def testNoWeightedExamples(self):
# Setup test data with 1 positive, and 1 negative example.
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [1]}, 1),
]
# Zeroed out example weights.
example_weights = [0.0, 0.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.5,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
self.assertAllClose([0.5, 0.5], lr.predictions(examples).eval())
with self.assertRaisesOpError(
'No weighted examples in 2 training examples'):
lr.minimize().run()
self.assertAllClose([0.5, 0.5], lr.predictions(examples).eval())
def testDuplicateExampleIds(self):
# Setup test data with 1 positive, and 1 negative example.
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [1]}, 1),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
examples['example_ids'] = ['duplicate_id'
for x in examples['example_ids']]
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.5,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
self.assertAllClose([0.5, 0.5], lr.predictions(examples).eval())
with self.assertRaisesOpError('Detected 1 duplicates in example_ids'):
lr.minimize().run()
self.assertAllClose([0.5, 0.5], lr.predictions(examples).eval())
def testSomeUnweightedExamples(self):
# Setup test data with 4 examples, but should produce the same
# results as testSimple.
example_protos = [
# Will be used.
make_example_proto({"age": [0], "gender": [0]}, 0),
# Will be ignored.
make_example_proto({"age": [1], "gender": [0]}, 0),
# Will be used.
make_example_proto({"age": [1], "gender": [1]}, 1),
# Will be ignored.
make_example_proto({"age": [1], "gender": [0]}, 1),
]
example_weights = [1.0, 0.0, 1.0, 0.0]
with self._single_threaded_test_session():
# Only use examples 0 and 2
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="logistic_loss")
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in xrange(_MAX_ITERATIONS):
train_op.run()
self.assertAllClose(0.411608, unregularized_loss.eval(), atol=0.05)
self.assertAllClose(0.525457, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllClose([0, 1, 1, 1], predicted_labels.eval())
self.assertAllClose(0.01, lr.approximate_duality_gap().eval(), rtol=1e-2, atol=1e-2)
def testSimpleNoL2(self):
# Same as test above (so comments from above apply) but without an L2.
# The algorithm should behave as if we have an L2 of 1 in optimization but
# 0 in regularized_loss.
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [1]}, 1),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0, symmetric_l1_regularization=0, loss_type="logistic_loss")
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
self.assertAllClose(0.693147, unregularized_loss.eval())
self.assertAllClose(0.693147, loss.eval())
train_op = lr.minimize()
for _ in xrange(_MAX_ITERATIONS):
train_op.run()
# There is neither L1 nor L2 loss, so regularized and unregularized losses
# should be exactly the same.
self.assertAllClose(0.40244, unregularized_loss.eval(), atol=0.01)
self.assertAllClose(0.40244, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 1], predicted_labels.eval())
self.assertAllClose(0.01, lr.approximate_duality_gap().eval(), rtol=1e-2, atol=1e-2)
def testSimple(self):
# Setup test data
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [1]}, 1),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="logistic_loss")
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
self.assertAllClose(0.693147, unregularized_loss.eval())
self.assertAllClose(0.693147, loss.eval())
train_op = lr.minimize()
for _ in xrange(_MAX_ITERATIONS):
train_op.run()
# The high tolerance in unregularized_loss comparisons is due to the
# fact that it's possible to trade off unregularized_loss vs.
# regularization and still have a sum that is quite close to the
# optimal regularized_loss value. SDCA's duality gap only ensures that
# the regularized_loss is within 0.01 of optimal.
# 0.525457 is the optimal regularized_loss.
# 0.411608 is the unregularized_loss at that optimum.
self.assertAllClose(0.411608, unregularized_loss.eval(), atol=0.05)
self.assertAllClose(0.525457, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 1], predicted_labels.eval())
self.assertAllClose(0.01, lr.approximate_duality_gap().eval(), rtol=1e-2, atol=1e-2)
def testImbalanced(self):
# Setup test data with 1 positive, and 3 negative examples.
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [2], "gender": [0]}, 0),
make_example_proto({"age": [3], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [1]}, 1),
]
example_weights = [1.0, 1.0, 1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(3, 1)
options = dict(
symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="logistic_loss", prior=-1.09861
)
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
prediction = lr.predictions(examples)
lr.minimize().run()
self.assertAllClose(0.331710, unregularized_loss.eval(), rtol=3e-2, atol=3e-2)
self.assertAllClose(0.591295, loss.eval(), rtol=3e-2, atol=3e-2)
predicted_labels = tf.cast(tf.greater_equal(prediction, tf.ones_like(prediction) * 0.5), tf.float32)
self.assertAllEqual([0, 0, 0, 1], predicted_labels.eval())
def testSomeUnweightedExamples(self):
# Setup test data with 4 examples, but should produce the same
# results as testSimple.
example_protos = [
# Will be used.
make_example_proto({"age": [0], "gender": [0]}, 0),
# Will be ignored.
make_example_proto({"age": [1], "gender": [0]}, 0),
# Will be used.
make_example_proto({"age": [1], "gender": [1]}, 1),
# Will be ignored.
make_example_proto({"age": [1], "gender": [0]}, 1),
]
example_weights = [1.0, 0.0, 1.0, 0.0]
with self._single_threaded_test_session():
# Only use examples 0 and 2
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="logistic_loss")
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
prediction = lr.predictions(examples)
lr.minimize().run()
self.assertAllClose(0.395226, unregularized_loss.eval(), rtol=3e-2, atol=3e-2)
self.assertAllClose(0.657446, loss.eval(), rtol=3e-2, atol=3e-2)
predicted_labels = tf.cast(tf.greater_equal(prediction, tf.ones_like(prediction) * 0.5), tf.float32)
self.assertAllClose([0, 1, 1, 1], predicted_labels.eval())
def testHingeDenseFeaturesWeightedExamples(self):
with self._single_threaded_test_session():
examples = make_dense_examples_dict(
dense_feature_values=[[1.0, 1.0], [0.5, -0.5]],
weights=[3.0, 1.0],
labels=[1.0, 0.0])
variables = make_dense_variable_dict(2, 2)
options = dict(symmetric_l2_regularization=1.0,
symmetric_l1_regularization=0,
loss_type='hinge_loss')
tf.initialize_all_variables().run()
model = SdcaModel(CONTAINER, examples, variables, options)
predictions = model.predictions(examples)
binary_predictions = get_binary_predictions_for_hinge(predictions)
model.minimize().run()
# Point (1.0, 0.5) has higher weight than (1.0, -0.5) so the model will
# try to increase the margin from (1.0, 0.5). Due to regularization,
# (1.0, -0.5) will be within the margin. For these points and example
# weights, the optimal weights are w_1~=0.4 and w_2~=1.2 which give an L2
# loss of 0.25 * 1.6 = 0.4. The binary predictions will be correct, but
# the boundary will be much closer to the 2nd point than the first one.
self.assertAllClose([1.0, -0.2], predictions.eval(), atol=0.05)
self.assertAllClose([1.0, 0.0], binary_predictions.eval(), atol=0.05)
unregularized_loss = model.unregularized_loss(examples)
regularized_loss = model.regularized_loss(examples)
self.assertAllClose(0.2, unregularized_loss.eval(), atol=0.02)
self.assertAllClose(0.6, regularized_loss.eval(), atol=0.02)
def testImbalanced(self):
# Setup test data with 1 positive, and 3 negative examples.
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [2], "gender": [0]}, 0),
make_example_proto({"age": [3], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [1]}, 1),
]
example_weights = [1.0, 1.0, 1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(3, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="logistic_loss")
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in xrange(_MAX_ITERATIONS):
train_op.run()
self.assertAllClose(0.226487 + 0.102902, unregularized_loss.eval(), atol=0.08)
self.assertAllClose(0.328394 + 0.131364, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 0, 0, 1], predicted_labels.eval())
self.assertAllClose(0.01, lr.approximate_duality_gap().eval(), rtol=1e-2, atol=1e-2)
def testDenseFeaturesWeightedExamples(self):
with self._single_threaded_test_session():
examples, variables = make_dense_examples_and_variables_dicts(
dense_features_values=[[[1.0], [1.0]], [[0.5], [-0.5]]], weights=[3.0, 1.0], labels=[1.0, 0.0]
)
options = dict(symmetric_l2_regularization=1.0, symmetric_l1_regularization=0, loss_type="hinge_loss")
model = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = model.predictions(examples)
binary_predictions = get_binary_predictions_for_hinge(predictions)
train_op = model.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# Point (1.0, 0.5) has higher weight than (1.0, -0.5) so the model will
# try to increase the margin from (1.0, 0.5). Due to regularization,
# (1.0, -0.5) will be within the margin. For these points and example
# weights, the optimal weights are w_1~=0.4 and w_2~=1.2 which give an L2
# loss of 0.5 * 0.25 * 0.25 * 1.6 = 0.2. The binary predictions will be
# correct, but the boundary will be much closer to the 2nd point than the
# first one.
self.assertAllClose([1.0, -0.2], predictions.eval(), atol=0.05)
self.assertAllEqual([1, 0], binary_predictions.eval())
unregularized_loss = model.unregularized_loss(examples)
regularized_loss = model.regularized_loss(examples)
self.assertAllClose(0.2, unregularized_loss.eval(), atol=0.02)
self.assertAllClose(0.4, regularized_loss.eval(), atol=0.02)
def testLinearFeatureValues(self):
# Setup test data
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, -10.0, -2.0),
make_example_proto(
{'age': [1],
'gender': [1]}, 14.0, 2.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.5,
symmetric_l1_regularization=0,
loss_type='squared_loss',
prior=0.0)
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
prediction = lr.predictions(examples)
lr.minimize().run()
# Predictions should be 8/9 of label due to minimizing regularized loss:
# (label - 2 * 2 * weight)^2 / 2 + L2 * 2 * weight^2
self.assertAllClose([-10.0 * 8 / 9, 14.0 * 8 / 9],
prediction.eval(),
rtol=0.07)
def testDenseFeatures(self):
with self._single_threaded_test_session():
examples = make_dense_examples_dict(
dense_feature_values=[[-2.0, 0.0], [0.0, 2.0]],
weights=[1.0, 1.0],
labels=[-10.0, 14.0])
variables = make_dense_variable_dict(2, 2)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='squared_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
for _ in xrange(20):
lr.minimize().run()
# Predictions should be 4/5 of label due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * weight^2
self.assertAllClose([-10.0 * 4 / 5, 14.0 * 4 / 5],
predictions.eval(),
rtol=0.01)
loss = lr.regularized_loss(examples)
self.assertAllClose(148.0 / 10.0, loss.eval(), atol=0.01)
def testSimple(self):
# Setup test data
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, -10.0),
make_example_proto(
{'age': [1],
'gender': [1]}, 14.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='squared_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
for _ in xrange(20):
lr.minimize().run()
# Predictions should be 2/3 of label due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * 2 * weight^2
self.assertAllClose([-20.0 / 3.0, 28.0 / 3.0],
predictions.eval(),
rtol=0.005)
self.assertAllClose(0.01,
lr.approximate_duality_gap().eval(),
rtol=1e-2,
atol=1e-2)
def testInstancesOfOneClassOnly(self):
# Setup test data with 1 positive (ignored), and 1 negative example.
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [0]}, 1), # Shares gender with the instance above.
]
example_weights = [1.0, 0.0] # Second example "omitted" from training.
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
for _ in xrange(5):
lr.minimize().run()
self.assertAllClose(0.411608, unregularized_loss.eval(), rtol=0.12)
self.assertAllClose(0.525457, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 0], predicted_labels.eval())
self.assertAllClose(0.01,
lr.approximate_duality_gap().eval(),
rtol=1e-2,
atol=1e-2)
def testInstancesOfOneClassOnly(self):
# Setup test data with 1 positive (ignored), and 1 negative example.
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [0]}, 1), # Shares gender with the instance above.
]
example_weights = [1.0, 0.0] # Second example "omitted" from training.
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.25,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
prediction = lr.predictions(examples)
lr.minimize().run()
self.assertAllClose(0.395226,
unregularized_loss.eval(),
rtol=3e-2,
atol=3e-2)
self.assertAllClose(0.460781, loss.eval(), rtol=3e-2, atol=3e-2)
predicted_labels = tf.cast(
tf.greater_equal(prediction,
tf.ones_like(prediction) * 0.5), tf.float32)
self.assertAllEqual([0, 0], predicted_labels.eval())
def testImbalancedWithExampleWeights(self):
# Setup test data with 1 positive, and 1 negative example.
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [1]}, 1),
]
example_weights = [3.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
for _ in xrange(5):
lr.minimize().run()
self.assertAllClose(0.284860, unregularized_loss.eval(), rtol=0.08)
self.assertAllClose(0.408044, loss.eval(), atol=0.012)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 1], predicted_labels.eval())
self.assertAllClose(0.01,
lr.approximate_duality_gap().eval(),
rtol=1e-2,
atol=1e-2)
def testImbalancedWithExampleWeights(self):
# Setup test data with 1 positive, and 3 negative examples.
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [1]}, 1),
]
example_weights = [3.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.25,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
prediction = lr.predictions(examples)
lr.minimize().run()
self.assertAllClose(0.266189, unregularized_loss.eval(),
rtol=3e-2, atol=3e-2)
self.assertAllClose(0.571912, loss.eval(), rtol=3e-2, atol=3e-2)
predicted_labels = tf.cast(
tf.greater_equal(prediction,
tf.ones_like(prediction) * 0.5), tf.float32)
self.assertAllEqual([0, 1], predicted_labels.eval())
def testFeatureValues(self):
# Setup test data
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, -10.0, -2.0),
make_example_proto({"age": [1], "gender": [1]}, 14.0, 2.0),
]
example_weights = [5.0, 3.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="squared_loss")
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# There are 4 (sparse) variable weights to be learned. 2 for age and 2 for
# gender. Let w_1, w_2 be age weights, w_3, w_4 be gender weights, y_1,
# y_2 be the labels for examples 1 and 2 respectively and s_1, s_2 the
# corresponding *example* weights. With the given feature values, the loss
# function is given by:
# s_1/2(y_1 + 2w_1 + 2w_3)^2 + s_2/2(y_2 - 2w_2 - 2w_4)^2
# + \lambda/2 (w_1^2 + w_2^2 + w_3^2 + w_4^2). Solving for the optimal, it
# can be verified that:
# w_1* = w_3* = -2.0 s_1 y_1/(\lambda + 8 s_1) and
# w_2* = w_4* = 2 \cdot s_2 y_2/(\lambda + 8 s_2). Equivalently, due to
# regularization and example weights, the predictions are within:
# 8 \cdot s_i /(\lambda + 8 \cdot s_i) of the labels.
self.assertAllClose([-10 * 40.0 / 41.0, 14.0 * 24 / 25.0], predictions.eval(), atol=0.01)
def testL1Regularization(self):
# Setup test data
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, -10.0),
make_example_proto({"age": [1], "gender": [1]}, 14.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1.0, symmetric_l1_regularization=4.0, loss_type="squared_loss")
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
prediction = lr.predictions(examples)
loss = lr.regularized_loss(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# Predictions should be -4.0, 48/5 due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * 2 * weight^2 + L1 * 4 * weight
self.assertAllClose([-4.0, 20.0 / 3.0], prediction.eval(), rtol=0.08)
# Loss should be the sum of the regularized loss value from above per
# example after plugging in the optimal weights.
self.assertAllClose(308.0 / 6.0, loss.eval(), atol=0.01)
def testDenseFeaturesPerfectlySeparable(self):
with self._single_threaded_test_session():
examples, variables = make_dense_examples_and_variables_dicts(
dense_features_values=[[1.0, 1.0], [1.0, -1.0]], weights=[1.0, 1.0], labels=[1.0, 0.0]
)
options = dict(symmetric_l2_regularization=1.0, symmetric_l1_regularization=0, loss_type="hinge_loss")
model = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = model.predictions(examples)
binary_predictions = get_binary_predictions_for_hinge(predictions)
train_op = model.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
self.assertAllClose([1.0, -1.0], predictions.eval(), atol=0.05)
self.assertAllEqual([1, 0], binary_predictions.eval())
# (1.0, 1.0) and (1.0, -1.0) are perfectly separable by x-axis (that is,
# the SVM's functional margin >=1), so the unregularized loss is ~0.0.
# There is only loss due to l2-regularization. For these datapoints, it
# turns out that w_1~=0.0 and w_2~=1.0 which means that l2 loss is ~0.25.
unregularized_loss = model.unregularized_loss(examples)
regularized_loss = model.regularized_loss(examples)
self.assertAllClose(0.0, unregularized_loss.eval(), atol=0.02)
self.assertAllClose(0.25, regularized_loss.eval(), atol=0.02)
def testSimple(self):
# Setup test data
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, -10.0),
make_example_proto({"age": [1], "gender": [1]}, 14.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="squared_loss")
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# Predictions should be 2/3 of label due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * 2 * weight^2
self.assertAllClose([-20.0 / 3.0, 28.0 / 3.0], predictions.eval(), rtol=0.005)
# Approximate gap should be very close to 0.0. (In fact, because the gap
# is only approximate, it is likely that upon convergence the duality gap
# can have a tiny negative value).
self.assertAllClose(0.0, lr.approximate_duality_gap().eval(), atol=1e-2)
def testL2Regularization(self):
# Setup test data
example_protos = [
# 2 identical examples
make_example_proto({"age": [0], "gender": [0]}, -10.0),
make_example_proto({"age": [0], "gender": [0]}, -10.0),
# 2 more identical examples
make_example_proto({"age": [1], "gender": [1]}, 14.0),
make_example_proto({"age": [1], "gender": [1]}, 14.0),
]
example_weights = [1.0, 1.0, 1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=16, symmetric_l1_regularization=0, loss_type="squared_loss")
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# Predictions should be 1/5 of label due to minimizing regularized loss:
# (label - 2 * weight)^2 + L2 * 16 * weight^2
optimal1 = -10.0 / 5.0
optimal2 = 14.0 / 5.0
self.assertAllClose([optimal1, optimal1, optimal2, optimal2], predictions.eval(), rtol=0.01)
def testImbalancedWithExampleWeights(self):
# Setup test data with 1 positive, and 1 negative example.
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [1]}, 1),
]
example_weights = [3.0, 1.0]
for num_shards in _SHARD_NUMBERS:
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(
symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
num_table_shards=num_shards,
loss_type="logistic_loss",
)
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
self.assertAllClose(0.284860, unregularized_loss.eval(), atol=0.08)
self.assertAllClose(0.408044, loss.eval(), atol=0.012)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 1], predicted_labels.eval())
self.assertAllClose(0.0, lr.approximate_duality_gap().eval(), rtol=2e-2, atol=1e-2)
def testInstancesOfOneClassOnly(self):
# Setup test data with 1 positive (ignored), and 1 negative example.
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [0]}, 1), # Shares gender with the instance above.
]
example_weights = [1.0, 0.0] # Second example "omitted" from training.
for num_shards in _SHARD_NUMBERS:
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(
symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
num_table_shards=num_shards,
loss_type="logistic_loss",
)
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
self.assertAllClose(0.411608, unregularized_loss.eval(), atol=0.05)
self.assertAllClose(0.525457, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 0], predicted_labels.eval())
self.assertAllClose(0.01, lr.approximate_duality_gap().eval(), rtol=1e-2, atol=1e-2)
def testDenseFeaturesSeparableWithinMargins(self):
with self._single_threaded_test_session():
examples, variables = make_dense_examples_and_variables_dicts(
dense_features_values=[[[1.0, 0.5], [1.0, -0.5]]], weights=[1.0, 1.0], labels=[1.0, 0.0]
)
options = dict(symmetric_l2_regularization=1.0, symmetric_l1_regularization=0, loss_type="hinge_loss")
model = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = model.predictions(examples)
binary_predictions = get_binary_predictions_for_hinge(predictions)
train_op = model.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# (1.0, 0.5) and (1.0, -0.5) are separable by x-axis but the datapoints
# are within the margins so there is unregularized loss (1/2 per example).
# For these datapoints, optimal weights are w_1~=0.0 and w_2~=1.0 which
# gives an L2 loss of ~0.25.
self.assertAllClose([0.5, -0.5], predictions.eval(), rtol=0.05)
self.assertAllEqual([1, 0], binary_predictions.eval())
unregularized_loss = model.unregularized_loss(examples)
regularized_loss = model.regularized_loss(examples)
self.assertAllClose(0.5, unregularized_loss.eval(), atol=0.02)
self.assertAllClose(0.75, regularized_loss.eval(), atol=0.02)
def testDenseFeaturesWithDefaultWeights(self):
with self._single_threaded_test_session():
examples, variables = make_dense_examples_and_variables_dicts(
dense_features_values=[[[1.0], [0.0]], [0.0, 1.0]],
weights=[1.0, 1.0],
labels=[10.0, -5.0])
options = dict(
symmetric_l2_regularization=1.0,
symmetric_l1_regularization=0,
loss_type='squared_loss')
lr = SdcaModel(examples, variables, options)
variables_lib.global_variables_initializer().run()
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
lr.update_weights(train_op).run()
# The loss function for these particular features is given by:
# 1/2(label_1-w_1)^2 + 1/2(label_2-w_2)^2 + \lambda/2 (w_1^2 + w_2^2). So,
# differentiating wrt to w_1, w_2 yields the following optimal values:
# w_1* = label_1/(\lambda + 1)= 10/2, w_2* =label_2/(\lambda + 1)= -5/2.
# In this case the (unnormalized regularized) loss will be:
# 1/2(10-5)^2 + 1/2(5-5/2)^2 + 1/2(5^2 + (5/2)^2) = 125.0/4. The actual
# loss should be further normalized by the sum of example weights.
self.assertAllClose([5.0, -2.5], predictions.eval(), rtol=0.01)
loss = lr.regularized_loss(examples)
self.assertAllClose(125.0 / 8.0, loss.eval(), atol=0.01)
def testDenseFeaturesWithArbitraryWeights(self):
with self._single_threaded_test_session():
examples, variables = make_dense_examples_and_variables_dicts(
dense_features_values=[[[1.0, 0.0], [0.0, 1.0]]], weights=[20.0, 10.0], labels=[10.0, -5.0]
)
options = dict(symmetric_l2_regularization=5.0, symmetric_l1_regularization=0, loss_type="squared_loss")
lr = SdcaModel(examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
# The loss function for these particular features is given by:
# 1/2 s_1 (label_1-w_1)^2 + 1/2 s_2(label_2-w_2)^2 +
# \lambda/2 (w_1^2 + w_2^2) where s_1, s_2 are the *example weights. It
# turns out that the optimal (variable) weights are given by:
# w_1* = label_1 \cdot s_1/(\lambda + s_1)= 8.0 and
# w_2* =label_2 \cdot s_2/(\lambda + s_2)= -10/3.
# In this case the (unnormalized regularized) loss will be:
# s_1/2(8-10)^2 + s_2/2(5-10/3)^2 + 5.0/2(8^2 + (10/3)^2) = 2175.0/9. The
# actual loss should be further normalized by the sum of example weights.
self.assertAllClose([8.0, -10.0 / 3], predictions.eval(), rtol=0.01)
loss = lr.regularized_loss(examples)
self.assertAllClose(2175.0 / 270.0, loss.eval(), atol=0.01)
def testSimpleLogistic(self):
# Setup test data
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, 0),
make_example_proto(
{'age': [1],
'gender': [1]}, 1),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.5,
symmetric_l1_regularization=0,
loss_type='logistic_loss',
prior=0.0)
tf.initialize_all_variables().run()
lr = SdcaModel(CONTAINER, examples, variables, options)
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
prediction = lr.predictions(examples)
self.assertAllClose(0.693147, unregularized_loss.eval())
self.assertAllClose(0.693147, loss.eval())
lr.minimize().run()
self.assertAllClose(0.395226, unregularized_loss.eval(),
rtol=3e-2, atol=3e-2)
self.assertAllClose(0.657446, loss.eval(),
rtol=3e-2, atol=3e-2)
predicted_labels = tf.cast(
tf.greater_equal(prediction,
tf.ones_like(prediction) * 0.5), tf.float32)
self.assertAllEqual([0, 1], predicted_labels.eval())
def testDistributedSimple(self):
# Setup test data
example_protos = [
make_example_proto({'age': [0],
'gender': [0]}, 0),
make_example_proto({'age': [1],
'gender': [1]}, 1),
]
example_weights = [1.0, 1.0]
for num_shards in _SHARD_NUMBERS:
for num_loss_partitions in _NUM_LOSS_PARTITIONS:
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(
symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='logistic_loss',
num_table_shards=num_shards,
num_loss_partitions=num_loss_partitions)
lr = SdcaModel(examples, variables, options)
tf.global_variables_initializer().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
self.assertAllClose(0.693147, unregularized_loss.eval())
self.assertAllClose(0.693147, loss.eval())
train_op = lr.minimize()
def Minimize():
with self._single_threaded_test_session():
for _ in range(_MAX_ITERATIONS):
train_op.run()
threads = []
for _ in range(num_loss_partitions):
threads.append(Thread(target=Minimize))
threads[-1].start()
for t in threads:
t.join()
lr.update_weights(train_op).run()
# The high tolerance in unregularized_loss comparisons is due to the
# fact that it's possible to trade off unregularized_loss vs.
# regularization and still have a sum that is quite close to the
# optimal regularized_loss value. SDCA's duality gap only ensures
# that the regularized_loss is within 0.01 of optimal.
# 0.525457 is the optimal regularized_loss.
# 0.411608 is the unregularized_loss at that optimum.
self.assertAllClose(0.411608, unregularized_loss.eval(), atol=0.05)
self.assertAllClose(0.525457, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 1], predicted_labels.eval())
self.assertTrue(lr.approximate_duality_gap().eval() < 0.02)
def testNoWeightedExamples(self):
# Setup test data with 1 positive, and 1 negative example.
example_protos = [
make_example_proto({"age": [0], "gender": [0]}, 0),
make_example_proto({"age": [1], "gender": [1]}, 1),
]
# Zeroed out example weights.
example_weights = [0.0, 0.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1, symmetric_l1_regularization=0, loss_type="logistic_loss")
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
self.assertAllClose([0.5, 0.5], lr.predictions(examples).eval())
lr.minimize().run()
self.assertAllClose([0.5, 0.5], lr.predictions(examples).eval())
with self.assertRaisesOpError("No examples found or all examples have zero weight."):
lr.approximate_duality_gap().eval()
def testSimple(self):
# Setup test data
example_protos = [
make_example_proto(
{'age': [0],
'gender': [0]}, -10.0),
make_example_proto(
{'age': [1],
'gender': [1]}, 14.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='squared_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in xrange(_MAX_ITERATIONS):
train_op.run()
# Predictions should be 2/3 of label due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * 2 * weight^2
self.assertAllClose([-20.0 / 3.0, 28.0 / 3.0],
predictions.eval(),
rtol=0.005)
# Approximate gap should be very close to 0.0. (In fact, because the gap
# is only approximate, it is likely that upon convergence the duality gap
# can have a tiny negative value).
self.assertAllClose(0.00,
lr.approximate_duality_gap().eval(),
atol=1e-2)
def testSimpleLinear(self):
# Setup test data
example_protos = [
make_example_proto({
'age': [0],
'gender': [0]
}, -10.0),
make_example_proto({
'age': [1],
'gender': [1]
}, 14.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='squared_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
predictions = lr.predictions(examples)
for _ in xrange(20):
lr.minimize().run()
# Predictions should be 2/3 of label due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * 2 * weight^2
self.assertAllClose([-20.0 / 3.0, 28.0 / 3.0],
predictions.eval(),
rtol=0.005)
self.assertAllClose(0.01,
lr.approximate_duality_gap().eval(),
rtol=1e-2,
atol=1e-2)
def testInstancesOfOneClassOnly(self):
# Setup test data with 1 positive (ignored), and 1 negative example.
example_protos = [
make_example_proto({
'age': [0],
'gender': [0]
}, 0),
make_example_proto({
'age': [1],
'gender': [0]
}, 1), # Shares gender with the instance above.
]
example_weights = [1.0, 0.0] # Second example "omitted" from training.
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
train_op = lr.minimize()
for _ in xrange(_MAX_ITERATIONS):
train_op.run()
self.assertAllClose(0.411608, unregularized_loss.eval(), atol=0.05)
self.assertAllClose(0.525457, loss.eval(), atol=0.01)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 0], predicted_labels.eval())
self.assertAllClose(0.01,
lr.approximate_duality_gap().eval(),
rtol=1e-2,
atol=1e-2)
def testLinearL1Regularization(self):
# Setup test data
example_protos = [
make_example_proto({
'age': [0],
'gender': [0]
}, -10.0),
make_example_proto({
'age': [1],
'gender': [1]
}, 14.0),
]
example_weights = [1.0, 1.0]
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=1.0,
symmetric_l1_regularization=4.0,
loss_type='squared_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
prediction = lr.predictions(examples)
loss = lr.regularized_loss(examples)
for _ in xrange(5):
lr.minimize().run()
# Predictions should be -4.0, 48/5 due to minimizing regularized loss:
# (label - 2 * weight)^2 / 2 + L2 * 2 * weight^2 + L1 * 4 * weight
self.assertAllClose([-4.0, 20.0 / 3.0],
prediction.eval(),
rtol=0.08)
# Loss should be the sum of the regularized loss value from above per
# example after plugging in the optimal weights.
self.assertAllClose(308.0 / 6.0, loss.eval(), atol=0.01)
def testDistributedSimple(self):
# Distributed SDCA may not converge if the workers update concurrently the
# same example. In this test the examples are partitioned across workers.
# The examples are the same for all workers, just the example_ids are
# different.
example_protos = [
make_example_proto({
'age': [0],
'gender': [0]
}, 0),
make_example_proto({
'age': [1],
'gender': [1]
}, 1),
]
example_weights = [1.0, 1.0]
examples = make_example_dict(example_protos, example_weights)
example_ids = array_ops.placeholder(
dtypes.string, shape=(len(example_weights),))
examples['example_ids'] = example_ids
variables = make_variable_dict(1, 1)
for num_shards in _SHARD_NUMBERS:
for num_loss_partitions in _NUM_LOSS_PARTITIONS:
with self._single_threaded_test_session():
options = dict(
# Keep the same solution as for TestSimple: since the number of
# examples is multplied by num_loss_partitions, multiply also
# L2 by the same value.
symmetric_l2_regularization=num_loss_partitions,
symmetric_l1_regularization=0,
loss_type='logistic_loss',
num_table_shards=num_shards,
num_loss_partitions=num_loss_partitions)
lr = SdcaModel(examples, variables, options)
variables_lib.global_variables_initializer().run()
unregularized_loss = lr.unregularized_loss(examples)
loss = lr.regularized_loss(examples)
predictions = lr.predictions(examples)
self.assertAllClose(0.693147, unregularized_loss.eval())
self.assertAllClose(0.693147, loss.eval())
train_op = lr.minimize()
def minimize(worker_id):
with self._single_threaded_test_session():
feed_dict = {example_ids: [
str(i + worker_id*len(example_weights)) for i in range(
len(example_weights))]}
for _ in range(_MAX_ITERATIONS):
train_op.run(feed_dict=feed_dict) # pylint: disable=cell-var-from-loop
threads = []
for worker_id in range(num_loss_partitions):
threads.append(threading.Thread(target=minimize, args=(worker_id,)))
threads[-1].start()
for t in threads:
t.join()
lr.update_weights(train_op).run(feed_dict={
example_ids: [str(i) for i in range(len(example_weights))]})
# Test only the unregularized loss because the optimal value of the
# regularized loss depends on num_loss_partitions.
self.assertAllClose(0.411608, unregularized_loss.eval(), atol=0.02)
predicted_labels = get_binary_predictions_for_logistic(predictions)
self.assertAllEqual([0, 1], predicted_labels.eval())
self.assertNear(0.0, lr.approximate_duality_gap().eval(), 0.02)
