def sanitize(samples, alpha, beta, eps, delta):
"""
:param samples:
:param alpha:
:param beta:
:param eps:
:param delta:
:return:
"""
max_sample = max(samples)
dim = ceil(log2(max_sample + 1))
end_domain = 2 ** int(dim)
remaining_samples = set(range(end_domain))
est = dict.fromkeys(remaining_samples, 0)
new_beta = alpha * beta / 4
new_eps = eps / sqrt(32 * log(5 / delta) / alpha)
new_delta = alpha * delta / 5
for i in range(int(2 / alpha)):
q = __point_choice_quality__(remaining_samples)
b = choosing_mechanism_big(samples, remaining_samples, q, 1, alpha / 2, new_beta, new_eps, new_delta)
if b != "bottom":
remaining_samples.remove(b)
# remaining_samples[b] -= 1
# remaining_samples += Counter()
est[b] = concept_query(samples, point_concept(b)) + laplace(0, 1 / eps / len(samples), 1)[0]
return est
def sanitize(samples, alpha, beta, eps, delta):
"""
:param samples:
:param alpha:
:param beta:
:param eps:
:param delta:
:return:
"""
max_sample = max(samples)
dim = ceil(log2(max_sample + 1))
end_domain = 2**int(dim)
remaining_samples = set(range(end_domain))
est = dict.fromkeys(remaining_samples, 0)
new_beta = alpha * beta / 4
new_eps = eps / sqrt(32 * log(5/delta) / alpha)
new_delta = alpha * delta / 5
for i in range(int(2/alpha)):
q = __point_choice_quality__(remaining_samples)
b = choosing_mechanism_big(samples, remaining_samples, q, 1, alpha/2, new_beta, new_eps, new_delta)
if b != 'bottom':
remaining_samples.remove(b)
# remaining_samples[b] -= 1
# remaining_samples += Counter()
est[b] = concept_query(samples, point_concept(b)) + laplace(0, 1 / eps / len(samples), 1)[0]
return est
def find(data, number_of_points, data_dimension, radius, points_in_ball,
failure, approximation, eps, delta, shrink=False, use_histograms=False):
# TODO number_of_points is redundant
"""
Given a data set, desired number of points and a radius finds the center a cluster with approximately
that number of points and approximately that radius
:param data: list of points in R^dimension
:param number_of_points: number of points in the input data
:param data_dimension: the dimension of the space which the points are taken from
:param radius: the radius of cluster to find
:param points_in_ball: the number of desired points in the resulting cluster
:param approximation: 0 < float < 1. the approximation level of the result
:param failure: 0 < float < 1. chances that the procedure will fail to return an answer
:param eps: float > 0. privacy parameter
:param delta: 1 > float > 0. privacy parameter
:param shrink: boolean. default=False. if set to True will try to reduce the dimension to
obtain a better answer (not relevant in dimension < 600)
:param use_histograms: boolean. default=False. if set to True will use Theorem 2.5 from the paper
instead of using the choosing-mechanism (as in the older versions of the paper)
:return: the center a cluster with approximately that number of points and approximately that radius
"""
# step 1
# print "step 1"
if shrink:
new_dimension = int(46 * np.log2(2 * number_of_points / failure))
else:
new_dimension = data_dimension
box_side_length = 300 * radius
# step 2
# print "step 2"
if shrink:
transform = jl_init(data_dimension, new_dimension)
projected_data = transform(data)
else:
def transform(x): return x
projected_data = data
threshold = points_in_ball - 100 * np.log2(2 * number_of_points / failure) / eps
# print "the threshold is: %f" % threshold
above_thresh = above_threshold(projected_data, threshold, eps/4.0)
# step 3
# print "step 3"
boxes_shift = [] # just to make sure the list is defined in step 7
found_max = False
tries = 2 * number_of_points * int(np.log2(1 / failure)) / failure
# print "maximum no. of tries: %d" % tries
while not found_max and tries > 0:
boxes_shift = np.random.uniform(0, box_side_length, new_dimension)
# step 5
# print "step 5"
def partition_quality(data_base):
# TODO seems like I am ignoring 0-quality elements. Need fix?
boxes = (__box_containing_point__(p, boxes_shift, new_dimension, box_side_length) for p in data_base)
c = Counter(boxes)
return c[max(c, key=c.get)]
# print "maximum number of points in a single box: %d" % partition_quality(projected_data)
find_best_box = above_thresh(partition_quality)
if find_best_box == 'up':
found_max = True
else: # find_best_box == 'bottom'
tries -= 1
# step 6
# print "step 6"
if not found_max:
return -1
# step 7
# print "step 7"
box_containing_point_our_case = partial(__box_containing_point__, partition=boxes_shift, dimension=new_dimension,
side_length=box_side_length)
boxes = (box_containing_point_our_case(point) for point in projected_data)
boxes_quality = Counter(boxes)
# we add data_base to the signature to match the requirements of choosing_mechanism
def box_quality(data_base, box):
return boxes_quality[box]
boxes_set = list(set(box_containing_point_our_case(p) for p in projected_data))
if use_histograms:
best_box = histograms(projected_data, new_dimension, boxes_shift, box_side_length, eps / 4., delta / 4.)
else:
best_box = choosing_mechanism_big(projected_data, boxes_set, box_quality, 1, approximation, failure, eps/4.0, delta/4.0)
if type(best_box) == str:
raise ValueError("choosing mechanism returned 'bottom'")
# the first reshape is due to the signature of the transform method
# the second reshape returns the box to the original structure so we can compare to the best_box
points_in_best_box = [p for p in data
if box_containing_point_our_case(transform(p.reshape(1, data_dimension)).reshape(new_dimension,)) == best_box]
# print len(points_in_best_box)
# print "step 8"
interval_length = 450 * radius * np.sqrt(new_dimension)
center_box = []
for axis in xrange(data_dimension):
# TODO check if there a build-in function for projecting
projection_on_axis = np.array([d[axis] for d in points_in_best_box])
eps_tag = eps / np.sqrt(data_dimension * np.log(8/delta)) / 10.0
delta_tag = delta / data_dimension / 8.0
if use_histograms:
best_interval = histograms(projection_on_axis, 1, 0, interval_length, eps_tag, delta_tag)
extended_interval = ((best_interval - 1) * interval_length, (best_interval + 2) * interval_length)
center_box.append(extended_interval)
else:
axis_projection = np.array([__interval_containing_point__(d[axis], interval_length)
for d in points_in_best_box])
axis_counter = Counter(axis_projection)
def interval_quality(data_base, interval_index):
return axis_counter[interval_index]
# TODO what is the failure and approximation parameter?
# TODO should I use the 'sparse' version?
best_interval = choosing_mechanism_big(projected_data, axis_projection, interval_quality,
1, approximation, failure, eps_tag, delta_tag)
try:
extended_interval = ((best_interval-1) * interval_length, (best_interval+2) * interval_length)
center_box.append(extended_interval)
except TypeError:
raise ValueError("choosing mechanism returned 'bottom'")
# print "step 9"
center_of_chosen_box = [(i[1]-i[0])/2. for i in center_box]
try:
chosen_ball = [tuple(p) for p in data if distance.euclidean(center_of_chosen_box, p) <= interval_length*3]
# TODO when does this error rise?
except ValueError:
raise ValueError("something wrong! the center found is %s" % (str(center_of_chosen_box)))
if not chosen_ball:
print "chosen ball is empty!"
return center_of_chosen_box
# TODO when done - change the return to the error
# raise ValueError("chosen ball is empty! the center found is %s" % (str(center_of_chosen_box)))
# step 10
# print "step 10"
def predictor(x):
return x in chosen_ball
# TODO delete (was in use in the past)
# delta_g = max(norm(v) for v in chosen_ball)
# best_box, box_quality(data, best_box), center_box, chosen_ball
return noisy_avg(chosen_ball, predictor, data_dimension, eps/4., delta/4.)
