python实现差分隐私Laplace机制

Laplace分布定义：

下面先给出Laplace分布实现代码：

import matplotlib.pyplot as plt
import numpy as np

def laplace_function(x,beta):
    result = (1/(2*beta)) * np.e**(-1*(np.abs(x)/beta))
    return result
#在-5到5之间等间隔的取10000个数
x = np.linspace(-5,5,10000)
y1 = [laplace_function(x_,0.5) for x_ in x]
y2 = [laplace_function(x_,1) for x_ in x]
y3 = [laplace_function(x_,2) for x_ in x]


plt.plot(x,y1,color='r',label='beta:0.5')
plt.plot(x,y2,color='g',label='beta:1')
plt.plot(x,y3,color='b',label='beta:2')
plt.title("Laplace distribution")
plt.legend()
plt.show()

效果图如下：

接下来给出Laplace机制实现：

Laplace机制，即在操作函数结果中加入服从Laplace分布的噪声。

Laplace概率密度函数Lap(x|b)=1/2b exp(-|x|/b)正比于exp(-|x|/b)。

import numpy as np

def noisyCount(sensitivety,epsilon):
    beta = sensitivety/epsilon
    u1 = np.random.random()
    u2 = np.random.random()
    if u1 <= 0.5:
        n_value = -beta*np.log(1.-u2)
    else:
        n_value = beta*np.log(u2)
    print(n_value)
    return n_value

def laplace_mech(data,sensitivety,epsilon):
    for i in range(len(data)):
        data[i] += noisyCount(sensitivety,epsilon)
    return data

if __name__ =='__main__':
    x = [1.,1.,0.]
    sensitivety = 1
    epsilon = 1
    data = laplace_mech(x,sensitivety,epsilon)
    for j in data:
        print(j)