Laplace分布定义：

下面先给出Laplace分布实现代码：

import matplotlib.pyplot as pltimport 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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