def from_discrete_gaussian_mechanism(
cls,
sigma: float,
sensitivity: int = 1,
truncation_bound: typing.Optional[int] = None,
pessimistic_estimate: bool = True,
value_discretization_interval: float = 1e-4) -> 'PrivacyLossDistribution':
"""Creates the privacy loss distribution of the discrete Gaussian mechanism.
Args:
sigma: the parameter of the discrete Gaussian distribution. Note that
unlike the (continuous) Gaussian distribution this is not equal to the
standard deviation of the noise.
sensitivity: the sensitivity of function f. (i.e. the maximum absolute
change in f when an input to a single user changes.)
truncation_bound: bound for truncating the noise, i.e. the noise will only
have a support in [-truncation_bound, truncation_bound]. When not
specified, truncation_bound will be chosen in such a way that the mass
of the noise outside of this range is at most 1e-30.
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 discrete Gaussian
mechanism with given parameters.
"""
return PrivacyLossDistribution.create_from_additive_noise(
privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity, truncation_bound=truncation_bound),
pessimistic_estimate=pessimistic_estimate,
value_discretization_interval=value_discretization_interval)
def test_discrete_gaussian_value_errors(self,
sigma,
sensitivity,
truncation_bound=None):
with self.assertRaises(ValueError):
privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity, truncation_bound=truncation_bound)
def test_discrete_gaussian_privacy_loss_value_errors(
self, sigma, sensitivity, sampling_prob, adjacency_type, x):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
with self.assertRaises(ValueError):
pl.privacy_loss(x)
def test_discrete_gaussian_privacy_loss(self, sigma, sensitivity,
sampling_prob, adjacency_type, x,
expected_privacy_loss):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma,
sensitivity=sensitivity,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
self.assertAlmostEqual(expected_privacy_loss, pl.privacy_loss(x))
def test_discrete_gaussian_value_errors(self,
sigma,
sensitivity,
sampling_prob=1.0,
adjacency_type=ADD,
truncation_bound=None):
with self.assertRaises(ValueError):
privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma,
sensitivity=sensitivity,
truncation_bound=truncation_bound,
sampling_prob=sampling_prob,
adjacency_type=adjacency_type)
def test_discrete_gaussian_privacy_loss_tail(
self, sigma, sensitivity, truncation_bound, expected_lower_x_truncation,
expected_upper_x_truncation, expected_tail_probability_mass_function):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity, truncation_bound=truncation_bound)
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_discrete_gaussian_std(self, sigma, sensitivity, truncation_bound,
expected_std):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity, truncation_bound=truncation_bound)
self.assertAlmostEqual(expected_std, pl.standard_deviation())
def test_discrete_gaussian_noise_cdf(self, sigma, sensitivity,
truncation_bound, x_to_cdf_value):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity, truncation_bound=truncation_bound)
for x, cdf_value in x_to_cdf_value.items():
self.assertAlmostEqual(cdf_value, pl.noise_cdf(x))
def test_discrete_gaussian_inverse_privacy_loss(self, sigma, sensitivity,
privacy_loss, expected_x):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity)
self.assertAlmostEqual(expected_x,
pl.inverse_privacy_loss(privacy_loss))
def test_discrete_gaussian_privacy_loss(self, sigma, sensitivity, x,
expected_privacy_loss):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity)
self.assertAlmostEqual(expected_privacy_loss, pl.privacy_loss(x))
def test_discrete_gaussian_privacy_loss_value_errors(
self, sigma, sensitivity, x):
pl = privacy_loss_mechanism.DiscreteGaussianPrivacyLoss(
sigma, sensitivity=sensitivity)
with self.assertRaises(ValueError):
pl.privacy_loss(x)
