#### Michael I. Jordan概率图模型tutorial（一）

independence networks, Markov random fields, loglinear models, influence diagrams等很多模型也都属于概率图模型的范畴，下面从基本概念开始介绍：

## 1.Directed Graph

Define: Random variable $X$ is marginal independent of random variable $Y$ if, for all $x_i \in dom(X), y_k \in dom(Y)$ , we have

Define: Random variable $X$ is conditionally independent of random variable $Y$ given random variable $Z$ if, for all  $x_i \in dom(X), y_k \in dom(Y), z_m \in dom(Z)$ , we have

$P(X=x_i|Y=y_k, Z=z_m) = P(X=x_i, Z=z_m)$ </span>

## 4.Inference

Inference的意思就是求边缘分布。

### 4.1.Inference of Directed Graph Model

We say a cycle in G is chordless is all pairs of vertices that are not adjacent in the cycle are not neighbors.

A graph is triangulated if it contains no chordless cycles of length greater than 3.