def __rec_concave_basis__(range_max_value,
quality_function,
eps,
data,
bulk=False):
"""recursion basis for the reconcave procedure - execute the exponential mechanism
note that the parameters r,alpha,delta and N are not being used
reconcave_basis(solution set size, quality function of sensitivity 1, eps privacy parameter, solution set)
"""
return basicdp.exponential_mechanism(data, range(int(range_max_value) + 1),
quality_function, eps, bulk)
def __rec_sanitize__(samples, domain_range, alpha, beta, eps, delta, dimension):
# print domain_range
# print calls
global calls
global san_data
# step 1
if calls == 0:
return
calls -= 1
# step 2
# the use of partial is redundant
samples_domain_points = partial(points_in_subset, samples)
noisy_points_in_range = samples_domain_points(subset=domain_range) + laplace(0, 1/eps, 1)
sample_size = len(samples)
# step 3
if noisy_points_in_range < alpha*sample_size/8:
base_range = domain_range
san_data.extend(base_range[1] * noisy_points_in_range)
return san_data
# step 4
domain_size = domain_range[1] - domain_range[0] + 1
log_size = int(ceil(log(domain_size, 2)))
# not needed
# size_tag = 2**log_size
# step 6
def quality(data, j):
return min(point_count_intervals_bounding(data, domain_range, j)-alpha * sample_size / 32,
3 * alpha * sample_size / 32 - point_count_intervals_bounding(data, domain_range, j-1))
# not needed if using exponential_mechanism
# step 7
# promise = alpha * sample_size / 32
# step 8
new_eps = eps/3/log_star(dimension)
# new_delta = delta/3/log_star(dimension)
# note the use of exponential_mechanism instead of rec_concave
z_tag = exponential_mechanism(samples, range(log_size+1), quality, new_eps)
z = 2 ** z_tag
# step 9
if z_tag == 0:
point_counter = Counter(samples)
def special_quality(data, b):
return point_counter[b]
b = choosing_mechanism(samples, range(domain_range[0], domain_range[1] + 1), special_quality,
1, alpha/64., beta, eps, delta)
a = b
# step 10
else:
first_intervals = __build_intervals_set__(samples, 2*z, domain_range[0], domain_range[1] + 1)
second_intervals = __build_intervals_set__(samples, 2*z_tag, domain_range[0], domain_range[1] + 1, True)
intervals = [(i, i+2*z-1) for i in first_intervals+second_intervals]
a, b = choosing_mechanism(samples, intervals, points_in_subset, 2, alpha/64., beta, eps, delta)
if type(a) == str:
raise ValueError("stability problem - choosing_mechanism returned 'bottom'")
# step 11
# although not mentioned I assume the noisy value should be rounded
noisy_count_ab = int(samples_domain_points((a, b)) + laplace(0, 1/eps, 1))
san_data.extend([b] * noisy_count_ab)
# step 12
if a > domain_range[0]:
rec_range = (domain_range[0], a - 1)
__rec_sanitize__(samples, rec_range, alpha, beta, eps, delta, dimension)
if b < domain_range[1]:
rec_range = (b + 1, domain_range[1])
__rec_sanitize__(samples, rec_range, alpha, beta, eps, delta, dimension)
return san_data
def __rec_concave_basis__(range_max_value, quality_function, eps, data, bulk=False):
"""recursion basis for the reconcave procedure - execute the exponential mechanism
note that the parameters r,alpha,delta and N are not being used
reconcave_basis(solution set size, quality function of sensitivity 1, eps privacy parameter, solution set)
"""
return basicdp.exponential_mechanism(data, range(int(range_max_value)+1), quality_function, eps, bulk)
def evaluate(data, range_max_value, quality_function, quality_promise,
approximation, eps, delta, recursion_bound, bulk=False):
# TODO fix so it will work
# TODO add docstring
# TODO go through variables names
if recursion_bound == 1 or range_max_value <= 32:
return __rec_concave_basis__(range_max_value, quality_function, eps, data, bulk)
else:
recursion_bound -= 1
# step 2
print "step 2"
log_of_range = int(math.ceil(math.log(range_max_value, 2)))
range_max_value_tag = 2 ** log_of_range
if bulk:
qualities = quality_function(data, range(int(range_max_value)+1))
else:
qualities = [quality_function(data, i) for i in range(int(range_max_value)+1)]
qualities.extend([min(0, qualities[range_max_value]) for _ in xrange(range_max_value, range_max_value_tag)])
def extended_quality_function(j):
return qualities[j]
# same but with signature that fits exponential mechanism requirements (used in step 10)
def extended_quality_function_for_exponential_mechanism(data_set, j):
return qualities[j]
# step 3
print "step 3"
def intervals_bounding(j):
if j == log_of_range+1:
return min(0, intervals_bounding(log_of_range))
return max(min(extended_quality_function(e) for e in xrange(a, a+2**j-1))
for a in xrange(0, range_max_value_tag-2**j+1))
# step 4
print "step 4"
def recursive_quality_function(data_base, range_element):
return min(intervals_bounding(range_element) - (1 - approximation) * quality_promise,
quality_promise - intervals_bounding(range_element + 1))
# step 5
print "step 5"
recursive_quality_promise = quality_promise * approximation / 2
# step 6 - recursion call
print "step 6 - recursive call"
recursion_returned = evaluate(data, log_of_range, recursive_quality_function, recursive_quality_promise, 1/4,
eps, delta, recursion_bound, True)
good_interval = 8 * (2 ** recursion_returned)
print "good interval: %d" % good_interval
# step 7
print "step 7"
first_intervals = [range(range_max_value_tag)[i:i + good_interval]
for i in xrange(0, range_max_value_tag, good_interval)]
second_intervals = [range(good_interval/2, range_max_value_tag)[i:i + good_interval]
for i in xrange(0, range_max_value_tag-good_interval/2, good_interval)]
# step 8
print "step 8"
def interval_quality(data_base, interval):
return max([extended_quality_function(j) for j in interval])
# TODO temp - remove later
# plotting for testing
fq = [interval_quality(data, i) for i in first_intervals]
plt.plot(range(len(fq)), fq, 'bo', range(len(fq)), fq, 'r')
lower_bound = max(fq) - math.log(1/delta)/eps
plt.axhspan(lower_bound, lower_bound, color='green', alpha=0.5)
plt.show()
# step 9 ( using 'dist' algorithm)
print "step 9"
first_chosen_interval = basicdp.a_dist(data, first_intervals, interval_quality, eps, delta)
second_chosen_interval = basicdp.a_dist(data, second_intervals, interval_quality, eps, delta)
print "first A_dist returned: %s" % str(type(first_chosen_interval))
print "second A_dist returned: %s" % str(type(second_chosen_interval))
if type(first_chosen_interval) != list or type(second_chosen_interval) != list:
raise ValueError('stability problem')
# step 10
print "step 10"
return basicdp.exponential_mechanism(data, first_chosen_interval + second_chosen_interval,
extended_quality_function_for_exponential_mechanism, eps, False)
def evaluate(data,
range_max_value,
quality_function,
quality_promise,
approximation,
eps,
delta,
recursion_bound,
bulk=False):
# TODO fix so it will work
# TODO add docstring
# TODO go through variables names
if recursion_bound == 1 or range_max_value <= 32:
return __rec_concave_basis__(range_max_value, quality_function, eps,
data, bulk)
else:
recursion_bound -= 1
# step 2
print "step 2"
log_of_range = int(math.ceil(math.log(range_max_value, 2)))
range_max_value_tag = 2**log_of_range
if bulk:
qualities = quality_function(data, range(int(range_max_value) + 1))
else:
qualities = [
quality_function(data, i) for i in range(int(range_max_value) + 1)
]
qualities.extend([
min(0, qualities[range_max_value])
for _ in xrange(range_max_value, range_max_value_tag)
])
def extended_quality_function(j):
return qualities[j]
# same but with signature that fits exponential mechanism requirements (used in step 10)
def extended_quality_function_for_exponential_mechanism(data_set, j):
return qualities[j]
# step 3
print "step 3"
def intervals_bounding(j):
if j == log_of_range + 1:
return min(0, intervals_bounding(log_of_range))
return max(
min(extended_quality_function(e) for e in xrange(a, a + 2**j - 1))
for a in xrange(0, range_max_value_tag - 2**j + 1))
# step 4
print "step 4"
def recursive_quality_function(data_base, range_element):
return min(
intervals_bounding(range_element) -
(1 - approximation) * quality_promise,
quality_promise - intervals_bounding(range_element + 1))
# step 5
print "step 5"
recursive_quality_promise = quality_promise * approximation / 2
# step 6 - recursion call
print "step 6 - recursive call"
recursion_returned = evaluate(data, log_of_range,
recursive_quality_function,
recursive_quality_promise, 1 / 4, eps, delta,
recursion_bound, True)
good_interval = 8 * (2**recursion_returned)
print "good interval: %d" % good_interval
# step 7
print "step 7"
first_intervals = [
range(range_max_value_tag)[i:i + good_interval]
for i in xrange(0, range_max_value_tag, good_interval)
]
second_intervals = [
range(good_interval / 2, range_max_value_tag)[i:i + good_interval]
for i in xrange(0, range_max_value_tag -
good_interval / 2, good_interval)
]
# step 8
print "step 8"
def interval_quality(data_base, interval):
return max([extended_quality_function(j) for j in interval])
# TODO temp - remove later
# plotting for testing
fq = [interval_quality(data, i) for i in first_intervals]
plt.plot(range(len(fq)), fq, 'bo', range(len(fq)), fq, 'r')
lower_bound = max(fq) - math.log(1 / delta) / eps
plt.axhspan(lower_bound, lower_bound, color='green', alpha=0.5)
plt.show()
# step 9 ( using 'dist' algorithm)
print "step 9"
first_chosen_interval = basicdp.a_dist(data, first_intervals,
interval_quality, eps, delta)
second_chosen_interval = basicdp.a_dist(data, second_intervals,
interval_quality, eps, delta)
print "first A_dist returned: %s" % str(type(first_chosen_interval))
print "second A_dist returned: %s" % str(type(second_chosen_interval))
if type(first_chosen_interval) != list or type(
second_chosen_interval) != list:
raise ValueError('stability problem')
# step 10
print "step 10"
return basicdp.exponential_mechanism(
data, first_chosen_interval + second_chosen_interval,
extended_quality_function_for_exponential_mechanism, eps, False)