of Statistics]]
|journal=Annals of Statistics
统计年鉴
|volume=30 |issue=4 |year=2002 |pages=962–1030
|volume=30 |issue=4 |year=2002 |pages=962–1030
第三十卷，第四期2002年，第962-1030页
|doi=10.1214/aos/1031689015
|doi=10.1214/aos/1031689015
|doi=10.1214/aos/1031689015
|mr=1926166 | zbl = 1033.60008
|mr=1926166 | zbl = 1033.60008
1926 / 166先生1033.60008
|citeseerx=10.1.1.33.4906}}</ref>
|citeseerx=10.1.1.33.4906}}</ref>
10.1.1.33.4906} / ref
* [[Random field]] techniques
** A [[Markov random field]], also known as a Markov network, is a model over an [[undirected graph]]. A graphical model with many repeated subunits can be represented with [[plate notation]].
** A [[conditional random field]] is a [[discriminative model]] specified over an undirected graph.
* A [[restricted Boltzmann machine]] is a [[Bipartite graph|bipartite]] [[generative model]] specified over an undirected graph.
==Applications==
The framework of the models, which provides algorithms for discovering and analyzing structure in complex distributions to describe them succinctly and extract the unstructured information, allows them to be constructed and utilized effectively.<ref name=koller09/> Applications of graphical models include [[causal inference]], [[information extraction]], [[speech recognition]], [[computer vision]], decoding of [[low-density parity-check codes]], modeling of [[gene regulatory network]]s, gene finding and diagnosis of diseases, and [[graphical models for protein structure]].
The framework of the models, which provides algorithms for discovering and analyzing structure in complex distributions to describe them succinctly and extract the unstructured information, allows them to be constructed and utilized effectively. Applications of graphical models include causal inference, information extraction, speech recognition, computer vision, decoding of low-density parity-check codes, modeling of gene regulatory networks, gene finding and diagnosis of diseases, and graphical models for protein structure.
该模型的框架为发现和分析复杂分布中的结构、简洁地描述结构和提取非结构化信息提供了算法，使模型得到有效的构建和利用。图形模型的应用包括因果推理、信息抽取、语音识别、计算机视觉、低密度奇偶校验码的解码、基因调控网络的建模、基因发现和疾病诊断，以及蛋白质结构的图形模型。
==See also==
* [[Belief propagation]]
* [[Structural equation model]]
==Notes==
{{reflist}}
==Further reading==
===Books and book chapters===
*{{cite book
| last = Barber
| last = Barber
理发师
| first = David
| first = David
首先是大卫
| title = Bayesian Reasoning and Machine Learning
| title = Bayesian Reasoning and Machine Learning
贝叶斯推理和机器学习
| publisher = Cambridge University Press
| publisher = Cambridge University Press
出版商剑桥大学出版社
| year = 2012
| year = 2012
2012年
| isbn = 978-0-521-51814-7
| isbn = 978-0-521-51814-7
[国际标准图书编号978-0-521-51814-7]
}}
}}
}}
* {{cite book
| last = Bishop
| last = Bishop
最后一个主教
| first = Christopher M.
| first = Christopher M.
首先是克里斯托弗 m。
| authorlink = Christopher Bishop
| authorlink = Christopher Bishop
克里斯托弗 · 毕晓普
| title = Pattern Recognition and Machine Learning
| title = Pattern Recognition and Machine Learning
模式识别与机器学习
| publisher = Springer
| publisher = Springer
出版商斯普林格
| year = 2006
| year = 2006
2006年
| url = https://www.springer.com/us/book/9780387310732
| url = https://www.springer.com/us/book/9780387310732
Https://www.springer.com/us/book/9780387310732
| isbn=978-0-387-31073-2
| isbn=978-0-387-31073-2
[国际标准图书编号978-0-387-31073-2]
| chapter= Chapter 8. Graphical Models
| chapter= Chapter 8. Graphical Models
| 第八章。图形模型
| chapterurl=https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/Bishop-PRML-sample.pdf
| chapterurl=https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/Bishop-PRML-sample.pdf
Https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/bishop-prml-sample.pdf
| pages=359–422
| pages=359–422
第359-422页
| mr=2247587
| mr=2247587
2247587先生
}}
}}
}}
* {{cite book
|author=Cowell, Robert G.
|author=Cowell, Robert G.
作者: 罗伯特 · g。
|author2=Dawid, A. Philip |author3=Lauritzen, Steffen L. |author4-link=David Spiegelhalter |author4=Spiegelhalter, David J.
|author2=Dawid, A. Philip |author3=Lauritzen, Steffen L. |author4-link=David Spiegelhalter |author4=Spiegelhalter, David J.
2 Dawid，a. Philip | author3 Lauritzen，Steffen l. | author4-link David Spiegelhalter | author4 Spiegelhalter，David j.
|title=Probabilistic networks and expert systems |publisher=Springer |location=Berlin |year=1999 |pages= |isbn=978-0-387-98767-5 |doi= |accessdate= |mr=1697175 |ref=cowell |author2-link=Philip Dawid }} A more advanced and statistically oriented book
|title=Probabilistic networks and expert systems |publisher=Springer |location=Berlin |year=1999 |pages= |isbn=978-0-387-98767-5 |doi= |accessdate= |mr=1697175 |ref=cowell |author2-link=Philip Dawid }} A more advanced and statistically oriented book
一本更先进和面向统计的书。1697175
* {{cite book |author=Jensen, Finn |title=An introduction to Bayesian networks |publisher=Springer |location=Berlin |year=1996 |pages= |isbn=978-0-387-91502-9 |doi= |accessdate=}}
* {{Cite book
|first=Judea |last=Pearl |authorlink = Judea Pearl
|first=Judea |last=Pearl |authorlink = Judea Pearl
朱迪亚珍珠
| year = 1988
| year = 1988
1988年
| title = Probabilistic Reasoning in Intelligent Systems
| title = Probabilistic Reasoning in Intelligent Systems
| 题目: 智能系统中的概率推理
| edition = 2nd revised
| edition = 2nd revised
第二版修订版
| location = San Mateo, CA
| location = San Mateo, CA
| 地点: 加利福尼亚州圣马特奥
| publisher = [[Morgan Kaufmann]]
| publisher = Morgan Kaufmann
出版商摩根 · 考夫曼
| mr = 0965765
| mr = 0965765
0965765先生
|isbn = 978-1-55860-479-7
|isbn = 978-1-55860-479-7
[国际标准图书编号978-1-55860-479-7]
}} A computational reasoning approach, where the relationships between graphs and probabilities were formally introduced.
}} A computational reasoning approach, where the relationships between graphs and probabilities were formally introduced.
一种计算推理方法，图和概率之间的关系被正式引入。
===Journal articles===
* {{Cite journal
| author = Edoardo M. Airoldi |authorlink1=Edoardo Airoldi
| author = Edoardo M. Airoldi |authorlink1=Edoardo Airoldi
1 Edoardo Airoldi
| title = Getting Started in Probabilistic Graphical Models
| title = Getting Started in Probabilistic Graphical Models
开始使用概率图模型
| journal = [[PLoS Computational Biology]]
| journal = PLoS Computational Biology
2012年3月24日 | PLoS 计算生物学
| volume = 3
| volume = 3
第三卷
| issue = 12
| issue = 12
第12期
| pages = e252
| pages = e252
第252页
| year = 2007
| year = 2007
2007年
| doi = 10.1371/journal.pcbi.0030252
| doi = 10.1371/journal.pcbi.0030252
10.1371 / journal.pcbi. 0030252
| pmid = 18069887
| pmid = 18069887
18069887
| pmc = 2134967
| pmc = 2134967
2134967
}}
}}
}}
*{{Cite journal | last1 = Jordan | first1 = M. I. | authorlink=Michael I. Jordan| doi = 10.1214/088342304000000026 | title = Graphical Models | journal = Statistical Science | volume = 19 | pages = 140–155| year = 2004 | pmid = | pmc = | doi-access = free }}
*{{Cite journal|last=Ghahramani|first=Zoubin|date=May 2015|title=Probabilistic machine learning and artificial intelligence|journal=Nature|language=English|volume=521|issue=7553|pages= 452–459|doi=10.1038/nature14541|pmid=26017444}}
===Other===
*[http://research.microsoft.com/en-us/um/people/heckerman/tutorial.pdf Heckerman's Bayes Net Learning Tutorial]
*[http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html A Brief Introduction to Graphical Models and Bayesian Networks]
*[http://www.cedar.buffalo.edu/~srihari/CSE574 Sargur Srihari's lecture slides on probabilistic graphical models]
==External links==
* [http://sandeep-aparajit.blogspot.com/2013/06/how-does-conditional-random-field-crf.html Graphical models and Conditional Random Fields]
* [https://www.cs.cmu.edu/~epxing/Class/10708/ Probabilistic Graphical Models taught by Eric Xing at CMU]
{{Statistics|analysis}}
[[Category:Bayesian statistics]]
Category:Bayesian statistics
类别: 贝叶斯统计
[[Category:Graphical models| ]]
<noinclude>
<small>This page was moved from [[wikipedia:en:Graphical model]]. Its edit history can be viewed at [[概率图模型/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{machine learning bar}}
{{More footnotes|date=May 2017}}
A '''graphical model''' or '''probabilistic graphical model''' ('''PGM''') or '''structured probabilistic model''' is a [[probabilistic model]] for which a [[Graph (discrete mathematics)|graph]] expresses the [[conditional dependence]] structure between [[random variable]]s. They are commonly used in [[probability theory]], [[statistics]]—particularly [[Bayesian statistics]]—and [[machine learning]].
A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
图模型或概率图模型(PGM)或结构化概率模型是一种用图表示随机变量之间条件依赖结构的概率模型。它们通常用于概率论、统计学---- 尤其是贝叶斯统计学---- 和机器学习。
[[File:Graph model.svg|thumb|right|alt=An example of a graphical model.| An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent.]]
An example of a graphical model. Each arrow indicates a dependency. In this example: D depends on A, B, and C; and C depends on B and D; whereas A and B are each independent.
一个图形模型的例子。每个箭头表示一个依赖项。在这个例子中: d 依赖于 a、 b 和 c; c 依赖于 b 和 d; 而 a 和 b 各自独立。
==Types of graphical models==
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or [[Factor graph|factorized]] representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, [[Bayesian network]]s and [[Markov random field]]s. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce.<ref name=koller09>{{cite book
一般来说，概率图模型使用基于图的表示作为对多维空间上的分布进行编码的基础，而图是一组独立分布的紧凑或分解表示。分布的图形表示常用的两个分支，即贝叶斯网络和马尔可夫随机场。这两个族都包含因子分解和独立性的性质，但是它们在它们可以编码的独立性集合和它们所诱导的分布的因子分解上有所不同。 09{ cite book
|author=Koller, D.
|author=Koller, D.
作者 Koller，d。
|author2=Friedman, N.
|author2=Friedman, N.
弗里德曼，n。
|title=Probabilistic Graphical Models
|title=Probabilistic Graphical Models
| 题目概率图形模型
|url=http://pgm.stanford.edu/
|url=http://pgm.stanford.edu/
Http://pgm.stanford.edu/
|publisher=MIT Press
|publisher=MIT Press
出版商: MIT 出版社
|location=Massachusetts
|location=Massachusetts
马萨诸塞州 | 地点
|year=2009
|year=2009
2009年
|pages=1208
|pages=1208
第1208页
|isbn=978-0-262-01319-2
|isbn=978-0-262-01319-2
[国际标准图书编号978-0-262-01319-2]
|doi=
|doi=
不会吧
|accessdate=
|accessdate=
访问日期
|author2-link=Nir Friedman
|author2-link=Nir Friedman
| author2-link Nir Friedman
|author-link=Daphne Koller
|author-link=Daphne Koller
作者链接 Daphne Koller
|archive-url=https://web.archive.org/web/20140427083249/http://pgm.stanford.edu/
|archive-url=https://web.archive.org/web/20140427083249/http://pgm.stanford.edu/
| 档案-网址 https://web.archive.org/web/20140427083249/http://pgm.stanford.edu/
|archive-date=2014-04-27
|archive-date=2014-04-27
| 档案-日期2014-04-27
|url-status=dead
|url-status=dead
状态死机
}}</ref>
}}</ref>
{} / ref
===Bayesian network===
{{main|Bayesian network}}
If the network structure of the model is a [[directed acyclic graph]], the model represents a factorization of the joint [[probability]] of all random variables. More precisely, if the events are <math>X_1,\ldots,X_n</math> then the joint probability satisfies
If the network structure of the model is a directed acyclic graph, the model represents a factorization of the joint probability of all random variables. More precisely, if the events are <math>X_1,\ldots,X_n</math> then the joint probability satisfies
如果模型的网络结构是有向无环图，则模型表示所有随机变量的联合概率的因子分解。更确切地说，如果事件是数学 x1， ldots，xn / math，那么联合概率满足
:<math>P[X_1,\ldots,X_n]=\prod_{i=1}^nP[X_i|\text{pa}(X_i)]</math>
<math>P[X_1,\ldots,X_n]=\prod_{i=1}^nP[X_i|\text{pa}(X_i)]</math>
数学 p [ x1， ldots，xn ] prod { i 1} nP [ xi | text { pa }(xi)] / math
where <math>\text{pa}(X_i)</math> is the set of parents of node <math>X_i</math> (nodes with edges directed towards <math>X_i</math>). In other words, the [[joint distribution]] factors into a product of conditional distributions. For example, the graphical model in the Figure shown above (which is actually not a directed acyclic graph, but an [[ancestral graph]]) consists of the random variables <math>A, B, C, D</math>
where <math>\text{pa}(X_i)</math> is the set of parents of node <math>X_i</math> (nodes with edges directed towards <math>X_i</math>). In other words, the joint distribution factors into a product of conditional distributions. For example, the graphical model in the Figure shown above (which is actually not a directed acyclic graph, but an ancestral graph) consists of the random variables <math>A, B, C, D</math>
其中 math text { pa }(xi) / math 是节点 math x i / math 的父节点集(边指向 math x i / math 的节点)。换句话说，联合分布因子成为条件分布的乘积。例如，上面图中的图形模型(实际上不是有向无环图，而是祖先的图形)由随机变量数学 a，b，c，d / math 组成
with a joint probability density that factors as
with a joint probability density that factors as
联合概率密度
:<math>P[A,B,C,D] = P[A]\cdot P[B]\cdot P[C,D|A,B]</math>
<math>P[A,B,C,D] = P[A]\cdot P[B]\cdot P[C,D|A,B]</math>
数学[ a，b，c，d ] p [ a ] cdot p [ b ] cdot p [ c，d | a，b ] / 数学
Any two nodes are [[Conditional independence|conditionally independent]] given the values of their parents. In general, any two sets of nodes are conditionally independent given a third set if a criterion called [[d-separation|''d''-separation]] holds in the graph. Local independences and global independences are equivalent in Bayesian networks.
Any two nodes are conditionally independent given the values of their parents. In general, any two sets of nodes are conditionally independent given a third set if a criterion called d-separation holds in the graph. Local independences and global independences are equivalent in Bayesian networks.
任何两个节点都是根据其父节点的值条件独立的。一般来说，如果一个称为 d- 分离的准则在图中成立，那么给定第三个集合的任意两组节点都是条件独立的。贝叶斯网络中的局部独立性和全局独立性是等价的。
This type of graphical model is known as a directed graphical model, [[Bayesian network]], or belief network. Classic machine learning models like [[hidden Markov models]], [[neural networks]] and newer models such as [[variable-order Markov model]]s can be considered special cases of Bayesian networks.
This type of graphical model is known as a directed graphical model, Bayesian network, or belief network. Classic machine learning models like hidden Markov models, neural networks and newer models such as variable-order Markov models can be considered special cases of Bayesian networks.
这种类型的图形模型被称为有向图形模型、贝氏网路或信念网络。经典的机器学习模型如隐马尔可夫模型、神经网络和新的模型如可变阶马尔可夫模型都可以看作是贝叶斯网络的特殊情况。
===Other types===
*[[Naive Bayes classifier]] where we use a tree with a single root
*[[Dependency network (graphical model)|Dependency network]] where cycles are allowed
*Tree-augmented classifier or '''TAN model'''
*A [[factor graph]] is an undirected [[bipartite graph]] connecting variables and factors. Each factor represents a function over the variables it is connected to. This is a helpful representation for understanding and implementing [[belief propagation]].
* A [[clique tree]] or junction tree is a [[tree (graph theory)|tree]] of [[clique (graph theory)|cliques]], used in the [[junction tree algorithm]].
* A [[chain graph]] is a graph which may have both directed and undirected edges, but without any directed cycles (i.e. if we start at any vertex and move along the graph respecting the directions of any arrows, we cannot return to the vertex we started from if we have passed an arrow). Both directed acyclic graphs and undirected graphs are special cases of chain graphs, which can therefore provide a way of unifying and generalizing Bayesian and Markov networks.<ref>{{cite journal|last=Frydenberg|first=Morten|year=1990|title=The Chain Graph Markov Property|journal=[[Scandinavian Journal of Statistics]]|volume=17|issue=4|pages=333–353|mr=1096723|jstor=4616181 }}
</ref>
</ref>
/ 参考
* An [[ancestral graph]] is a further extension, having directed, bidirected and undirected edges.<ref>{{cite journal
|first1=Thomas |last1=Richardson |first2=Peter |last2=Spirtes
|first1=Thomas |last1=Richardson |first2=Peter |last2=Spirtes
1 Thomas | last 1 Richardson | first2 Peter | last 2 Spirtes
|title=Ancestral graph Markov models
|title=Ancestral graph Markov models
| 标题祖先图马尔科夫模型
|journal=[[Annals of Statistics]]
|journal=Annals of Statistics
统计年鉴
|volume=30 |issue=4 |year=2002 |pages=962–1030
|volume=30 |issue=4 |year=2002 |pages=962–1030
第三十卷，第四期2002年，第962-1030页
|doi=10.1214/aos/1031689015
|doi=10.1214/aos/1031689015
|doi=10.1214/aos/1031689015
|mr=1926166 | zbl = 1033.60008
|mr=1926166 | zbl = 1033.60008
1926 / 166先生1033.60008
|citeseerx=10.1.1.33.4906}}</ref>
|citeseerx=10.1.1.33.4906}}</ref>
10.1.1.33.4906} / ref
* [[Random field]] techniques
** A [[Markov random field]], also known as a Markov network, is a model over an [[undirected graph]]. A graphical model with many repeated subunits can be represented with [[plate notation]].
** A [[conditional random field]] is a [[discriminative model]] specified over an undirected graph.
* A [[restricted Boltzmann machine]] is a [[Bipartite graph|bipartite]] [[generative model]] specified over an undirected graph.
==Applications==
The framework of the models, which provides algorithms for discovering and analyzing structure in complex distributions to describe them succinctly and extract the unstructured information, allows them to be constructed and utilized effectively.<ref name=koller09/> Applications of graphical models include [[causal inference]], [[information extraction]], [[speech recognition]], [[computer vision]], decoding of [[low-density parity-check codes]], modeling of [[gene regulatory network]]s, gene finding and diagnosis of diseases, and [[graphical models for protein structure]].
The framework of the models, which provides algorithms for discovering and analyzing structure in complex distributions to describe them succinctly and extract the unstructured information, allows them to be constructed and utilized effectively. Applications of graphical models include causal inference, information extraction, speech recognition, computer vision, decoding of low-density parity-check codes, modeling of gene regulatory networks, gene finding and diagnosis of diseases, and graphical models for protein structure.
该模型的框架为发现和分析复杂分布中的结构、简洁地描述结构和提取非结构化信息提供了算法，使模型得到有效的构建和利用。图形模型的应用包括因果推理、信息抽取、语音识别、计算机视觉、低密度奇偶校验码的解码、基因调控网络的建模、基因发现和疾病诊断，以及蛋白质结构的图形模型。
==See also==
* [[Belief propagation]]
* [[Structural equation model]]
==Notes==
{{reflist}}
==Further reading==
===Books and book chapters===
*{{cite book
| last = Barber
| last = Barber
理发师
| first = David
| first = David
首先是大卫
| title = Bayesian Reasoning and Machine Learning
| title = Bayesian Reasoning and Machine Learning
贝叶斯推理和机器学习
| publisher = Cambridge University Press
| publisher = Cambridge University Press
出版商剑桥大学出版社
| year = 2012
| year = 2012
2012年
| isbn = 978-0-521-51814-7
| isbn = 978-0-521-51814-7
[国际标准图书编号978-0-521-51814-7]
}}
}}
}}
* {{cite book
| last = Bishop
| last = Bishop
最后一个主教
| first = Christopher M.
| first = Christopher M.
首先是克里斯托弗 m。
| authorlink = Christopher Bishop
| authorlink = Christopher Bishop
克里斯托弗 · 毕晓普
| title = Pattern Recognition and Machine Learning
| title = Pattern Recognition and Machine Learning
模式识别与机器学习
| publisher = Springer
| publisher = Springer
出版商斯普林格
| year = 2006
| year = 2006
2006年
| url = https://www.springer.com/us/book/9780387310732
| url = https://www.springer.com/us/book/9780387310732
Https://www.springer.com/us/book/9780387310732
| isbn=978-0-387-31073-2
| isbn=978-0-387-31073-2
[国际标准图书编号978-0-387-31073-2]
| chapter= Chapter 8. Graphical Models
| chapter= Chapter 8. Graphical Models
| 第八章。图形模型
| chapterurl=https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/Bishop-PRML-sample.pdf
| chapterurl=https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/Bishop-PRML-sample.pdf
Https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/bishop-prml-sample.pdf
| pages=359–422
| pages=359–422
第359-422页
| mr=2247587
| mr=2247587
2247587先生
}}
}}
}}
* {{cite book
|author=Cowell, Robert G.
|author=Cowell, Robert G.
作者: 罗伯特 · g。
|author2=Dawid, A. Philip |author3=Lauritzen, Steffen L. |author4-link=David Spiegelhalter |author4=Spiegelhalter, David J.
|author2=Dawid, A. Philip |author3=Lauritzen, Steffen L. |author4-link=David Spiegelhalter |author4=Spiegelhalter, David J.
2 Dawid，a. Philip | author3 Lauritzen，Steffen l. | author4-link David Spiegelhalter | author4 Spiegelhalter，David j.
|title=Probabilistic networks and expert systems |publisher=Springer |location=Berlin |year=1999 |pages= |isbn=978-0-387-98767-5 |doi= |accessdate= |mr=1697175 |ref=cowell |author2-link=Philip Dawid }} A more advanced and statistically oriented book
|title=Probabilistic networks and expert systems |publisher=Springer |location=Berlin |year=1999 |pages= |isbn=978-0-387-98767-5 |doi= |accessdate= |mr=1697175 |ref=cowell |author2-link=Philip Dawid }} A more advanced and statistically oriented book
一本更先进和面向统计的书。1697175
* {{cite book |author=Jensen, Finn |title=An introduction to Bayesian networks |publisher=Springer |location=Berlin |year=1996 |pages= |isbn=978-0-387-91502-9 |doi= |accessdate=}}
* {{Cite book
|first=Judea |last=Pearl |authorlink = Judea Pearl
|first=Judea |last=Pearl |authorlink = Judea Pearl
朱迪亚珍珠
| year = 1988
| year = 1988
1988年
| title = Probabilistic Reasoning in Intelligent Systems
| title = Probabilistic Reasoning in Intelligent Systems
| 题目: 智能系统中的概率推理
| edition = 2nd revised
| edition = 2nd revised
第二版修订版
| location = San Mateo, CA
| location = San Mateo, CA
| 地点: 加利福尼亚州圣马特奥
| publisher = [[Morgan Kaufmann]]
| publisher = Morgan Kaufmann
出版商摩根 · 考夫曼
| mr = 0965765
| mr = 0965765
0965765先生
|isbn = 978-1-55860-479-7
|isbn = 978-1-55860-479-7
[国际标准图书编号978-1-55860-479-7]
}} A computational reasoning approach, where the relationships between graphs and probabilities were formally introduced.
}} A computational reasoning approach, where the relationships between graphs and probabilities were formally introduced.
一种计算推理方法，图和概率之间的关系被正式引入。
===Journal articles===
* {{Cite journal
| author = Edoardo M. Airoldi |authorlink1=Edoardo Airoldi
| author = Edoardo M. Airoldi |authorlink1=Edoardo Airoldi
1 Edoardo Airoldi
| title = Getting Started in Probabilistic Graphical Models
| title = Getting Started in Probabilistic Graphical Models
开始使用概率图模型
| journal = [[PLoS Computational Biology]]
| journal = PLoS Computational Biology
2012年3月24日 | PLoS 计算生物学
| volume = 3
| volume = 3
第三卷
| issue = 12
| issue = 12
第12期
| pages = e252
| pages = e252
第252页
| year = 2007
| year = 2007
2007年
| doi = 10.1371/journal.pcbi.0030252
| doi = 10.1371/journal.pcbi.0030252
10.1371 / journal.pcbi. 0030252
| pmid = 18069887
| pmid = 18069887
18069887
| pmc = 2134967
| pmc = 2134967
2134967
}}
}}
}}
*{{Cite journal | last1 = Jordan | first1 = M. I. | authorlink=Michael I. Jordan| doi = 10.1214/088342304000000026 | title = Graphical Models | journal = Statistical Science | volume = 19 | pages = 140–155| year = 2004 | pmid = | pmc = | doi-access = free }}
*{{Cite journal|last=Ghahramani|first=Zoubin|date=May 2015|title=Probabilistic machine learning and artificial intelligence|journal=Nature|language=English|volume=521|issue=7553|pages= 452–459|doi=10.1038/nature14541|pmid=26017444}}
===Other===
*[http://research.microsoft.com/en-us/um/people/heckerman/tutorial.pdf Heckerman's Bayes Net Learning Tutorial]
*[http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html A Brief Introduction to Graphical Models and Bayesian Networks]
*[http://www.cedar.buffalo.edu/~srihari/CSE574 Sargur Srihari's lecture slides on probabilistic graphical models]
==External links==
* [http://sandeep-aparajit.blogspot.com/2013/06/how-does-conditional-random-field-crf.html Graphical models and Conditional Random Fields]
* [https://www.cs.cmu.edu/~epxing/Class/10708/ Probabilistic Graphical Models taught by Eric Xing at CMU]
{{Statistics|analysis}}
[[Category:Bayesian statistics]]
Category:Bayesian statistics
类别: 贝叶斯统计
[[Category:Graphical models| ]]
<noinclude>
<small>This page was moved from [[wikipedia:en:Graphical model]]. Its edit history can be viewed at [[概率图模型/edithistory]]</small></noinclude>
[[Category:待整理页面]]