def from_gaussian_mechanism(
cls,
standard_deviation: float,
sensitivity: float = 1,
pessimistic_estimate: bool = True,
value_discretization_interval: float = 1e-4,
log_mass_truncation_bound: float = -50) -> 'PrivacyLossDistribution':
"""Creates the privacy loss distribution of the Gaussian mechanism.
Args:
standard_deviation: the standard_deviation of the Gaussian distribution.
sensitivity: the sensitivity of function f. (i.e. the maximum absolute
change in f when an input to a single user changes.)
pessimistic_estimate: a value indicating whether the rounding is done in
such a way that the resulting epsilon-hockey stick divergence
computation gives an upper estimate to the real value.
value_discretization_interval: the length of the dicretization interval
for the privacy loss distribution. The values will be rounded up/down to
be integer multiples of this number.
log_mass_truncation_bound: the ln of the probability mass that might be
discarded from the noise distribution. The larger this number, the more
error it may introduce in divergence calculations.
Returns:
The privacy loss distribution corresponding to the Gaussian mechanism with
given parameters.
"""
return PrivacyLossDistribution.create_from_additive_noise(
privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity,
pessimistic_estimate=pessimistic_estimate,
log_mass_truncation_bound=log_mass_truncation_bound),
pessimistic_estimate=pessimistic_estimate,
value_discretization_interval=value_discretization_interval)
def test_gaussian_get_delta_for_epsilon(self, standard_deviation,
sensitivity, epsilon,
expected_delta):
pl = privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation, sensitivity=sensitivity)
self.assertAlmostEqual(expected_delta,
pl.get_delta_for_epsilon(epsilon))
def test_gaussian_inverse_privacy_loss(self, standard_deviation,
sensitivity, privacy_loss,
expected_x):
pl = privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation, sensitivity=sensitivity)
self.assertAlmostEqual(expected_x,
pl.inverse_privacy_loss(privacy_loss))
def test_gaussian_value_errors(self, standard_deviation, sensitivity,
log_mass_truncation_bound=-50):
with self.assertRaises(ValueError):
privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity,
log_mass_truncation_bound=log_mass_truncation_bound)
def test_gaussian_privacy_loss(self, standard_deviation, sensitivity,
sampling_prob, adjacency_type, x,
expected_privacy_loss):
pl = privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
self.assertAlmostEqual(expected_privacy_loss, pl.privacy_loss(x))
def test_gaussian_get_delta_for_epsilon(self, standard_deviation,
sensitivity, sampling_prob,
adjacency_type, epsilon,
expected_delta):
pl = privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
self.assertAlmostEqual(expected_delta,
pl.get_delta_for_epsilon(epsilon))
def test_gaussian_value_errors(self,
standard_deviation,
sensitivity,
sampling_prob=1.0,
adjacency_type=ADD,
log_mass_truncation_bound=-50):
with self.assertRaises(ValueError):
privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity,
log_mass_truncation_bound=log_mass_truncation_bound,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
def test_gaussian_privacy_loss_tail(
self, standard_deviation, sensitivity, expected_lower_x_truncation,
expected_upper_x_truncation, pessimistic_estimate,
expected_tail_probability_mass_function):
pl = privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity,
pessimistic_estimate=pessimistic_estimate,
log_mass_truncation_bound=math.log(2) + stats.norm.logcdf(-1))
tail_pld = pl.privacy_loss_tail()
self.assertAlmostEqual(expected_lower_x_truncation,
tail_pld.lower_x_truncation)
self.assertAlmostEqual(expected_upper_x_truncation,
tail_pld.upper_x_truncation)
test_util.dictionary_almost_equal(
self, expected_tail_probability_mass_function,
tail_pld.tail_probability_mass_function)
def test_gaussian_privacy_loss(self, standard_deviation, sensitivity, x,
expected_privacy_loss):
pl = privacy_loss_mechanism.GaussianPrivacyLoss(
standard_deviation,
sensitivity=sensitivity)
self.assertAlmostEqual(expected_privacy_loss, pl.privacy_loss(x))
