staircase.py

# MIT License
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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


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)

    @copy_docstring(Laplace.bias)
    def bias(self, value):
        return 0.0

    @copy_docstring(Laplace.variance)
    def variance(self, value):
        raise NotImplementedError

    @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))