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# Copyright (C) IBM Corporation 2019
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"""
The staircase mechanism in differential privacy.
"""
import secrets
from numbers import Real
import numpy as np
from diffprivlib.mechanisms.laplace import Laplace
from diffprivlib.utils import copy_docstring
[docs]
class Staircase(Laplace):
r"""
The staircase mechanism in differential privacy.
The staircase mechanism is an optimisation of the classical Laplace Mechanism (:class:`.Laplace`), described as a
"geometric mixture of uniform random variables".
Paper link: https://arxiv.org/pdf/1212.1186.pdf
Parameters
----------
epsilon : float
Privacy parameter :math:`\epsilon` for the mechanism. Must be in (0, ∞].
sensitivity : float
The sensitivity of the mechanism. Must be in [0, ∞).
gamma : float, default: 1 / (1 + exp(epsilon/2))
Value of the tuning parameter gamma for the mechanism. Must be in [0, 1].
random_state : int or RandomState, optional
Controls the randomness of the mechanism. To obtain a deterministic behaviour during randomisation,
``random_state`` has to be fixed to an integer.
"""
def __init__(self, *, epsilon, sensitivity, gamma=None, random_state=None):
super().__init__(epsilon=epsilon, delta=0, sensitivity=sensitivity, random_state=random_state)
self.gamma = self._check_gamma(gamma, epsilon=self.epsilon)
if isinstance(self._rng, secrets.SystemRandom):
self._rng = np.random.default_rng()
@classmethod
def _check_gamma(cls, gamma, epsilon=None):
if gamma is None and epsilon is not None:
gamma = 1 / (1 + np.exp(epsilon / 2))
if not isinstance(gamma, Real):
raise TypeError("Gamma must be numeric")
if not 0.0 <= gamma <= 1.0:
raise ValueError("Gamma must be in [0,1]")
return float(gamma)
@copy_docstring(Laplace._check_all)
def _check_all(self, value):
super()._check_all(value)
self._check_gamma(self.gamma)
return True
@classmethod
def _check_epsilon_delta(cls, epsilon, delta):
if not delta == 0:
raise ValueError("Delta must be zero")
return super()._check_epsilon_delta(epsilon, delta)
[docs]
@copy_docstring(Laplace.bias)
def bias(self, value):
return 0.0
@copy_docstring(Laplace.variance)
def variance(self, value):
raise NotImplementedError
[docs]
@copy_docstring(Laplace.randomise)
def randomise(self, value):
self._check_all(value)
sign = -1 if self._rng.random() < 0.5 else 1
geometric_rv = self._rng.geometric(1 - np.exp(- self.epsilon)) - 1
unif_rv = self._rng.random()
binary_rv = 0 if self._rng.random() < self.gamma / (self.gamma +
(1 - self.gamma) * np.exp(- self.epsilon)) else 1
return value + sign * ((1 - binary_rv) * ((geometric_rv + self.gamma * unif_rv) * self.sensitivity) +
binary_rv * ((geometric_rv + self.gamma + (1 - self.gamma) * unif_rv) *
self.sensitivity))