def find(data, domain, goal_number, failure, eps, sparse=True): """ Based on "Locating a Small Cluster Privately" by Kobbi Nissim, Uri Stemmer, and Salil Vadhan. PODS 2016. Given a data set, finds the radius of an approximately minimal cluster of points with approximately the desired amount of points :param data: list of points in R^dimension :param domain: tuple(absolute value of domain's end as int, minimum intervals in domain as float) :param goal_number: the number of desired points in the resulting cluster :param failure: 0 < float < 1. chances that the procedure will fail to return an answer :param eps: float > 0. privacy parameter :param sparse: 1 > float > 0. privacy parameter :return: the radius of the resulting cluster """ # max(abs(np.min(data)), np.max(data)) all_distances = distances(data) # TODO change variable name # 'a' need to greater than - log(domain[0] / failure) / eps a = 2 * log(domain[0] / failure) / eps thresh = goal_number - a - log(1 / failure) / eps # TODO verify that the noise addition is correct if __max_average_ball__(0, all_distances, goal_number) + laplace(0, 1 / eps, 1) > thresh: return 0 dimension = data.shape[1] # TODO maybe a little less sparse? if sparse: new_domain = __sparse_domain__(domain, dimension) else: new_domain = __create_regular_domain__(domain, dimension) def quality(d, r): return min(goal_number - __max_average_ball__(r / 2, all_distances, goal_number), __max_average_ball__(r, all_distances, goal_number) - goal_number + 2*a) / 2 return exponential_mechanism_big(data, new_domain, quality, eps / 2)
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 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 )