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dp_computations.py
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dp_computations.py
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# Copyright 2022 OpenMined.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Differential privacy computing of count, sum, mean, variance."""
import numpy as np
import pipeline_dp
# TODO: import only modules https://google.github.io/styleguide/pyguide.html#22-imports
from pipeline_dp.aggregate_params import NoiseKind
from dataclasses import dataclass
from pydp.algorithms import numerical_mechanisms as dp_mechanisms
@dataclass
class MeanVarParams:
"""The parameters used for computing the dp sum, count, mean, variance."""
eps: float
delta: float
min_value: float
max_value: float
max_partitions_contributed: int
max_contributions_per_partition: int
noise_kind: NoiseKind # Laplace or Gaussian
def l0_sensitivity(self):
""""Returns the L0 sensitivity of the parameters."""
return self.max_partitions_contributed
def squares_interval(self):
"""Returns the bounds of the interval [min_value^2, max_value^2]."""
if self.min_value < 0 and self.max_value > 0:
return 0, max(self.min_value**2, self.max_value**2)
return self.min_value**2, self.max_value**2
def compute_middle(min_value: float, max_value: float):
""""Returns the middle point of the interval [min_value, max_value]."""
# (min_value + max_value) / 2 may cause an overflow or loss of precision if
# min_value and max_value are large.
return min_value + (max_value - min_value) / 2
def compute_l1_sensitivity(l0_sensitivity: float, linf_sensitivity: float):
"""Calculates the L1 sensitivity based on the L0 and Linf sensitivities.
Args:
l0_sensitivity: The L0 sensitivity.
linf_sensitivity: The Linf sensitivity.
Returns:
The L1 sensitivity.
"""
return l0_sensitivity * linf_sensitivity
def compute_l2_sensitivity(l0_sensitivity: float, linf_sensitivity: float):
"""Calculates the L2 sensitivity based on the L0 and Linf sensitivities.
Args:
l0_sensitivity: The L0 sensitivity.
linf_sensitivity: The Linf sensitivity.
Returns:
The L2 sensitivity.
"""
return np.sqrt(l0_sensitivity) * linf_sensitivity
def compute_sigma(eps: float, delta: float, l2_sensitivity: float):
"""Returns the optimal value of sigma for the Gaussian mechanism.
Args:
eps: The epsilon value.
delta: The delta value.
l2_sensitivity: The L2 sensitivity.
"""
# TODO: use named arguments, when argument names are added in PyDP on PR
# https://github.com/OpenMined/PyDP/pull/398.
return dp_mechanisms.GaussianMechanism(eps, delta, l2_sensitivity).std
def apply_laplace_mechanism(value: float, eps: float, l1_sensitivity: float):
"""Applies the Laplace mechanism to the value.
Args:
value: The initial value.
eps: The epsilon value.
l1_sensitivity: The L1 sensitivity.
Returns:
The value resulted after adding the noise.
"""
mechanism = dp_mechanisms.LaplaceMechanism(epsilon=eps,
sensitivity=l1_sensitivity)
return mechanism.add_noise(1.0 * value)
def apply_gaussian_mechanism(value: float, eps: float, delta: float,
l2_sensitivity: float):
"""Applies the Gaussian mechanism to the value.
Args:
value: The initial value.
eps: The epsilon value.
delta: The delta value.
l2_sensitivity: The L2 sensitivity.
Returns:
The value resulted after adding the noise.
"""
# TODO: use named arguments, when argument names are added in PyDP on PR
# https://github.com/OpenMined/PyDP/pull/398.
mechanism = dp_mechanisms.GaussianMechanism(eps, delta, l2_sensitivity)
return mechanism.add_noise(1.0 * value)
def _add_random_noise(
value: float,
eps: float,
delta: float,
l0_sensitivity: float,
linf_sensitivity: float,
noise_kind: NoiseKind,
):
"""Adds random noise according to the parameters.
Args:
value: The initial value.
eps: The epsilon value.
delta: The delta value.
l0_sensitivity: The L0 sensitivity.
linf_sensitivity: The Linf sensitivity.
noise_kind: The kind of noise used.
Returns:
The value resulted after adding the random noise.
"""
if noise_kind == NoiseKind.LAPLACE:
l1_sensitivity = compute_l1_sensitivity(l0_sensitivity,
linf_sensitivity)
return apply_laplace_mechanism(value, eps, l1_sensitivity)
if noise_kind == NoiseKind.GAUSSIAN:
l2_sensitivity = compute_l2_sensitivity(l0_sensitivity,
linf_sensitivity)
return apply_gaussian_mechanism(value, eps, delta, l2_sensitivity)
raise ValueError("Noise kind must be either Laplace or Gaussian.")
@dataclass
class AdditiveVectorNoiseParams:
eps_per_coordinate: float
delta_per_coordinate: float
max_norm: float
l0_sensitivity: float
linf_sensitivity: float
norm_kind: pipeline_dp.aggregate_params.NormKind
noise_kind: NoiseKind
def _clip_vector(vec: np.ndarray, max_norm: float,
norm_kind: pipeline_dp.aggregate_params.NormKind):
norm_kind = norm_kind.value # type: str
if norm_kind == "linf":
return np.clip(vec, -max_norm, max_norm)
if norm_kind in {"l1", "l2"}:
norm_kind = int(norm_kind[-1])
vec_norm = np.linalg.norm(vec, ord=norm_kind)
mul_coef = min(1, max_norm / vec_norm)
return vec * mul_coef
raise NotImplementedError(
f"Vector Norm of kind '{norm_kind}' is not supported.")
def add_noise_vector(vec: np.ndarray, noise_params: AdditiveVectorNoiseParams):
"""Adds noise to vector to make the vector sum computation (eps, delta)-DP.
Args:
vec: the queried raw vector
noise_params: parameters of the noise to add to the computation
"""
vec = _clip_vector(vec, noise_params.max_norm, noise_params.norm_kind)
vec = np.array([
_add_random_noise(
s,
noise_params.eps_per_coordinate,
noise_params.delta_per_coordinate,
noise_params.l0_sensitivity,
noise_params.linf_sensitivity,
noise_params.noise_kind,
) for s in vec
])
return vec
def equally_split_budget(eps: float, delta: float, no_mechanisms: int):
"""Equally splits the budget (eps, delta) between a given number of mechanisms.
Args:
eps, delta: The available budget.
no_mechanisms: The number of mechanisms between which we split the budget.
Raises:
ValueError: The number of mechanisms must be a positive integer.
Returns:
An array with the split budgets.
"""
if no_mechanisms <= 0:
raise ValueError("The number of mechanisms must be a positive integer.")
# These variables are used to keep track of the budget used.
# In this way, we can improve accuracy of floating-point operations.
eps_used = delta_used = 0
budgets = []
for _ in range(no_mechanisms - 1):
budget = (eps / no_mechanisms, delta / no_mechanisms)
eps_used += budget[0]
delta_used += budget[1]
budgets.append(budget)
budgets.append((eps - eps_used, delta - delta_used))
return budgets
def compute_dp_count(count: int, dp_params: MeanVarParams):
"""Computes DP count.
Args:
count: Non-DP count.
dp_params: The parameters used at computing the noise.
Raises:
ValueError: The noise kind is invalid.
"""
l0_sensitivity = dp_params.l0_sensitivity()
linf_sensitivity = dp_params.max_contributions_per_partition
return _add_random_noise(
count,
dp_params.eps,
dp_params.delta,
l0_sensitivity,
linf_sensitivity,
dp_params.noise_kind,
)
def compute_dp_sum(sum: float, dp_params: MeanVarParams):
"""Computes DP sum.
Args:
sum: Non-DP sum.
dp_params: The parameters used at computing the noise.
Raises:
ValueError: The noise kind is invalid.
"""
l0_sensitivity = dp_params.l0_sensitivity()
linf_sensitivity = dp_params.max_contributions_per_partition * max(
abs(dp_params.min_value), abs(dp_params.max_value))
if linf_sensitivity == 0:
return 0
return _add_random_noise(
sum,
dp_params.eps,
dp_params.delta,
l0_sensitivity,
linf_sensitivity,
dp_params.noise_kind,
)
def _compute_mean(
count: float,
dp_count: float,
sum: float,
min_value: float,
max_value: float,
eps: float,
delta: float,
l0_sensitivity: float,
max_contributions_per_partition: float,
noise_kind: NoiseKind,
):
"""Helper function to compute the DP mean of a raw sum using the DP count.
Args:
count: Non-DP count.
dp_count: DP count.
sum: Non-DP sum.
min_value, max_value: The lowest/highest contribution.
eps, delta: The budget allocated.
l0_sensitivity: The L0 sensitivity.
max_contributions_per_partition: The maximum number of contributions
per partition.
noise_kind: The kind of noise used.
Raises:
ValueError: The noise kind is invalid.
Returns:
The anonymized mean.
"""
if min_value == max_value:
return min_value
middle = compute_middle(min_value, max_value)
linf_sensitivity = max_contributions_per_partition * abs(middle - min_value)
normalized_sum = sum - count * middle
dp_normalized_sum = _add_random_noise(normalized_sum, eps, delta,
l0_sensitivity, linf_sensitivity,
noise_kind)
# Clamps dp_count to 1.0. We know that actual count > 1 except when the
# input set is empty, in which case it shouldn't matter much what the
# denominator is.
dp_count_clamped = max(1.0, dp_count)
return dp_normalized_sum / dp_count_clamped + middle
def compute_dp_mean(count: int, sum: float, dp_params: MeanVarParams):
"""Computes DP mean.
Args:
count: Non-DP count.
sum: Non-DP sum.
dp_params: The parameters used at computing the noise.
Raises:
ValueError: The noise kind is invalid.
Returns:
The tuple of anonymized count, sum and mean.
"""
# Splits the budget equally between the two mechanisms.
(count_eps, count_delta), (sum_eps, sum_delta) = equally_split_budget(
dp_params.eps, dp_params.delta, 2)
l0_sensitivity = dp_params.l0_sensitivity()
dp_count = _add_random_noise(
count,
count_eps,
count_delta,
l0_sensitivity,
dp_params.max_contributions_per_partition,
dp_params.noise_kind,
)
dp_mean = _compute_mean(
count,
dp_count,
sum,
dp_params.min_value,
dp_params.max_value,
sum_eps,
sum_delta,
l0_sensitivity,
dp_params.max_contributions_per_partition,
dp_params.noise_kind,
)
return dp_count, dp_mean * dp_count, dp_mean
def compute_dp_var(count: int, sum: float, sum_squares: float,
dp_params: MeanVarParams):
"""Computes DP variance.
Args:
count: Non-DP count.
sum: Non-DP sum.
sum_squares: Non-DP sum of squares.
dp_params: The parameters used at computing the noise.
Raises:
ValueError: The noise kind is invalid.
Returns:
The tuple of anonymized count, sum, sum_squares and variance.
"""
# Splits the budget equally between the three mechanisms.
(
(count_eps, count_delta),
(sum_eps, sum_delta),
(sum_squares_eps, sum_squares_delta),
) = equally_split_budget(dp_params.eps, dp_params.delta, 3)
l0_sensitivity = dp_params.l0_sensitivity()
dp_count = _add_random_noise(
count,
count_eps,
count_delta,
l0_sensitivity,
dp_params.max_contributions_per_partition,
dp_params.noise_kind,
)
# Computes and adds noise to the mean.
dp_mean = _compute_mean(
count,
dp_count,
sum,
dp_params.min_value,
dp_params.max_value,
sum_eps,
sum_delta,
l0_sensitivity,
dp_params.max_contributions_per_partition,
dp_params.noise_kind,
)
squares_min_value, squares_max_value = dp_params.squares_interval()
# Computes and adds noise to the mean of squares.
dp_mean_squares = _compute_mean(count, dp_count, sum_squares,
squares_min_value, squares_max_value,
sum_squares_eps, sum_squares_delta,
l0_sensitivity,
dp_params.max_contributions_per_partition,
dp_params.noise_kind)
dp_var = dp_mean_squares - dp_mean**2
return dp_count, dp_mean * dp_count, dp_mean_squares * dp_count, dp_var