python实现差分隐私Laplace机制详解

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)

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