CS50_AI_2_Uncertainty 概率 （Python实现 - 英文注释）

主要内容

1. 概率论基础, 贝叶斯公式, 贝叶斯网络
2. 似然估计
3. 马尔可夫模型, 马尔可夫链, 隐马尔可夫模型

课程笔记地址 ： https://cs50.harvard.edu/ai/2020/notes/2/#joint-probability
官网：https://cs50.harvard.edu/ai/2020/weeks/2/
上课源码： http://cdn.cs50.net/ai/2020/spring/lectures/2/src2.zip

代码讲解

本人概率论学不好, 所以只讲贝叶斯网络的部分 (

likelihood.py

from model import model

# Calculate probability for a given observation
# none rain, no maintenance, train on time, appointment attend 的 概率
probability = model.probability([["heavy", "yes", "delayed", "miss"]])

print(probability)
1
2
3
4
5
6
7

model.py

from pomegranate import *

# Rain node has no parents: root Node
# rain's probability
rain = Node(DiscreteDistribution({
    "none": 0.7,
    "light": 0.2,
    "heavy": 0.1
}), name="rain")

# Track maintenance node is conditional on rain
# rain -> maintenance
maintenance = Node(ConditionalProbabilityTable([
    ["none", "yes", 0.4],
    ["none", "no", 0.6],

    ["light", "yes", 0.2],
    ["light", "no", 0.8],

    ["heavy", "yes", 0.1],
    ["heavy", "no", 0.9]
], [rain.distribution]), name="maintenance")

# Train node is conditional on rain and maintenance
# rain -> Train,  maintenance -> Train
train = Node(ConditionalProbabilityTable([
    ["none", "yes", "on time", 0.8],
    ["none", "yes", "delayed", 0.2],

    ["none", "no", "on time", 0.9],
    ["none", "no", "delayed", 0.1],

    ["light", "yes", "on time", 0.6],
    ["light", "yes", "delayed", 0.4],

    ["light", "no", "on time", 0.7],
    ["light", "no", "delayed", 0.3],

    ["heavy", "yes", "on time", 0.4],
    ["heavy", "yes", "delayed", 0.6],

    ["heavy", "no", "on time", 0.5],
    ["heavy", "no", "delayed", 0.5],
], [rain.distribution, maintenance.distribution]), name="train")

# Appointment node is conditional on train
# train -> appointment 
appointment = Node(ConditionalProbabilityTable([
    ["on time", "attend", 0.9],
    ["on time", "miss", 0.1],

    ["delayed", "attend", 0.6],
    ["delayed", "miss", 0.4]
], [train.distribution]), name="appointment")

# Create a Bayesian Network and add states
model = BayesianNetwork()
model.add_states(rain, maintenance, train, appointment) # Bayesian's Node

# Add edges connecting nodes
model.add_edge(rain, maintenance)
model.add_edge(rain, train)
model.add_edge(maintenance, train)
model.add_edge(train, appointment)

# Finalize model
model.bake()
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67

讲解

关系图

[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-6CrdEPg9-1668324150628)(https://cdn.acwing.com/media/article/image/2022/11/13/157227_0034576763-QQ图片20221113151541.png)]
就是一棵树, 其中父节点的情况影响子节点的情况, 然后根据给出的各个条件的情况, 来计算最后约会准时的概率

1. 其中Node 为一个类型转换, 转换为了一个树上的节点Node
2. 然后add_edge 这些应该配合注释都能看懂, 就是 加边 add 函数, 不由感慨 Python的方便
3. 如果你发现有些库名未定义, 在vscode中的终端下输入: pip install 库名