《机器学习》 周志华学习笔记第十四章 概率图模型（课后习题）python实现

由于题目较多，我这里只列出部分题目的代码实现，供您参考。

14.2 贝叶斯网络

14.2.1 习题1

import numpy as np

# 构建贝叶斯网络的结构，定义每个节点的父节点
parents = {
    'D': [],
    'I': [],
    'G': ['I', 'D'],
    'S': ['I'],
    'L': ['G']
}

# 定义概率表
prob_tables = {
    'D': np.array([0.6, 0.4]),
    'I': np.array([0.7, 0.3]),
    'G': np.array([
        [0.3, 0.4, 0.3, 0.05, 0.95, 0.9],
        [0.7, 0.6, 0.7, 0.95, 0.05, 0.1]
    ]),
    'S': np.array([
        [0.95, 0.2],
        [0.05, 0.8]
    ]),
    'L': np.array([
        [0.1, 0.4],
        [0.9, 0.6]
    ])
}

def get_prob(node, values, evidences):
    """
    计算节点的概率
    :param node: 节点名称
    :param values: 取值
    :param evidences: 证据
    """
    if len(parents[node]) == 0:  # 如果节点没有父节点
        return prob_tables[node][values]
    else:
        parent_values = [evidences[parent] for parent in parents[node]]
        return prob_tables[node][tuple(parent_values)][values]

def inference(query, evidences):
    """
    推断函数
    :param query: 查询节点
    :param evidences: 证据
    """
    values = [0, 1]  # 取值为0或1
    q = np.zeros((2,))
    for value in values:
        evidences[query] = value  # 将查询节点的取值设置为当前值
        p = 1
        for node in prob_tables.keys():
            p *= get_prob(node, evidences[node], evidences)
        q[value] = p
    q /= np.sum(q)  # 归一化
    return q

query = 'G'
evidences = {'D': 0, 'I': 1, 'S': 1, 'L': 1}
q = inference(query, evidences)
print('P(G=0|D=0,I=1,S=1,L=1)={:.4f}'.format(q[0]))
print('P(G=1|D=0,I=1,S=1,L=1)={:.4f}'.format(q[1]))

14.3 马尔可夫网络

14.3.1 习题1

import numpy as np

# 构建马尔可夫网络的结构
structure = {
    'A': ['C', 'D'],
    'B': ['D'],
    'C': ['E'],
    'D': ['E'],
    'E': []
}

# 定义概率表
prob_tables = {
    'A': np.array([
        [0.4, 0.6],
        [0.2, 0.8]
    ]),
    'B': np.array([0.2, 0.8]),
    'C': np.array([
        [0.5, 0.5],
        [0.3, 0.7]
    ]),
    'D': np.array([
        [0.6, 0.4],
        [0.1, 0.9]
    ]),
    'E': np.array([
        [0.3, 0.7],
        [0.8, 0.2]
    ])
}

def inference(query, evidences):
    """
    推断函数
    :param query: 查询节点
    :param evidences: 证据
    """
    values = [0, 1]  # 取值为0或1
    q = np.zeros((2,))
    for value in values:
        # 构建条件概率表
        cpts = {}
        for node in structure.keys():
            parents = structure[node]
            if len(parents) == 0:  # 如果节点没有父节点
                cpts[node] = prob_tables[node][value]
            else:
                parent_values = tuple([evidences[parent] for parent in parents])
                cpts[node] = prob_tables[node][parent_values][value]
        # 计算联合概率
        p = 1
        for node in structure.keys():
            parents = structure[node]
            if len(parents) == 0:  # 如果节点没有父节点
                p *= cpts[node]
            else:
                parent_values = tuple([evidences[parent] for parent in parents])
                p *= cpts[node]
        q[value] = p
    q /= np.sum(q)  # 归一化
    return q

query = 'E'
evidences = {'A': 1, 'B': 0}
q = inference(query, evidences)
print('P(E=0|A=1,B=0)={:.4f}'.format(q[0]))
print('P(E=1|A=1,B=0)={:.4f}'.format(q[1]))