def from_laplace_mechanism(
cls,
parameter: float,
sensitivity: float = 1,
pessimistic_estimate: bool = True,
value_discretization_interval: float = 1e-4
) -> 'PrivacyLossDistribution':
"""Computes the privacy loss distribution of the Laplace mechanism.
Args:
parameter: the parameter of the Laplace 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.
Returns:
The privacy loss distribution corresponding to the Laplace mechanism with
given parameters.
"""
return PrivacyLossDistribution.create_from_additive_noise(
privacy_loss_mechanism.LaplacePrivacyLoss(parameter,
sensitivity=sensitivity),
pessimistic_estimate=pessimistic_estimate,
value_discretization_interval=value_discretization_interval)
def test_laplace_privacy_loss(self, parameter, sensitivity, sampling_prob,
adjacency_type, x, expected_privacy_loss):
pl = privacy_loss_mechanism.LaplacePrivacyLoss(
parameter,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
self.assertAlmostEqual(expected_privacy_loss, pl.privacy_loss(x))
def test_laplace_get_delta_for_epsilon(self, parameter, sensitivity,
sampling_prob, adjacency_type,
epsilon, expected_delta):
pl = privacy_loss_mechanism.LaplacePrivacyLoss(
parameter,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
self.assertAlmostEqual(expected_delta,
pl.get_delta_for_epsilon(epsilon))
def test_laplace_value_errors(self,
parameter,
sensitivity,
sampling_prob=1.0,
adjacency_type=ADD):
with self.assertRaises(ValueError):
privacy_loss_mechanism.LaplacePrivacyLoss(
parameter,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
def test_laplace_privacy_loss_tail(self, parameter, sensitivity,
expected_lower_x_truncation,
expected_upper_x_truncation,
expected_tail_probability_mass_function):
pl = privacy_loss_mechanism.LaplacePrivacyLoss(
parameter, sensitivity=sensitivity)
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_laplace_get_delta_for_epsilon(
self, parameter, sensitivity, epsilon, expected_delta):
pl = privacy_loss_mechanism.LaplacePrivacyLoss(
parameter, sensitivity=sensitivity)
self.assertAlmostEqual(expected_delta, pl.get_delta_for_epsilon(epsilon))
def test_laplace_inverse_privacy_loss(self, parameter, sensitivity,
privacy_loss, expected_x):
pl = privacy_loss_mechanism.LaplacePrivacyLoss(
parameter, sensitivity=sensitivity)
self.assertAlmostEqual(expected_x, pl.inverse_privacy_loss(privacy_loss))
def test_laplace_privacy_loss(self, parameter, sensitivity, x,
expected_privacy_loss):
pl = privacy_loss_mechanism.LaplacePrivacyLoss(
parameter, sensitivity=sensitivity)
self.assertAlmostEqual(expected_privacy_loss, pl.privacy_loss(x))
def test_laplace_value_errors(self, parameter, sensitivity):
with self.assertRaises(ValueError):
privacy_loss_mechanism.LaplacePrivacyLoss(
parameter, sensitivity=sensitivity)
