def testResolveQuestion(self):
# First check that we get nothing back when we test with an empty model:
cm = confusion_matrices.ConfusionMatrices()
cm.priors = {}
cm.confusion_matrices = {}
resolution_map = cm.ResolveQuestion(test_util.IPEIROTIS_RESPONSES[0])
test_util.AssertMapsAlmostEqual(self, {}, resolution_map)
# Use data from the solution to the Ipeirotis example:
cm = confusion_matrices.ConfusionMatrices()
cm.priors = IPEIROTIS_MLE_PRIORS
cm.confusion_matrices = IPEIROTIS_MLE_CM
for i in range(len(test_util.IPEIROTIS_DATA)):
resolution_map = cm.ResolveQuestion(test_util.IPEIROTIS_RESPONSES[i])
test_util.AssertMapsAlmostEqual(self,
test_util.IPEIROTIS_ALL_ANSWERS[i],
resolution_map,
label='question ' + str(i) + ', answer')
# And again for the Dawid & Skene example:
cm.priors = DS_MLE_PRIORS
cm.confusion_matrices = DS_MLE_CM
for i in range(len(test_util.DS_DATA)):
resolution_map = cm.ResolveQuestion(test_util.DS_RESPONSES[i])
test_util.AssertMapsAlmostEqual(self,
test_util.DS_EM_CM_RESOLUTIONS[i],
resolution_map,
label='question ' + str(i) + ', answer')
def testIntegrate(self):
# Seed the random number generator to produce deterministic test results:
numpy.random.seed(0)
# TODO(tpw): This is necessary but not sufficient. Python's arbitrary
# ordering of dict iteration makes some deeper calls
# non-deterministic, and thus this test may exhibit flakiness.
# Initialize a confusion matrices model:
cm = confusion_matrices.ConfusionMatrices()
# First check the estimated answers for the Ipeirotis example, using the
# EM algorithm's results as a starting point for the sampling chain:
data = test_util.IPEIROTIS_DATA_FINAL
sampler = substitution_sampling.SubstitutionSampling()
sampler.Integrate(data, cm, golden_questions=['url1', 'url2'],
number_of_samples=20000)
result = cm.ExtractResolutions(data)
test_util.AssertResolutionsAlmostEqual(self,
IPEIROTIS_SS_CM_RESOLUTIONS, result,
places=1)
# Now check the estimated answers for the Dawid & Skene example, again using
# the EM algorithm's results as a starting point for the sampling chain:
numpy.random.seed(0)
data = test_util.DS_DATA_FINAL
sampler = substitution_sampling.SubstitutionSampling()
sampler.Integrate(data, cm, number_of_samples=20000)
result = cm.ExtractResolutions(data)
test_util.AssertResolutionsAlmostEqual(self, DS_SS_CM_RESOLUTIONS, result,
places=2)
def testIterateUntilConvergence(self):
# Initialize a confusion matrices model and a VB object:
cm = confusion_matrices.ConfusionMatrices()
vb = alternating_resolution.VariationalBayes()
# First test with the Ipeirotis example:
data = test_util.IPEIROTIS_DATA
cm.InitializeResolutions(data)
self.assertTrue(
vb.IterateUntilConvergence(data,
cm,
golden_questions=['url1', 'url2']))
result = cm.ExtractResolutions(data)
test_util.AssertResolutionsAlmostEqual(self,
IPEIROTIS_VB_CM_RESOLUTIONS,
result)
# Now test with the Dawid & Skene example:
data = test_util.DS_DATA
cm.InitializeResolutions(data)
# VB is a little slower than EM, so we'll give it algorithm up to 50
# iterations to converge:
self.assertTrue(vb.IterateUntilConvergence(data, cm,
max_iterations=50))
result = cm.ExtractResolutions(data)
test_util.AssertResolutionsAlmostEqual(self, DS_VB_CM_RESOLUTIONS,
result)
def testMutualInformation(self):
# Use data from the solution to the Ipeirotis example:
cm = confusion_matrices.ConfusionMatrices()
cm.priors = IPEIROTIS_MLE_PRIORS
cm.confusion_matrices = IPEIROTIS_MLE_CM
# First we'll test for a first judgment:
expected = {'worker1': 0.0,
'worker2': 0.419973,
'worker3': 0.970951,
'worker4': 0.970951,
'worker5': 0.970951}
result = {}
for contributor in expected:
result[contributor] = cm.MutualInformation(contributor)
test_util.AssertMapsAlmostEqual(self, expected, result, label='contributor')
# Now we'll test for a second judgment:
previous_responses = [('worker2', 'p**n', {})]
expected = {'worker1': 0.0,
'worker2': 0.4581059,
'worker3': 0.9182958,
'worker4': 0.9182958,
'worker5': 0.9182958}
result = {}
for contributor in expected:
result[contributor] = cm.MutualInformation(
contributor, previous_responses=previous_responses)
test_util.AssertMapsAlmostEqual(self, expected, result, label='contributor')
# However, if the first judgment was given by a perfect contributor (for
# example, worker3), then no second judgment can give any more information:
previous_responses = [('worker3', 'notporn', {})]
self.assertAlmostEqual(0.0, cm.MutualInformation(
'worker2', previous_responses=previous_responses))
def testSetMLEParameters(self):
# Use data from the solution to the Ipeirotis example:
cm = confusion_matrices.ConfusionMatrices()
cm.SetMLEParameters(test_util.IPEIROTIS_DATA_FINAL)
# Check that cm.priors was set correctly:
test_util.AssertMapsAlmostEqual(self, IPEIROTIS_MLE_PRIORS, cm.priors,
label='answer')
# Check that cm.confusion_matrices was set correctly:
test_util.AssertConfusionMatricesAlmostEqual(self,
IPEIROTIS_MLE_CM,
cm.confusion_matrices)
def testQuestionEntropy(self):
# Use data from the solution to the Ipeirotis example:
cm = confusion_matrices.ConfusionMatrices()
cm.priors = IPEIROTIS_MLE_PRIORS
# Test in binary:
self.assertAlmostEqual(0.9709506, cm.QuestionEntropy())
# And in digits:
self.assertAlmostEqual(0.2922853, cm.QuestionEntropy(radix=10))
# Ensure that we correctly normalize non-normalized priors (those produced
# by VariationalParameters, for example):
cm.priors = {k: v * 3.0 for k, v in IPEIROTIS_MLE_PRIORS.iteritems()}
self.assertAlmostEqual(0.9709506, cm.QuestionEntropy())
self.assertAlmostEqual(0.2922853, cm.QuestionEntropy(radix=10))
def testIterateUntilConvergence(self):
# Initialize a confusion matrices model and an EM object:
cm = confusion_matrices.ConfusionMatrices()
maximizer = alternating_resolution.ExpectationMaximization()
# First with the Ipeirotis example:
data = test_util.IPEIROTIS_DATA
cm.InitializeResolutions(data)
self.assertTrue(maximizer.IterateUntilConvergence(data, cm))
expected = cm.ExtractResolutions(test_util.IPEIROTIS_DATA_FINAL)
result = cm.ExtractResolutions(data)
test_util.AssertResolutionsAlmostEqual(self, expected, result)
# Now with the Dawid & Skene example:
data = test_util.DS_DATA
cm.InitializeResolutions(data)
# The algorithm takes more than 10 steps to converge, so we expect
# IterateUntilConvergence to return False:
self.assertFalse(
maximizer.IterateUntilConvergence(data, cm, max_iterations=10))
# Nevertheless, its results are accurate to 3 places:
expected = cm.ExtractResolutions(test_util.DS_DATA_FINAL)
result = cm.ExtractResolutions(data)
test_util.AssertResolutionsAlmostEqual(self, expected, result)
def testPointwiseMutualInformation(self):
# Use data from the solution to the Ipeirotis example:
cm = confusion_matrices.ConfusionMatrices()
cm.priors = IPEIROTIS_MLE_PRIORS
cm.confusion_matrices = IPEIROTIS_MLE_CM
# First we'll test the information of a first judgment.
# We're going to define four helper variables:
# Two for the information conent of the true resolutions:
notporn_inf = -math.log(cm.priors['notporn'], 2)
porn_inf = -math.log(cm.priors['p**n'], 2)
# Two for the information given by contributor 'worker2', judgment 'p**n':
norm = (cm.priors['notporn'] *
cm.confusion_matrices['worker2']['notporn']['p**n'] +
cm.priors['p**n'] *
cm.confusion_matrices['worker2']['p**n']['p**n'])
inf_01 = math.log(
cm.confusion_matrices['worker2']['notporn']['p**n'] / norm, 2)
inf_11 = math.log(
cm.confusion_matrices['worker2']['p**n']['p**n'] / norm, 2)
# Now, worker1 is a spammer which always gives us zero information.
# worker2 gives us complete information when it gives judgment 'notporn',
# but partial information when it gives judgment 'p**n'.
# The other three contributors give us complete information for all of
# their judgments, even though worker5 always lies.
# Entries for impossible contingencies in the matrix below are filled in
# with 0.0.
expected = {'worker1': {'notporn': {'notporn': 0.0, 'p**n': 0.0},
'p**n': {'notporn': 0.0, 'p**n': 0.0}},
'worker2': {'notporn': {'notporn': notporn_inf, 'p**n': inf_01},
'p**n': {'notporn': 0.0, 'p**n': inf_11}},
'worker3': {'notporn': {'notporn': notporn_inf, 'p**n': 0.0},
'p**n': {'notporn': 0.0, 'p**n': porn_inf}},
'worker4': {'notporn': {'notporn': notporn_inf, 'p**n': 0.0},
'p**n': {'notporn': 0.0, 'p**n': porn_inf}},
'worker5': {'notporn': {'notporn': 0.0, 'p**n': notporn_inf},
'p**n': {'notporn': porn_inf, 'p**n': 0.0}}}
# Pack the results into a structure having the same form as
# cm.confusion_matrices:
result = {}
for contributor in expected:
result[contributor] = {}
for answer in expected[contributor]:
result[contributor][answer] = {}
for judgment in expected[contributor][answer]:
result[contributor][answer][judgment] = cm.PointwiseMutualInformation(
contributor, answer, judgment)
# Thus, we can use the method test_util.AssertConfusionMatricesAlmostEqual:
test_util.AssertConfusionMatricesAlmostEqual(self, expected, result)
# Now we'll test the information of a second judgment.
# Start by supposing that worker2 gave judgment 'p**n':
previous_responses = [('worker2', 'p**n', {})]
# Suppose the correct answer is 'notporn', and the next judgment is
# worker2 giving another 'p**n' judgment. After the first judgment, the
# probability of the correct answer is 1/3. After the second judgment, the
# probability of the correct answer is 1/7. So the change in information is
# log(3/7), or about -1.222392 bits:
self.assertAlmostEqual(math.log(3.0/7.0, 2), cm.PointwiseMutualInformation(
'worker2', 'notporn', 'p**n', previous_responses=previous_responses))
# Now suppose the correct answer is 'p**n', and the next judgment is
# worker2 giving another 'p**n' judgment. After the first judgment, the
# probability of the correct answer is 2/3. After the second judgment, the
# probability of the correct answer is 6/7. So the change in information is
# log(9/7):
self.assertAlmostEqual(math.log(9.0/7.0, 2), cm.PointwiseMutualInformation(
'worker2', 'p**n', 'p**n', previous_responses=previous_responses))
# Now suppose the correct answer is 'notporn', and the next judgment is
# worker2 giving a 'notporn' judgment. After the first judgment, the
# probability of the correct answer is 1/3. After the second judgment, the
# probability of the correct answer is 1. So the change in information is
# log(3):
self.assertAlmostEqual(math.log(3.0, 2), cm.PointwiseMutualInformation(
'worker2', 'notporn', 'notporn', previous_responses=previous_responses))
# Finally, suppose the correct answer is 'p**n', and the next judgment is
# worker5 giving a 'notporn' judgment. After the first judgment, the
# probability of the correct answer is 2/3. After the second judgment, the
# probability of the correct answer is 1. So the change in information is
# log(3/2):
self.assertAlmostEqual(math.log(1.5, 2), cm.PointwiseMutualInformation(
'worker5', 'p**n', 'notporn', previous_responses=previous_responses))
def _CreateSubmodel(unused_path):
"""Returns a new ConfusionMatrix object. Convenient for overriding."""
return confusion_matrices.ConfusionMatrices()
