def evaluate(data,
range_max_value,
quality_function,
quality_promise,
approximation,
eps,
delta,
intervals_bounding,
max_in_interval,
use_exponential=True):
"""
RecConcave algorithm for the specific case of N=2
:param data: the main data-set
:param range_max_value: maximum possible output (the minimum output is 0)
:param quality_function: function that gets a domain-elements and returns its quality (in float)
:param quality_promise: float, quality value that we can assure that there exist a domain element with at least that quality
:param approximation: 0 < float < 1. the approximation level of the result
:param eps: float > 0. privacy parameter
:param delta: 1 > float > 0. privacy parameter
:param intervals_bounding: function L(data,domain_element)
:param max_in_interval: function u(data,interval) that returns the maximum of quality_function(data,j)
for j in the interval
:param use_exponential: the original version uses A_dist mechanism. for utility reasons the exponential-mechanism
is the default. turn to False to use A_dist instead
:return: an element of domain with approximately maximum value of quality function
"""
# 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
def extended_quality_function(data_base, j):
if range_max_value < j <= range_max_value_tag:
return min(0, quality_function(data_base, range_max_value))
else:
return quality_function(data_base, j)
# step 4
# print "step 4"
def recursive_quality_function(data_base, j):
return min(
intervals_bounding(data_base, range_max_value_tag, j) -
(1 - approximation) * quality_promise, quality_promise -
intervals_bounding(data_base, range_max_value_tag, j + 1))
# step 6
# print "step 6"
recursion_returned = basicdp.exponential_mechanism_big(
data, range(log_of_range + 1), recursive_quality_function, eps)
good_interval = 8 * (2**recursion_returned)
# print "good interval: %d" % good_interval
# step 7
# print "step 7"
first_intervals = __build_intervals_set__(data, good_interval, 0,
range_max_value_tag)
second_intervals = __build_intervals_set__(data, good_interval, 0,
range_max_value_tag, True)
max_quality = partial(max_in_interval, interval_length=good_interval)
# step 9 ( using 'dist' algorithm )
# print "step 9"
# TODO should I add switch for sparse?
# TODO make sure it is still generic!!!!!!!!!!!!!!
if use_exponential:
first_full_domain = xrange(0, range_max_value, good_interval)
second_full_domain = xrange(good_interval / 2, range_max_value,
good_interval)
first_chosen_interval = basicdp.sparse_domain(
basicdp.exponential_mechanism_big, data, first_full_domain,
first_intervals, max_quality, eps)
second_chosen_interval = basicdp.sparse_domain(
basicdp.exponential_mechanism_big, data, second_full_domain,
second_intervals, max_quality, eps)
else:
first_chosen_interval = basicdp.a_dist(data, first_intervals,
max_quality, eps, delta)
second_chosen_interval = basicdp.a_dist(data, second_intervals,
max_quality, eps, delta)
if type(first_chosen_interval) == str and type(
second_chosen_interval) == str:
raise ValueError("stability problem, try taking more samples!")
# step 10
# print "step 10"
if type(first_chosen_interval) == str:
first_chosen_interval_as_list = []
else:
first_chosen_interval_as_list = range(
first_chosen_interval, first_chosen_interval + good_interval)
if type(second_chosen_interval) == str:
second_chosen_interval_as_list = []
else:
second_chosen_interval_as_list = range(
second_chosen_interval, second_chosen_interval + good_interval)
return basicdp.exponential_mechanism_big(
data, first_chosen_interval_as_list + second_chosen_interval_as_list,
extended_quality_function, eps)
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 evaluate(
data,
range_max_value,
quality_function,
quality_promise,
approximation,
eps,
delta,
intervals_bounding,
max_in_interval,
use_exponential=True,
):
"""
RecConcave algorithm for the specific case of N=2
:param data: the main data-set
:param range_max_value: maximum possible output (the minimum output is 0)
:param quality_function: function that gets a domain-elements and returns its quality (in float)
:param quality_promise: float, quality value that we can assure that there exist a domain element with at least that quality
:param approximation: 0 < float < 1. the approximation level of the result
:param eps: float > 0. privacy parameter
:param delta: 1 > float > 0. privacy parameter
:param intervals_bounding: function L(data,domain_element)
:param max_in_interval: function u(data,interval) that returns the maximum of quality_function(data,j)
for j in the interval
:param use_exponential: the original version uses A_dist mechanism. for utility reasons the exponential-mechanism
is the default. turn to False to use A_dist instead
:return: an element of domain with approximately maximum value of quality function
"""
# 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
def extended_quality_function(data_base, j):
if range_max_value < j <= range_max_value_tag:
return min(0, quality_function(data_base, range_max_value))
else:
return quality_function(data_base, j)
# step 4
# print "step 4"
def recursive_quality_function(data_base, j):
return min(
intervals_bounding(data_base, range_max_value_tag, j) - (1 - approximation) * quality_promise,
quality_promise - intervals_bounding(data_base, range_max_value_tag, j + 1),
)
# step 6
# print "step 6"
recursion_returned = basicdp.exponential_mechanism_big(
data, range(log_of_range + 1), recursive_quality_function, eps
)
good_interval = 8 * (2 ** recursion_returned)
# print "good interval: %d" % good_interval
# step 7
# print "step 7"
first_intervals = __build_intervals_set__(data, good_interval, 0, range_max_value_tag)
second_intervals = __build_intervals_set__(data, good_interval, 0, range_max_value_tag, True)
max_quality = partial(max_in_interval, interval_length=good_interval)
# step 9 ( using 'dist' algorithm )
# print "step 9"
# TODO should I add switch for sparse?
# TODO make sure it is still generic!!!!!!!!!!!!!!
if use_exponential:
first_full_domain = xrange(0, range_max_value, good_interval)
second_full_domain = xrange(good_interval / 2, range_max_value, good_interval)
first_chosen_interval = basicdp.sparse_domain(
basicdp.exponential_mechanism_big, data, first_full_domain, first_intervals, max_quality, eps
)
second_chosen_interval = basicdp.sparse_domain(
basicdp.exponential_mechanism_big, data, second_full_domain, second_intervals, max_quality, eps
)
else:
first_chosen_interval = basicdp.a_dist(data, first_intervals, max_quality, eps, delta)
second_chosen_interval = basicdp.a_dist(data, second_intervals, max_quality, eps, delta)
if type(first_chosen_interval) == str and type(second_chosen_interval) == str:
raise ValueError("stability problem, try taking more samples!")
# step 10
# print "step 10"
if type(first_chosen_interval) == str:
first_chosen_interval_as_list = []
else:
first_chosen_interval_as_list = range(first_chosen_interval, first_chosen_interval + good_interval)
if type(second_chosen_interval) == str:
second_chosen_interval_as_list = []
else:
second_chosen_interval_as_list = range(second_chosen_interval, second_chosen_interval + good_interval)
return basicdp.exponential_mechanism_big(
data, first_chosen_interval_as_list + second_chosen_interval_as_list, extended_quality_function, eps
)
