Python手写贝叶斯网络

Python手写贝叶斯网络

1. 导图

贝叶斯网络

实现原理

手写必要性

市场调查

手写实现详细介绍

步骤1: 数据预处理

步骤2: 计算条件概率

步骤3: 推理和预测

步骤4: 模型评估

步骤5: 模型应用

步骤6: 总结和完整代码

2. 实现原理

贝叶斯网络是一种概率图模型，用于描述随机变量之间的依赖关系。它由节点和有向边组成，节点表示随机变量，有向边表示变量之间的依赖关系。

贝叶斯网络的原理基于贝叶斯定理和条件独立性假设。通过给定的数据集，我们可以通过学习数据集中的条件概率来构建贝叶斯网络模型。贝叶斯网络可以用于推理和预测，以及对模型进行评估和应用。

3. 手写必要性

手写贝叶斯网络的实现可以帮助我们更好地理解算法的原理和细节。通过手写实现，我们可以深入了解算法的每个步骤和关键概念，从而提高对算法的理解和掌握程度。

此外，手写实现还有助于调试和优化算法。在实现过程中，我们可以发现潜在的问题和改进点，并进行相应的调整和优化，从而提高算法的性能和准确性。

4. 市场调查

在市场调查中，我们可以发现贝叶斯网络在许多领域中的广泛应用。例如，贝叶斯网络在医学诊断、金融风险评估、自然语言处理等领域中具有重要作用。其应用前景非常广阔。

5. 手写实现详细介绍

步骤1: 数据预处理

数据预处理是贝叶斯网络实现的第一步。在这一步中，我们需要对原始数据进行清洗、转换和归一化等处理，以便后续的计算和分析。

# 代码示例
def preprocess_data(data):
    # 数据清洗和转换
    cleaned_data = clean_data(data)
    transformed_data = transform_data(cleaned_data)
    
    # 数据归一化
    normalized_data = normalize_data(transformed_data)
    
    return normalized_data

步骤2: 计算条件概率

计算条件概率是贝叶斯网络实现的核心步骤。在这一步中，我们需要根据给定的数据集，计算每个节点的条件概率。

# 代码示例
def calculate_conditional_probability(data):
    # 初始化概率表
    probability_table = {}
    
    # 遍历数据集，计算条件概率
    for sample in data:
        for node in sample:
            # 统计节点出现次数
            count = count_occurrences(data, node)
            
            # 计算条件概率
            probability = count / len(data)
            
            # 更新概率表
            if node not in probability_table:
                probability_table[node] = {}
            probability_table[node]['probability'] = probability
    
    return probability_table

步骤3: 推理和预测

推理和预测是贝叶斯网络实现的关键步骤。在这一步中，我们可以利用贝叶斯网络进行推理和预测，根据已知的观测值来计算目标变量的概率。

# 代码示例
def infer_and_predict(network, evidence):
    # 初始化概率表
    probability_table = {}
    
    # 遍历网络节点，进行推理和预测
    for node in network:
        if node in evidence:
            # 已知观测值的节点
            probability_table[node] = {}
            probability_table[node]['probability'] = 1.0
        else:
            # 需要推理和预测的节点
            probability = calculate_probability(network, node, evidence)
            probability_table[node] = {}
            probability_table[node]['probability'] = probability
    
    return probability_table

步骤4: 模型评估

模型评估是贝叶斯网络实现的重要步骤。在这一步中，我们需要利用给定的数据集对贝叶斯网络模型进行评估，计算模型的准确性和性能指标。

# 代码示例
def evaluate_model(network, test_data):
    # 初始化评估指标
    accuracy = 0.0
    precision = 0.0
    recall = 0.0
    
    # 遍历测试数据集，进行模型评估
    for sample in test_data:
        evidence = sample[:-1]
        target = sample[-1]
        
        # 进行推理和预测
        prediction = infer_and_predict(network, evidence)
        
        # 更新评估指标
        if prediction == target:
            accuracy += 1
        if prediction == target and prediction == 1:
            precision += 1
        if prediction == target and target == 1:
            recall += 1
    
    # 计算准确性、精确度和召回率
    accuracy /= len(test_data)
    precision /= len(test_data)
    recall /= len(test_data)
    
    return accuracy, precision, recall

步骤5: 模型应用

模型应用是贝叶斯网络实现的实际应用步骤。在这一步中，我们可以利用训练好的贝叶斯网络模型对新的数据进行分类和预测。

# 代码示例
def apply_model(network, new_data):
    # 初始化分类结果
    classifications = []
    
    # 遍历新数据集，进行模型应用
    for sample in new_data:
        evidence = sample[:-1]
        
        # 进行推理和预测
        prediction = infer_and_predict(network, evidence)
        
        # 添加分类结果
        classifications.append(prediction)
    
    return classifications

总结完整代码

以下是一个简单的贝叶斯网络实现的完整代码示例：

import numpy as np

def clean_data(data):
    # 数据清洗
    cleaned_data = []
    for sample in data:
        if '?' not in sample:
            cleaned_data.append(sample)
    return cleaned_data

def transform_data(data):
    # 数据转换
    transformed_data = []
    for sample in data:
        new_sample = []
        for value in sample:
            if value == 'yes':
                new_sample.append(1)
            elif value == 'no':
                new_sample.append(0)
            else:
                new_sample.append(float(value))
        transformed_data.append(new_sample)
    return transformed_data

def normalize_data(data):
    # 数据归一化
    normalized_data = []
    for i in range(len(data[0])):
        column = [sample[i] for sample in data]
        mean = np.mean(column)
        std = np.std(column)
        normalized_column = [(value - mean) / std for value in column]
        normalized_data.append(normalized_column)
    normalized_data = np.array(normalized_data).T.tolist()
    return normalized_data

def count_occurrences(data, node):
    # 统计节点出现次数
    count = 0
    for sample in data:
        if node in sample:
            count += 1
    return count

def calculate_probability(network, node, evidence):
    # 计算节点的条件概率
    parents = network[node]['parents']
    probability_table = network[node]['probability_table']
    if not parents:
        # 无父节点，直接返回概率表中的概率
        return probability_table[0]['probability'] if evidence[node] == 0 else probability_table[1]['probability']
    else:
        # 有父节点，需要计算条件概率
        parent_values = [evidence[parent] for parent in parents]
        index = parent_values.index(max(parent_values))
        parent_node = parents[index]
        parent_value = evidence[parent_node]
        if parent_value == 0:
            probability = probability_table[0]['probability']
        else:
            probability = probability_table[1]['probability']
        return probability

def learn_structure(data):
    # 学习网络结构
    network = {}
    for i in range(len(data[0])):
        node = 'x' + str(i)
        network[node] = {}
        network[node]['parents'] = []
        network[node]['children'] = []
        network[node]['probability_table'] = []
        for j in range(i):
            parent_node = 'x' + str(j)
            network[node]['parents'].append(parent_node)
            network[parent_node]['children'].append(node)
        network[node]['probability_table'] = [{'value': 0, 'probability': 0.0}, {'value': 1, 'probability': 0.0}]
    return network

def learn_parameters(network, data):
    # 学习网络参数
    for node in network:
        probability_table = network[node]['probability_table']
        parents = network[node]['parents']
        if not parents:
            # 无父节点，直接计算概率
            count_0 = count_occurrences(data, node + '=0')
            count_1 = count_occurrences(data, node + '=1')
            probability_0 = count_0 / len(data)
            probability_1 = count_1 / len(data)
            probability_table[0]['probability'] = probability_0
            probability_table[1]['probability'] = probability_1
        else:
            # 有父节点，需要计算条件概率
            parent_values = []
            for parent_node in parents:
                parent_value_0 = count_occurrences(data, parent_node + '=0') / len(data)
                parent_value_1 = count_occurrences(data, parent_node + '=1') / len(data)
                parent_values.append([parent_value_0, parent_value_1])
            for i in range(2):
                for j in range(2):
                    evidence = {parents[k]: parent_values[k][j] for k in range(len(parents))}
                    evidence[node] = i
                    count = count_occurrences(data, evidence)
                    probability = count / len(data)
                    probability_table[i]['probability'] = probability

def train_model(data):
    # 训练贝叶斯网络模型
    cleaned_data = clean_data(data)
    transformed_data = transform_data(cleaned_data)
    normalized_data = normalize_data(transformed_data)
    network = learn_structure(normalized_data)
    learn_parameters(network, normalized_data)
    return network

def classify_data(network, new_data):
    # 对新数据进行分类
    classifications = []
    for sample in new_data:
        evidence = {f'x{i}': sample[i] for i in range(len(sample))}
        probability_0 = 1.0
        probability_1 = 1.0
        for node in network:
            probability = calculate_probability(network, node, evidence)
            if evidence[node] == 0:
                probability_0 *= probability
            else:
                probability_1 *= probability
        prediction = 1 if probability_1 > probability_0 else 0
        classifications.append(prediction)
    return classifications

def evaluate_model(network, test_data):
    # 评估模型性能
    tp = 0
    tn = 0
    fp = 0
    fn = 0
    for sample in test_data:
        evidence = {f'x{i}': sample[i] for i in range(len(sample) - 1)}
        target = sample[-1]
        probability_0 = 1.0
        probability_1 = 1.0
        for node in network:
            probability = calculate_probability(network, node, evidence)
            if evidence[node] == 0:
                probability_0 *= probability
            else:
                probability_1 *= probability
        prediction = 1 if probability_1 > probability_0 else 0
        if prediction == target and prediction == 1:
            tp += 1
        elif prediction == target and prediction == 0:
            tn += 1
        elif prediction != target and prediction == 1:
            fp += 1
        elif prediction != target and prediction == 0:
            fn += 1
    accuracy = (tp + tn) / (tp + tn + fp + fn)
    precision = tp / (tp + fp)
    recall = tp / (tp + fn)
    return accuracy, precision, recall

if __name__ == '__main__':
    # 加载数据集
    data = []
    with open('breast-cancer-wisconsin.data', 'r') as f:
        for line in f.readlines():
            data.append(line.strip().split(','))
    
    # 划分训练集和测试集
    np.random.seed(0)
    np.random.shuffle(data)
    train_data = data[:int(0.8 * len(data))]
    test_data = data[int(0.8 * len(data)):]
    
    # 训练贝叶斯网络模型
    network = train_model(train_data)
    
    # 对测试集进行分类和评估
    classifications = classify_data(network, test_data)
    accuracy, precision, recall = evaluate_model(network, test_data)
    print(f'Accuracy: {accuracy}')
    print(f'Precision: {precision}')
    print(f'Recall: {recall}')
    print(f'Classifications: {classifications}')

这个代码示例使用了一个经典的数据集：威斯康辛州乳腺癌数据集。这个数据集包含了从细胞核的数字化图像中提取的30个特征，这些特征可以用来预测肿瘤是否为恶性。在这个例子中，我们使用了一个简单的贝叶斯网络模型来对这个数据集进行分类预测，同时对模型的性能进行了评估。