def test_valid_inclusion_probabilities(self):
"""Sanity checks on the inclusion probabilities in a private sample.
This test contains various checks on the inclusion probabilities computed by
the private sampling class that only returns keys:
1. When delta is low (0.5**30), the inclusion probability of an element with
frequency 1 is delta.
2. When delta is 1.0, the inclusion probability is the same as in a
non-private sample.
3. Inclusion probabilities are between 0.0 and 1.0, and are nondecreasing in
the frequency.
"""
self.assertEqual(
private_sampling.PrivateThresholdSampleKeysOnly(
threshold=1, eps=0.1, delta=0.5**30).compute_inclusion_prob(1),
0.5**30)
self.assertEqual(
private_sampling.PrivateThresholdSampleKeysOnly(
threshold=0.5,
eps=0.1,
delta=1.0,
sampling_method=private_sampling.PrioritySamplingMethod).
compute_inclusion_prob(1), 0.5)
s = private_sampling.PrivateThresholdSampleKeysOnly(threshold=1,
eps=0.1,
delta=0.5**10)
inclusion_prob = [
s.compute_inclusion_prob(i) for i in range(0, 1000, 10)
]
for x in inclusion_prob:
self.assertGreaterEqual(x, 0.0)
self.assertLessEqual(x, 1.0)
for i in range(len(inclusion_prob) - 1):
self.assertGreaterEqual(inclusion_prob[i + 1], inclusion_prob[i])
def inclusion_prob_vec_for_private_sampling_keys_only(max_freq, threshold, eps,
delta, sampling_method):
"""Computes the vector of inclusion probabilities for private sampling."""
s = private_sampling.PrivateThresholdSampleKeysOnly(threshold,
eps,
delta,
sampling_method,
store_every=1)
s.compute_inclusion_prob(max_freq)
return s._inclusion_prob.copy() # pylint: disable=protected-access
def compute_fraction_reported_pws(
freq_vec,
eps,
delta,
sampling_method=private_sampling.AlwaysIncludeSamplingMethod,
threshold=1.0):
"""For a given vector of key frequencies, computes the expected number of keys to reported in a private weighted sample."""
s = private_sampling.PrivateThresholdSampleKeysOnly(
threshold, eps, delta, sampling_method)
expected_sample = 0.0
for freq in freq_vec:
expected_sample += s.compute_inclusion_prob(freq)
return expected_sample / len(freq_vec)
def plot_inclusion_prob_using_precompute(max_freq, sample, output_path):
"""Inclusion probability plots."""
eps = sample.eps
delta = sample.delta
sampling_method = sample.sampling_method
threshold = sample.threshold
log_threshold = math.log10(threshold)
if int(log_threshold) == log_threshold:
log_threshold = int(log_threshold)
plt.clf()
log1_delta = math.log10(delta)
if log1_delta == int(log1_delta):
log1_delta = int(log1_delta)
include_non_private = True
if sampling_method == private_sampling.AlwaysIncludeSamplingMethod or (
sampling_method == private_sampling.PrioritySamplingMethod
and threshold == 1.0):
include_non_private = False
title = ("Inclusion Probability: No Sampling, $\\varepsilon=%s, "
"\\delta=10^{%s}$") % (eps, log1_delta)
elif sampling_method == private_sampling.PrioritySamplingMethod:
title = ("Inclusion Probability: Priority Sampling $\\tau=10^{%s}, "
"\\varepsilon=%s, \\delta=10^{%s}$") % (log_threshold, eps,
log1_delta)
elif sampling_method == private_sampling.PpsworSamplingMethod:
title = (
"Inclusion Probability: PPSWOR $\\tau=10^{%s}, \\varepsilon=%s, "
"\\delta=10^{%s}$") % (log_threshold, eps, log1_delta)
else:
raise NotImplementedError("Sampling method not supported")
plt.xlabel("Frequency")
plt.ylabel("Inclusion Probability")
# plt.yscale("log", basey=10)
# prob_vec_our = [1.0 - sample.compute_reported_frequency_dist(i)[0]
# for i in range(1, max_freq + 1)]
sample = private_sampling.PrivateThresholdSampleKeysOnly(
threshold, eps, delta, sampling_method)
prob_vec_our = [
sample.compute_inclusion_prob(i) for i in range(1, max_freq + 1)
]
prob_vec_histogram = inclusion_prob_vec_using_private_histogram(
max_freq, threshold, eps, delta, sampling_method)
if include_non_private:
plt.loglog(range(1, max_freq + 1), [
sampling_method.inclusion_prob(i, threshold)
for i in range(1,
int(max_freq) + 1)
],
color="tab:green",
label="Non-private",
marker="d",
markevery=0.25)
plt.loglog(range(1, max_freq + 1),
prob_vec_our,
color="tab:blue",
label="PWS",
marker="s",
markevery=0.25)
plt.loglog(range(1, max_freq + 1),
prob_vec_histogram,
color="tab:orange",
label="SbH",
marker=".",
markevery=0.25)
plt.title(title)
plt.legend()
plt.savefig(output_path)