# [PGM] Bayes Network and Conditional Independence

2 - 1 - Semantics & Factorization

2 - 2 - Reasoning Patterns

2 - 3 - Flow of Probabilistic Influence

2 - 4 - Conditional Independence

2 - 5 - Independencies in Bayesian Networks

2 - 6 - Naive Bayes

2 - 7 - Application Medical Diagnosis

2 - 8 - Knowledge Engineering Example-SAMIAM

### When can X influence Y?

作为两个分布的先验，

如果已知，俩分布当然各自独立；

如果未知，其中一个node的数据反推到的后验参数，自然会影响另一个分布。

如果已知，数据是由两个参数作用的，当然相互见有影响，例如：

• 参数1小一点，参数2大一点，可能也会是相同的data。

如果未知，两个参数的分布自然没什么关系。

### Conditional Independence

Notice: 思考是否受到了共同先验的影响。

### D-separation

X与Y是D分离的 given Z。

1. “Ancestral graph": this is a reduced version of the original net, 即只考虑长辈。
2. "Moralize":  伴侣两两连线。
3. “Disorient": 转为无向图。
4. “Delete the given and their edges"：去除条件部分。

• 不连接，则独立。
• 若连接，不独立。
• If one or both of the variables are missing (because they were givens, and weretherefore deleted), they are independent.

P(D|CEG) =? P(D|C)

Are D and E conditionally independent, given C? AND
Are D and G conditionally independent, given C?

### I-maps

P满足与图G相关的局部独立性，那么图G是P的一个I-map，P可能有多个I-map。

If P factorizes over G, then G is an I-map for P.

G1 is an I-map for P1.

G2 is an I-map for P1 and P2

• I-map的因子分解

Theorem: If G is an I-map for P, then P factorizes over G.

• 最小I-map

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### CPCS Network

The main network used in our tests is a subset of the CPCS (Computer-based Patient Case Study) model [Pradhan et al.1994], a large multiply-connected multi-layer network consisting of 422 multi-valued nodes and covering a subset of the domain of internal medicine.

Among the 422 nodes,

14 nodes describe diseases,  显眼的特征

33 nodes describe history and risk factors, and 相关指标特征

the remaining 375 nodes describe various findings related to the diseases. 不显眼的特征

To avoid complete table representation, 毕竟没人喜欢处理全连接网