def smooth_sensitivity_study(prior, sample_size, epsilon, delta, percentage):
Bayesian_Model = BayesInferwithDirPrior(prior, sample_size, epsilon, delta)
observation = [sample_size * i for i in percentage]
Bayesian_Model._set_observation([sample_size * i for i in percentage])
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_LS_Candidates()
xstick = [
str((r._minus(Bayesian_Model._prior))._alphas)
for r in Bayesian_Model._candidates
]
beta = 0.00000001
y = [
Bayesian_Model._LS_Candidates[r] *
math.exp(-beta * Hamming_Distance(observation, r._alphas))
for r in Bayesian_Model._candidates
]
scatter_plot(
y, xstick, 'Smooth Sensitivity Study w.r.t. x :' +
str([sample_size * i for i in percentage]) + r'; $\epsilon = $' +
str(epsilon) + r'; $\delta:$' + str(delta),
r"$\Delta_l(H(BI(x'),-))e^{- \gamma *d(x,x')}$")
def probability_values(datasize,epsilon,delta,prior,observation, mech):
Bayesian_Model = BayesInferwithDirPrior(prior, datasize, epsilon, delta)
Bayesian_Model._set_observation(observation)
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
if(mech == r'Alg 3 - $\mathsf{EHD}$'):
Bayesian_Model._set_up_exp_mech_with_GS()
elif(mech == r'Alg 4 - $\mathsf{EHDL}$'):
Bayesian_Model._set_up_exp_mech_with_LS()
elif(mech == r'Alg 5 - $\mathsf{EHDS}$'):
Bayesian_Model._set_up_exp_mech_with_gamma_SS()
probabilities_exp = {}
for i in range(len(Bayesian_Model._candidates)):
z = Bayesian_Model._candidates[i]
if(mech == r'Alg 3 - $\mathsf{EHD}$'):
probabilities_exp[str(z._alphas)] = Bayesian_Model._GS_probabilities[i]
elif(mech == r'Alg 4 - $\mathsf{EHDL}$'):
probabilities_exp[str(z._alphas)] = Bayesian_Model._LS_probabilities[i]
elif(mech == r'Alg 5 - $\mathsf{EHDS}$'):
probabilities_exp[str(z._alphas)] = Bayesian_Model._gamma_SS_probabilities[i]
return probabilities_exp
def ss_exponentiate_component_study(prior, sample_size, epsilon, delta,
percentage):
Bayesian_Model = BayesInferwithDirPrior(prior, sample_size, epsilon, delta)
observation = [sample_size * i for i in percentage]
Bayesian_Model._set_observation(observation)
Bayesian_Model._set_candidate_scores()
xstick = [
str((c._minus(Bayesian_Model._prior))._alphas)
for c in Bayesian_Model._candidates
]
# print [c._alphas for c in Bayesian_Model._candidates]
beta = math.log(1 - epsilon / (2.0 * math.log(delta / (2.0 *
(sample_size)))))
# y=[Hamming_Distance(Bayesian_Model._observation_counts, r._alphas) for r in Bayesian_Model._candidates]
# print y
y = [
math.exp(-beta * Hamming_Distance(observation, r._alphas))
for r in Bayesian_Model._candidates
]
scatter_plot(
y, xstick, 'Exponentiate Component of Smooth Sensitivity w.r.t. x :' +
str([sample_size * i for i in percentage]) + r'; $\epsilon:$' +
str(epsilon) + r'; $\delta:$' + str(delta), r"$e^{- \gamma *d(x,x')}$")
return
def exp_distribution_over_candidates(dataobs, prior, epsilon, mech):
n = sum(dataobs)
Bayesian_Model = BayesInferwithDirPrior(prior, n, epsilon)
Bayesian_Model._set_observation(dataobs)
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
if mech == "exp":
Bayesian_Model._set_up_exp_mech_with_GS()
elif mech == "gamma":
Bayesian_Model._set_up_exp_mech_with_gamma_SS()
exp_prob = {}
for i in range(len(Bayesian_Model._candidates)):
z = Bayesian_Model._candidates[i]._pointwise_sub(prior)
if mech == "exp":
exp_prob[list2key(z._alphas)] = Bayesian_Model._GS_probabilities[i]
elif mech == "gamma":
exp_prob[list2key(
z._alphas)] = Bayesian_Model._gamma_SS_probabilities[i]
# print exp_prob
return exp_prob
def privacy_loss_of_size_n(prior, datasize, epsilon, delta, mech): Bayesian_Model = BayesInferwithDirPrior(prior, datasize, epsilon, delta) Bayesian_Model._set_candidate_scores() candidates = Bayesian_Model._candidates ######################################################################################################################### #ALL POSSIBLE DATA SETS UNDER SIZE N for i in range(len(candidates)): candidates[i]._minus(prior) candidates = [c._alphas for c in candidates] privacyloss_of_n = 0.0 pair_of_n = [] candidates = [[datasize - 3,3], [datasize - 2, 2],[datasize - 1, 1],[datasize, 0],[0, datasize], [1, datasize - 1], [2, datasize - 2], [3, datasize - 3]] for C in candidates: ######################################################################################################################### #GET THE ADJACENT DATA SET OF DATA SET C C_adj = get_adjacent_set(C) ######################################################################################################################### #GET THE PRIVACY LOSS UNDER TWO ADJACENT DATA SET C AND loss = privacy_loss_one_pair(datasize,epsilon,delta,prior,C,C_adj, mech) if privacyloss_of_n < loss[-1][1]: privacyloss_of_n = loss[-1][1] pair_of_n = (C,C_adj) return privacyloss_of_n, pair_of_n
def get_steps_opt(dataobs, prior, epsilon):
n = sum(dataobs)
Bayesian_Model = BayesInferwithDirPrior(prior, n, epsilon)
Bayesian_Model._set_observation(dataobs)
Bayesian_Model._set_candidate_scores()
cpara = []
for c in Bayesian_Model._candidates:
cpara.append(list2key(c._minus(prior)._alphas))
return cpara
def ls_scaled_by_eps(n, prior, epsilon):
Bayesian_Model = BayesInferwithDirPrior(prior, n, epsilon)
Bayesian_Model._set_observation(gen_dataset_rand(len(prior._alphas), n))
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
ls = []
xstick = []
for c in Bayesian_Model._candidates:
ls.append(Bayesian_Model._LS_Candidates[c] / epsilon)
xstick.append(c._alphas)
return ls, xstick
def expect_errors_Lap(n, prior, epsilon):
Bayesian_Model = BayesInferwithDirPrior(prior, n, epsilon)
Bayesian_Model._set_observation(gen_dataset_rand(len(prior._alphas), n))
Bayesian_Model._set_candidate_scores()
candidates = Bayesian_Model._candidates
expecterror = []
xstick = []
for c in candidates:
expecterror.append(expect_error_Lap(c, prior, epsilon))
xstick.append(str(c._alphas))
return expecterror, xstick
def decomposed_probability_values(datasize,epsilon,delta,prior,observation):
Bayesian_Model = BayesInferwithDirPrior(prior, datasize, epsilon, delta)
Bayesian_Model._set_observation(observation)
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
nomalizer = Bayesian_Model._set_up_exp_mech_with_gamma_SS()
probabilities_exp = {}
for i in range(len(Bayesian_Model._candidates)):
z = Bayesian_Model._candidates[i]
probabilities_exp[str(z._alphas)] = nomalizer * Bayesian_Model._gamma_SS_probabilities[i]
return nomalizer, probabilities_exp
def sensitivities(datasets, prior, beta, delta, label):
sensitivities = []
for dataset in datasets:
Bayesian_Model = BayesInferwithDirPrior(prior, sum(dataset), epsilon, delta)
Bayesian_Model._set_observation(dataset)
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
candidates = Bayesian_Model._candidates
for c in candidates:
#########################################################################################################################
#GET THE ADJACENT DATA SET OF DATA SET C
if (label == r"Local Sensitivity ($LS(x')$)"):
sensitivities.append(Bayesian_Model._LS_Candidates[c])
elif (label == r"Our Sensitivity ($\frac{1}{\frac{1}{LS(x')} +\gamma \cdot d(x,x')}$)"):
sensitivities.append((1.0 / (1.0/Bayesian_Model._LS_Candidates[c] + 1.0 * Hamming_Distance(Bayesian_Model._observation_counts, [c._alphas[i] - Bayesian_Model._prior._alphas[i] for i in range(Bayesian_Model._prior._size)]))))
return sensitivities, [list(numpy.array(c._alphas) - 1) for c in candidates]
def exp_smooth_theoryProb(dataobs, prior, epsilon, gamma):
n = sum(dataobs)
Bayesian_Model = BayesInferwithDirPrior(prior, n, epsilon, 0.1, gamma)
Bayesian_Model._set_observation(dataobs)
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
Bayesian_Model._gamma = gamma
Bayesian_Model._set_up_exp_mech_with_gamma_SS()
exp_prob = {}
for i in range(len(Bayesian_Model._candidates)):
z = Bayesian_Model._candidates[i]._pointwise_sub(prior)
exp_prob[list2key(
z._alphas)] = Bayesian_Model._gamma_SS_probabilities[i]
return exp_prob
def smooth_sensitivity_study2(prior, sample_size, epsilon, delta, percentage):
Bayesian_Model = BayesInferwithDirPrior(prior, sample_size, epsilon, delta)
observation = [sample_size * i for i in percentage]
Bayesian_Model._set_observation([sample_size * i for i in percentage])
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_LS_Candidates()
x = [(c._minus(Bayesian_Model._prior)) for c in Bayesian_Model._candidates]
beta = 0.001 # math.log(1 - epsilon / (2.0 * math.log(delta / (2.0 * (sample_size)))))
max_value_list = []
xstick = [
str((r._minus(Bayesian_Model._prior))._alphas)
for r in Bayesian_Model._candidates
]
for t in x:
Bayesian_Model._set_observation(t._alphas)
# Bayesian_Model._set_candidate_scores()
# Bayesian_Model._set_LS_Candidates()
max_value = 0.0
max_y = ''
# max_y_list = []
for r in Bayesian_Model._candidates:
temp = Bayesian_Model._LS_Candidates[r] * math.exp(
-beta * Hamming_Distance(t._alphas, r._alphas))
if max_value < temp:
max_y = r._alphas
max_value = temp
# for r in Bayesian_Model._candidates:
# temp = Bayesian_Model._LS_Candidates[r] * math.exp(- beta * Hamming_Distance(observation, r._alphas))
# if max_value == temp:
# max_y_list.append(str(r._alphas))
max_value_list.append(max_value)
print "when data set x = " + str(
t._alphas) + ", smooth sensitivity: S(" + str(
t._alphas) + ") = " + str(max_value)
scatter_plot(
y,
xstick,
'Smooth Sensitivity Given Size' + str(sample_size),
)
def sensitivities_2(datasizes, prior, beta, delta, label, gamma=1.0):
sensitivities = []
candidates = []
for datasize in datasizes:
Bayesian_Model = BayesInferwithDirPrior(prior, datasize, epsilon, delta, gamma)
Bayesian_Model._set_observation(gen_dataset([0.5,0.5],datasize))
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
candidates = [list(numpy.array(c._alphas) - 1) for c in Bayesian_Model._candidates]
if(label == r"Local Sensitivity ($LS(x)$)"):
for c in Bayesian_Model._candidates:
sensitivities.append(Bayesian_Model._LS_Candidates[c])
elif(label == r"Our Sensitivity ($\max_{x'}(\frac{1}{\frac{1}{LS(x')} +\gamma \cdot d(x,x')})$)"):
for c in candidates:
Bayesian_Model._set_observation(c)
Bayesian_Model._set_up_exp_mech_with_LS()
Bayesian_Model._set_up_exp_mech_with_gamma_SS()
sensitivities.append(Bayesian_Model._gamma_SS)
return sensitivities, candidates
def ss_ls_component_study(prior, sample_size, epsilon, delta, percentage):
Bayesian_Model = BayesInferwithDirPrior(prior, sample_size, epsilon, delta)
observation = [sample_size * i for i in percentage]
Bayesian_Model._set_observation([sample_size * i for i in percentage])
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_LS_Candidates()
xstick = [str(c._alphas) for c in Bayesian_Model._candidates]
beta = math.log(1 - epsilon / (2.0 * math.log(delta / (2.0 *
(sample_size)))))
y = [
1.0 / ((1 - Bayesian_Model._LS_Candidates[r]**2))
for r in Bayesian_Model._candidates
]
print abs(y[2] - y[1])
scatter_plot(y, xstick, "", r"$\frac{1}{LS((\alpha, 100 - \alpha))}$")
return
def accuracy_VS_mean(sample_size, epsilon, delta, prior):
data = []
xstick = []
temp = BayesInferwithDirPrior(prior, sample_size, epsilon, delta)
temp._set_candidate_scores()
observations = temp._candidates
for i in range(len(observations)):
observations[i]._minus(prior)
for observation in observations:
Bayesian_Model = BayesInferwithDirPrior(prior, sample_size, epsilon,
delta)
Bayesian_Model._set_observation(observation._alphas)
Bayesian_Model._experiments(500)
data.append(Bayesian_Model._accuracy[Bayesian_Model._keys[3]])
data.append(Bayesian_Model._accuracy[Bayesian_Model._keys[0]])
xstick.append(str(observation._alphas) + "/ExpMech")
xstick.append(str(observation._alphas) + "/Laplace")
plot_error_box(data, "Different Prior Distributions", xstick,
"Accuracy VS. Prior Distribution")
return
def mean_error_fix_n(n, prior, epsilon, times, mech):
Bayesian_Model = BayesInferwithDirPrior(prior, n, epsilon)
Bayesian_Model._set_observation(gen_dataset_rand(len(prior._alphas), n))
Bayesian_Model._set_candidate_scores()
candidates = Bayesian_Model._candidates
meanerror = []
xstick = []
for c in candidates:
accuracy = []
Bayesian_Model._set_observation(c._alphas)
for i in range(times):
if (mech == "lap"):
Bayesian_Model._laplace_mechanism_no_post(sensitivity=1.0)
elif (mech == "lappost"):
Bayesian_Model._laplace_mechanism_symetric(sensitivity=1.0)
accuracy.append(Bayesian_Model._posterior -
Bayesian_Model._laplaced_posterior)
meanerror.append(numpy.mean(accuracy))
xstick.append(str(list(numpy.array(c._alphas) - 1)))
return meanerror, xstick
def row_discrete_probabilities(sample_size, epsilon, delta, prior,
observation):
Bayesian_Model = BayesInferwithDirPrior(prior, sample_size, epsilon, delta)
Bayesian_Model._set_observation(observation)
print Bayesian_Model._observation_counts
Bayesian_Model._set_candidate_scores()
Bayesian_Model._set_local_sensitivities()
Bayesian_Model._set_up_exp_mech_with_gamma_SS()
Bayesian_Model._set_up_exp_mech_with_SS()
Bayesian_Model._set_up_exp_mech_with_GS()
Bayesian_Model._set_up_exp_mech_with_LS()
#############################################################################
#SPLIT THE BINS
#############################################################################
Candidate_bins_by_step = {}
probability_distance_pairs_in_exp = []
nomalizer = 0.0
sorted_scores = sorted(Bayesian_Model._candidate_scores.items(),
key=operator.itemgetter(1))
counter = 0
while counter < len(sorted_scores):
flage = counter
key = str(sorted_scores[flage][1])
Candidate_bins_by_step[key] = []
# parameters_of_bin = []
while counter < len(sorted_scores) and sorted_scores[flage][
1] == sorted_scores[counter][1]:
Candidate_bins_by_step[key].append(sorted_scores[counter][0])
# parameters_of_bin.append(sorted_scores[counter][0]._alphas)
counter += 1
# print parameters_of_bin
print key
#############################################################################
#SPLIT THE BINS
#############################################################################
# Candidate_bins_by_step = {}
# for r in Bayesian_Model._candidates:
# if str(sorted(r._alphas)) not in Candidate_bins_by_step.keys():
# Candidate_bins_by_step[str(sorted(r._alphas))] = []
# for c in Bayesian_Model._candidates:
# if set(c._alphas) == set(r._alphas):
# Candidate_bins_by_step[str(sorted(r._alphas))].append(c)
#############################################################################
#SUM UP the prob within the same bin
#############################################################################
# exp = calculate_prob_exp(Candidate_bins_by_step, Bayesian_Model, mechanism_parameter = 4,
# sensitivity = Bayesian_Model._SS, savename = "_exp.txt")
#############################################################################
#SUM UP the prob within the same bin
#############################################################################
exp_gamma = calculate_prob_exp(Candidate_bins_by_step, Bayesian_Model,
"gamma")
#############################################################################
#SUM UP the prob within the same bin
#############################################################################
exp_LS = calculate_prob_exp(Candidate_bins_by_step, Bayesian_Model,
"local")
#############################################################################
#SUM UP the prob within the same bin
#############################################################################
exp_GS = calculate_prob_exp(Candidate_bins_by_step, Bayesian_Model, "exp")
#############################################################################
#SETTING THE SENSITIVITY
#############################################################################
if (len(prior._alphas) == 2):
sensitivity1 = 1.0
sensitivity2 = 2.0
else:
sensitivity1 = 2.0
sensitivity2 = len(prior._alphas) * 1.0
#############################################################################
#CALCULATE the Laplace prob within the same bin
#############################################################################
step, lap_1 = calculate_prob_lap(Candidate_bins_by_step,
Bayesian_Model,
sensitivity=sensitivity1,
savename="_lap_1.txt")
step, lap_2 = calculate_prob_lap(Candidate_bins_by_step,
Bayesian_Model,
sensitivity=sensitivity2,
savename="_lap_2.txt")
print step, exp_gamma, lap_1, lap_2
# return
#############################################################################
#PLOT the prob within the same bin
#############################################################################
#############################################################################
#LABELS SETTING
#############################################################################
labels = [
r'Alg 5 - $\mathsf{EHDS}$ ', r"Alg 4 - $\mathsf{EHDL}$",
r"Alg 3 - $\mathsf{EHD}$",
r'Alg 1 - $\mathsf{LSDim}$ (sensitivity = ' + str(sensitivity2) + ')',
r'Alg 2 - $\mathsf{LSHist}$ (sensitivity = ' + str(sensitivity1) + ')'
]
#############################################################################
#PLOTTING
#############################################################################
plt.figure()
plt.plot(step, lap_2, '-', color='lightblue', label=(labels[3]))
plt.plot(step, lap_1, '-', color='navy', label=(labels[4]))
plt.plot(step, exp_GS, '-', label=(labels[2]))
plt.plot(step, exp_LS, '-', label=(labels[1]))
plt.plot(step, exp_gamma, '-', label=(labels[0]))
# plt.plot(step, exp, label=(labels[0]))
# plt.plot(step, exp_new, label=(labels[1]))
# plt.plot(step, exp_LS, label=(labels[2]))
# plt.plot(step, exp_GS, label=(labels[3]))
# plt.plot(step, lap_1, color = 'navy', label=(labels[4]))
# plt.plot(step, lap_2, color = 'lightblue', label=(labels[5]))
#############################################################################
#PLOT FEATURE SETTING
#############################################################################
plt.xlabel("c / Hellinger distance from true posterior")
plt.ylabel("Pr[H(BI(x),r) = c]")
plt.title("Accuracy with Data size " + str(sample_size), fontsize=15)
plt.legend()
plt.grid()
plt.show()