154 lines
5.6 KiB
Python
154 lines
5.6 KiB
Python
# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Tests for rdp_accountant.py."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import sys
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from absl.testing import absltest
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from absl.testing import parameterized
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import mpmath as mp
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import numpy as np
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from privacy.analysis import rdp_accountant
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class TestGaussianMoments(parameterized.TestCase):
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#################################
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# HELPER FUNCTIONS: #
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# Exact computations using #
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# multi-precision arithmetic. #
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#################################
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def _log_float_mp(self, x):
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# Convert multi-precision input to float log space.
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if x >= sys.float_info.min:
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return float(mp.log(x))
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else:
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return -np.inf
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def _integral_mp(self, fn, bounds=(-mp.inf, mp.inf)):
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integral, _ = mp.quad(fn, bounds, error=True, maxdegree=8)
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return integral
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def _distributions_mp(self, sigma, q):
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def _mu0(x):
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return mp.npdf(x, mu=0, sigma=sigma)
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def _mu1(x):
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return mp.npdf(x, mu=1, sigma=sigma)
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def _mu(x):
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return (1 - q) * _mu0(x) + q * _mu1(x)
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return _mu0, _mu # Closure!
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def _mu1_over_mu0(self, x, sigma):
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# Closed-form expression for N(1, sigma^2) / N(0, sigma^2) at x.
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return mp.exp((2 * x - 1) / (2 * sigma**2))
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def _mu_over_mu0(self, x, q, sigma):
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return (1 - q) + q * self._mu1_over_mu0(x, sigma)
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def _compute_a_mp(self, sigma, q, alpha):
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"""Compute A_alpha for arbitrary alpha by numerical integration."""
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mu0, _ = self._distributions_mp(sigma, q)
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a_alpha_fn = lambda z: mu0(z) * self._mu_over_mu0(z, q, sigma)**alpha
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a_alpha = self._integral_mp(a_alpha_fn)
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return a_alpha
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# TEST ROUTINES
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def test_compute_rdp_no_data(self):
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# q = 0
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self.assertEqual(rdp_accountant.compute_rdp(0, 10, 1, 20), 0)
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def test_compute_rdp_no_sampling(self):
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# q = 1, RDP = alpha/2 * sigma^2
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self.assertEqual(rdp_accountant.compute_rdp(1, 10, 1, 20), 0.1)
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def test_compute_rdp_scalar(self):
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rdp_scalar = rdp_accountant.compute_rdp(0.1, 2, 10, 5)
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self.assertAlmostEqual(rdp_scalar, 0.07737, places=5)
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def test_compute_rdp_sequence(self):
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rdp_vec = rdp_accountant.compute_rdp(0.01, 2.5, 50,
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[1.5, 2.5, 5, 50, 100, np.inf])
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self.assertSequenceAlmostEqual(
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rdp_vec, [0.00065, 0.001085, 0.00218075, 0.023846, 167.416307, np.inf],
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delta=1e-5)
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params = ({'q': 1e-7, 'sigma': .1, 'order': 1.01},
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{'q': 1e-6, 'sigma': .1, 'order': 256},
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{'q': 1e-5, 'sigma': .1, 'order': 256.1},
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{'q': 1e-6, 'sigma': 1, 'order': 27},
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{'q': 1e-4, 'sigma': 1., 'order': 1.5},
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{'q': 1e-3, 'sigma': 1., 'order': 2},
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{'q': .01, 'sigma': 10, 'order': 20},
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{'q': .1, 'sigma': 100, 'order': 20.5},
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{'q': .99, 'sigma': .1, 'order': 256},
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{'q': .999, 'sigma': 100, 'order': 256.1})
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# pylint:disable=undefined-variable
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@parameterized.parameters(p for p in params)
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def test_compute_log_a_equals_mp(self, q, sigma, order):
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# Compare the cheap computation of log(A) with an expensive, multi-precision
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# computation.
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log_a = rdp_accountant._compute_log_a(q, sigma, order)
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log_a_mp = self._log_float_mp(self._compute_a_mp(sigma, q, order))
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np.testing.assert_allclose(log_a, log_a_mp, rtol=1e-4)
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def test_get_privacy_spent_check_target_delta(self):
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orders = range(2, 33)
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rdp = rdp_accountant.compute_rdp(0.01, 4, 10000, orders)
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eps, _, opt_order = rdp_accountant.get_privacy_spent(
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orders, rdp, target_delta=1e-5)
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self.assertAlmostEqual(eps, 1.258575, places=5)
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self.assertEqual(opt_order, 20)
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def test_get_privacy_spent_check_target_eps(self):
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orders = range(2, 33)
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rdp = rdp_accountant.compute_rdp(0.01, 4, 10000, orders)
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_, delta, opt_order = rdp_accountant.get_privacy_spent(
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orders, rdp, target_eps=1.258575)
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self.assertAlmostEqual(delta, 1e-5)
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self.assertEqual(opt_order, 20)
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def test_check_composition(self):
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orders = (1.25, 1.5, 1.75, 2., 2.5, 3., 4., 5., 6., 7., 8., 10., 12., 14.,
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16., 20., 24., 28., 32., 64., 256.)
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rdp = rdp_accountant.compute_rdp(q=1e-4,
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noise_multiplier=.4,
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steps=40000,
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orders=orders)
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eps, _, opt_order = rdp_accountant.get_privacy_spent(orders, rdp,
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target_delta=1e-6)
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rdp += rdp_accountant.compute_rdp(q=0.1,
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noise_multiplier=2,
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steps=100,
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orders=orders)
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eps, _, opt_order = rdp_accountant.get_privacy_spent(orders, rdp,
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target_delta=1e-5)
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self.assertAlmostEqual(eps, 8.509656, places=5)
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self.assertEqual(opt_order, 2.5)
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if __name__ == '__main__':
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absltest.main()
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