def test_gaussian_self_composition(self, standard_deviation, sensitivity,
num_times, expected_standard_deviation,
expected_sensitivity):
pld = privacy_loss_distribution.GaussianPrivacyLossDistribution(
standard_deviation,
sensitivity=sensitivity,
value_discretization_interval=1)
composed_pld = pld.self_compose(num_times)
self.assertAlmostEqual(expected_standard_deviation,
composed_pld._standard_deviation)
self.assertAlmostEqual(expected_sensitivity, composed_pld._sensitivity)
def test_gaussian_discretization(
self, value_discretization_interval,
expected_rounded_probability_mass_function):
pld = privacy_loss_distribution.GaussianPrivacyLossDistribution(
1,
value_discretization_interval=value_discretization_interval,
log_mass_truncation_bound=math.log(2) + stats.norm.logcdf(-1))
self.assertAlmostEqual(stats.norm.cdf(-1), pld.infinity_mass)
dictionary_almost_equal(self,
expected_rounded_probability_mass_function,
pld.rounded_probability_mass_function)
def test_gaussian_optimistic(self, sensitivity,
expected_rounded_probability_mass_function):
pld = privacy_loss_distribution.GaussianPrivacyLossDistribution(
1,
sensitivity=sensitivity,
pessimistic_estimate=False,
value_discretization_interval=1,
log_mass_truncation_bound=math.log(2) + stats.norm.logcdf(-0.9))
self.assertAlmostEqual(0, pld.infinity_mass)
dictionary_almost_equal(self,
expected_rounded_probability_mass_function,
pld.rounded_probability_mass_function)
def test_gaussian_varying_standard_deviation_and_sensitivity(
self, standard_deviation, sensitivity,
expected_rounded_probability_mass_function):
pld = privacy_loss_distribution.GaussianPrivacyLossDistribution(
standard_deviation,
sensitivity=sensitivity,
value_discretization_interval=1,
log_mass_truncation_bound=math.log(2) + stats.norm.logcdf(-0.9))
self.assertAlmostEqual(stats.norm.cdf(-0.9), pld.infinity_mass)
dictionary_almost_equal(self,
expected_rounded_probability_mass_function,
pld.rounded_probability_mass_function)
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):
pld = privacy_loss_distribution.GaussianPrivacyLossDistribution(
standard_deviation,
sensitivity=sensitivity,
value_discretization_interval=1,
pessimistic_estimate=pessimistic_estimate,
log_mass_truncation_bound=math.log(2) + stats.norm.logcdf(-1))
tail_pld = pld.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)
dictionary_almost_equal(self, expected_tail_probability_mass_function,
tail_pld.tail_probability_mass_function)
def main(argv):
if len(argv) > 1:
raise app.UsageError('Too many command-line arguments.')
# The parameter of Laplace Noise added
parameter_laplace = 3
# PLD for one execution of the Laplace Mechanism. (Throughout we assume that
# sensitivity = 1.)
laplace_pld = privacy_loss_distribution.LaplacePrivacyLossDistribution(
parameter_laplace, value_discretization_interval=1e-3)
# Number of times Laplace Mechanism is run
num_laplace = 40
# PLD for num_laplace executions of the Laplace Mechanism.
composed_laplace_pld = laplace_pld.self_compose(num_laplace)
epsilon = 10
delta = composed_laplace_pld.hockey_stick_divergence(epsilon)
print(f'An algorithm that executes the Laplace Mechanism with parameter '
f'{parameter_laplace} for a total of {num_laplace} times is '
f'({epsilon}, {delta})-DP.')
# PLDs for different mechanisms can also be composed. Below is an example in
# which we compose PLDs for Laplace Mechanism and Gaussian Mechanism.
# STD of the Gaussian Noise
standard_deviation = 5
# PLD for an execution of the Gaussian Mechanism.
gaussian_pld = privacy_loss_distribution.GaussianPrivacyLossDistribution(
standard_deviation, value_discretization_interval=1e-3)
# PLD for num_laplace executions of the Laplace Mechanism and one execution of
# the Gaussian Mechanism.
composed_laplace_and_gaussian_pld = composed_laplace_pld.compose(
gaussian_pld)
epsilon = 10
delta = composed_laplace_and_gaussian_pld.hockey_stick_divergence(epsilon)
print(f'An algorithm that executes the Laplace Mechanism with parameter '
f'{parameter_laplace} for a total of {num_laplace} times and in '
f'addition executes once the Gaussian Mechanism with STD '
f'{standard_deviation} is ({epsilon}, {delta})-DP.')
def test_gaussian_value_errors(self, standard_deviation, sensitivity):
with self.assertRaises(ValueError):
privacy_loss_distribution.GaussianPrivacyLossDistribution(
standard_deviation, sensitivity=sensitivity)
