马尔可夫随机场 (Markov's Random Fields)

Markov random model is a model which use an undirected graph. Undirected graphical models edge represents the potential between two variables, syntactically, Factorization distribution probabilities between variable. In each Individual variable connected with the edge represent a certain clique in the graph; means probability distribution of the variables in the graph can factorize an individual clique potential function.

马尔可夫随机模型是使用无向图的模型。 无向图形模型的边缘表示两个变量之间的电位，从句法上讲，变量之间的因式分解概率。 在每个与边相连的个人变量中，代表图中的某个集团。 表示图中变量的概率分布可以分解单个集团势函数。

Just as we had CPDs for Bayesian networks, we have tables to incorporate relations between nodes in Markov networks. However, there are two crucial differences between these tables and CPDs.

就像我们拥有贝叶斯网络的CPD一样，我们也有表格来合并Markov网络中节点之间的关系。 但是，这些表和CPD之间有两个关键区别。

Clique in graph theory.it is a subset of vertices of an undirected graph.

图论中的集团是无向图的顶点的子集。

P(A, B, C, D, E) α Ф(A,B) Ф (B,C) Ф (B,D) Ф (C,E) Ф (D,E)

P(A，B，C，D，E)αФ(A，B)Ф(B，C)Ф(B，D)Ф(C，E)Ф(D，E)

Such that: It induces sub graph is complete in every vertices in a clique is adjacent. So, clique in this graph adjust adjacently one by one.

这样：它在子群的每个顶点上都诱导出子图完成。 因此，该图中的小集团一个接一个地相邻调整。

Like,

喜欢，

It is some different if we join D,C and B,E clique over here then it is also change its probability.

如果我们在这里加入D，C和B，E集团，则有所不同，那也改变了它的概率。

P(A, B, C, D, E) α Ф(A,B) Ф (B,C,D) Ф (C,D,E)

P(A，B，C，D，E)αФ(A，B)Ф(B，C，D)Ф(C，D，E)

Some undirected graphic model has Markov Random Field. In MRF certain paths between A and C.

一些无向图形模型具有马尔可夫随机场。 在MRF中， A和C之间的某些路径。

   A -> B -> C
A -> B -> D -> E -> C

Note that: Markov networks do not need to be acyclic, as was the case with Bayesian networks.

注意：马尔可夫网络不需要像贝叶斯网络那样是非循环的。

Independence properties such as Markov properties:

独立属性，例如马尔可夫属性：

• Any 2 subsets if variables are conditionally independent given a separating subset.

  给定一个单独的子集，如果变量在条件上独立，则为任意两个子集。

• If we take 'A' as a subset and 'C' as one subset then there is wore between them. So, there is no way to go between 'A' and 'C' without getting threw the subset. So, we are using (A, B) than B, C, D, E.

  如果我们将“ A”作为一个子集，而将“ C”作为一个子集，那么它们之间就会出现问题。 因此，在不扔掉子集的情况下，无法在“ A”和“ C”之间切换。 因此，我们使用的是(A，B)而不是B，C，D，E 。

Therefore, A and C are separating subsets

因此 ，A和C是分离的子集

• Any 2 subset of variable are conditionally independent given a separating subset.

  给定一个单独的子集，变量的任何2个子集在条件上都是独立的。

• {B,D}, {B,E} and {B,D,E} are separating subsets.

  {B，D}，{B，E}和{B，D，E}是分离的子集。

Conclusion: In this article we will learn about Markov Random Field model, its potential function and its properties.

结论：在本文中，我们将了解马尔可夫随机场模型 ，其潜在功能及其性质。

Reference: Probabilistic Graphical Models Tutorial — Part 1

参考： 概率图形模型教程—第1部分

翻译自: https://www.includehelp.com/ml-ai/markov-random-field-model.aspx