Python代码实现本地化差分隐私：商品购买数据统计与扰动

以下是一个示例代码，用于获取txt文件中的数据并进行隐私保护：

import numpy as np

def get_data(file_path):
    data = []
    with open(file_path, 'r') as file:
        lines = file.readlines()
        for line in lines:
            line = line.strip()
            if line:
                items = line.split()
                user_items = [int(item) for item in items]
                data.append(user_items)
    return data

def randomized_response(data, epsilon):
    num_items = max([item for user_items in data for item in user_items]) + 1
    num_users = len(data)
    counts = np.zeros(num_items)
    for user_items in data:
        for item in user_items:
            counts[item] += 1

    noisy_counts = np.zeros(num_items)
    for item in range(num_items):
        for user_items in data:
            if item in user_items:
                noisy_counts[item] += np.random.laplace(scale=1/epsilon)
        noisy_counts[item] = max(0, noisy_counts[item])
    
    return counts, noisy_counts

def mse(counts, noisy_counts):
    return np.mean((counts - noisy_counts)**2)

# 获取数据
file_path = 'path/to/your/txt/file.txt'
data = get_data(file_path)

# 进行隐私保护
epsilons = [0.1, 1, 2, 4]
for epsilon in epsilons:
    counts, noisy_counts = randomized_response(data, epsilon)
    print(f'Epsilon: {epsilon}, MSE: {mse(counts, noisy_counts)}')

请注意，上述代码中的隐私保护部分使用了Laplace机制进行噪声添加，噪声的规模由隐私预算ε控制。根据差分隐私理论，隐私预算ε越小，添加的噪声越大，数据的隐私保护程度越高，但数据的精度也越低。因此，当隐私预算ε增大时，MSE会逐渐减小。