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drawFigure2d.py
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from protocols.LocalHashing import LocalHashing
from Components.Distribution import zipf
from Components.Draw import draw
import math
NUMBEROFAXIS = 10 #### 10
N = 10000 #### 10000
#### begin/BLH ####
# BLH, fixing g=2
def analytical_BLH(protocol, d, n):
vars = [] # return a list of variances
for step in range(NUMBEROFAXIS): # 10 values
epsilon = 0.5 + 0.5 * step
x = protocol(d, epsilon, g=2) # g=2
x.set_n(n)
var = x.var_analytical()
vars.append(math.log10(var)) # log10(var)
return vars
# zipf distribution, similar to experiments in 14-RAPPOR
# fixing d=2^10
def empirical_BLH(protocol, d, n):
vars = []
for step in range(NUMBEROFAXIS): # 10 values
epsilon = 0.5 + 0.5 * step
x = protocol(d, epsilon, g=2) # init
users = zipf.zipf(1.1, d, n)
for i in range(len(users)):
if i % 1000 == 0:
print(step, i, "BLH")
x.PE(users[i])
x.aggregation() # estimate couterEsti
f = zipf.probList(1.1, d, n)
var = x.var_empirical(f, n)
vars.append(math.log10(var))
return vars
#### end/BLH ####
#### begin/OLH ####
# g = math.exp(epsilon)+1, to the nearst prime
def analytical_OLH(protocol, d, n):
vars = [] # return a list of variances
primeList = [3, 3, 5, 7, 13, 23, 37, 53, 89, 149] # according to epsilon=[0.5, 1.0, ..., 5.0]
for step in range(NUMBEROFAXIS): # 10 values
epsilon = 0.5 + 0.5 * step
x = protocol(d, epsilon, g=primeList[step])
x.set_n(n)
var = x.var_analytical()
vars.append(math.log10(var)) # log10(var)
return vars
# zipf distribution, similar to experiments in 14-RAPPOR
# fixing d=2^10
def empirical_OLH(protocol, d, n):
vars = []
primeList = [3, 3, 5, 7, 13, 23, 37, 53, 89, 149] # according to epsilon=[0.5, 1.0, ..., 5.0]
for step in range(NUMBEROFAXIS): # 10 values
epsilon = 0.5 + 0.5 * step
x = protocol(d, epsilon, g=primeList[step]) # round(math.exp(epsilon)+1)效果不好，要取最近的素数（因为universal hashing！！)
users = zipf.zipf(1.1, d, n)
for i in range(len(users)):
if i % 1000 == 0:
print(step, i, "OLH")
x.PE(users[i])
x.aggregation() # estimate couterEsti
f = zipf.probList(1.1, d, n)
var = x.var_empirical(f, n)
vars.append(math.log10(var))
return vars
#### end/OLH ####
'''
Need run 10 times.
Temporarily run once.
'''
# Figure 2(d)
def Comparing_empirical_and_analytical_variance_d():
varslist = [] # return a list of (a list of variances)
# Analytical BLH
vars = analytical_BLH(LocalHashing, 2**10, N)
varslist.append(vars)
# Empirical BLH
vars = empirical_BLH(LocalHashing, 2**10, N)
varslist.append(vars)
# Analytical OLH
vars = analytical_OLH(LocalHashing, 2**10, N)
varslist.append(vars)
# Empirical OLH
vars = empirical_OLH(LocalHashing, 2**10, N)
varslist.append(vars)
# Draw
epss = [0.5+0.5*item for item in range(NUMBEROFAXIS)] # 0.5, 1.0, ..., 5.0
draw.lines(epss, varslist, ['Analytical BLH', 'Empirical BLH', 'Analytical OLH', 'Empirical OLH'], title='Comparing empirical and analytical variance', xlabel='Vary epsilon(log2(x))', ylabel='Var(log10(y))')
if __name__ == "__main__":
Comparing_empirical_and_analytical_variance_d()