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)
variables_lib.global_variables_initializer().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()
model.update_weights(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 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)
variables_lib.global_variables_initializer().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()
model.update_weights(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 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)
variables_lib.global_variables_initializer().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()
model.update_weights(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 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 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(CONTAINER, 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 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 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 = [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 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],
predictions.eval(),
rtol=0.07)
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 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 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.test_session(use_gpu=False):
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(examples, 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(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())
self.assertAllClose(0.657446, loss.eval())
predicted_labels = tf.cast(
tf.greater_equal(prediction,
tf.ones_like(prediction) * 0.5), tf.float32)
self.assertAllEqual([0, 1], predicted_labels.eval())
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.test_session(use_gpu=False):
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(examples, 1, 1)
options = dict(symmetric_l2_regularization=0.25,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(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 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.test_session(use_gpu=False):
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(examples, 1, 1)
options = dict(symmetric_l2_regularization=0.5,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(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 testSparseRandom(self):
dim = 20
num_examples = 1000
# Number of non-zero features per example.
non_zeros = 10
# Setup test data.
with self._single_threaded_test_session():
examples, variables = make_random_examples_and_variables_dicts(
num_examples, dim, non_zeros)
options = dict(
symmetric_l2_regularization=.1,
symmetric_l1_regularization=0,
num_table_shards=1,
adaptive=False,
loss_type='logistic_loss')
lr = SdcaModel(examples, variables, options)
variables_lib.global_variables_initializer().run()
train_op = lr.minimize()
for _ in range(4):
train_op.run()
lr.update_weights(train_op).run()
# Duality gap is 1.4e-5.
# It would be 0.01 without shuffling and 0.02 with adaptive sampling.
self.assertNear(0.0, lr.approximate_duality_gap().eval(), err=1e-3)
def testFractionalExampleLabel(self):
# Setup test data with 1 positive, and 1 mostly-negative example.
example_protos = [
make_example_proto({
'age': [0],
'gender': [0]
}, 0.1),
make_example_proto({
'age': [1],
'gender': [1]
}, 0.9),
]
example_weights = [1.0, 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)
variables_lib.global_variables_initializer().run()
with self.assertRaisesOpError(
'Only labels of 0.0 or 1.0 are supported right now.'):
lr.minimize().run()
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 _ in examples['example_ids']
]
variables = make_variable_dict(1, 1)
options = dict(symmetric_l2_regularization=0.5,
symmetric_l1_regularization=0,
loss_type='squared_loss')
lr = SdcaModel(CONTAINER, examples, variables, options)
tf.initialize_all_variables().run()
self.assertAllClose([0.0, 0.0], lr.predictions(examples).eval())
with self.assertRaisesOpError(
'Detected 1 duplicates in example_ids'):
lr.minimize().run()
self.assertAllClose([0.0, 0.0], lr.predictions(examples).eval())
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)
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 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 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 testOutOfRangeSparseFeatures(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(0, 0)
options = dict(
symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
lr = SdcaModel(examples, variables, options)
variables_lib.global_variables_initializer().run()
train_op = lr.minimize()
with self.assertRaisesRegexp(errors_impl.InvalidArgumentError,
'indices.*'):
train_op.run()
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]
for num_shards in _SHARD_NUMBERS:
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,
num_table_shards=num_shards)
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.assertAllClose([0, 1, 1, 1], predicted_labels.eval())
self.assertAllClose(0.01,
lr.approximate_duality_gap().eval(),
rtol=1e-2,
atol=1e-2)
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.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()
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 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]
for num_shards in _SHARD_NUMBERS:
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,
num_table_shards=num_shards)
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(0.226487 + 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 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]
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=0,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
lr = SdcaModel(CONTAINER,
examples,
variables,
options,
num_table_shards=num_shards)
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 range(_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 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)
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()
# 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 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=1.0,
symmetric_l1_regularization=0,
loss_type='hinge_loss')
model = SdcaModel(examples, variables, options)
variables_lib.global_variables_initializer().run()
# Before minimization, the weights default to zero. There is no loss due
# to regularization, only unregularized loss which is 0.5 * (1+1) = 1.0.
predictions = model.predictions(examples)
self.assertAllClose([0.0, 0.0], predictions.eval())
unregularized_loss = model.unregularized_loss(examples)
regularized_loss = model.regularized_loss(examples)
self.assertAllClose(1.0, unregularized_loss.eval())
self.assertAllClose(1.0, regularized_loss.eval())
# After minimization, the model separates perfectly the data points. There
# are 4 sparse weights: 2 for age (say w1, w2) and 2 for gender (say w3
# and w4). Solving the system w1 + w3 = 1.0, w2 + w4 = -1.0 and minimizing
# wrt to \|\vec{w}\|_2, gives w1=w3=1/2 and w2=w4=-1/2. This gives 0.0
# unregularized loss and 0.25 L2 loss.
train_op = model.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
model.update_weights(train_op).run()
binary_predictions = get_binary_predictions_for_hinge(predictions)
self.assertAllEqual([-1.0, 1.0], predictions.eval())
self.assertAllEqual([0, 1], binary_predictions.eval())
self.assertAllClose(0.0, unregularized_loss.eval())
self.assertAllClose(0.25, regularized_loss.eval(), atol=0.05)
def testPartitionedPrimals(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:
with self._single_threaded_test_session():
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(1, 1, partitioned=True)
options = dict(
symmetric_l2_regularization=1,
symmetric_l1_regularization=0,
num_table_shards=num_shards,
loss_type='logistic_loss')
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()
for _ in range(_MAX_ITERATIONS):
train_op.run()
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.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]
}, 2),
]
example_weights = [100.0, 100.0]
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=0,
loss_type='poisson_loss')
model = SdcaModel(examples, variables, options)
variables_lib.global_variables_initializer().run()
# Before minimization, the weights default to zero. There is no loss due
# to regularization, only unregularized loss which is 1 for each example.
predictions = model.predictions(examples)
self.assertAllClose([1.0, 1.0], predictions.eval())
unregularized_loss = model.unregularized_loss(examples)
regularized_loss = model.regularized_loss(examples)
approximate_duality_gap = model.approximate_duality_gap()
self.assertAllClose(1.0, unregularized_loss.eval())
self.assertAllClose(1.0, regularized_loss.eval())
# There are 4 sparse weights: 2 for age (say w1, w2) and 2 for gender
# (say w3 and w4). The minimization leads to:
# w1=w3=-1.96487, argmin of 100*(exp(2*w)-2*w*0)+w**2.
# w2=w4=0.345708, argmin of 100*(exp(2*w)-2*w*2)+w**2.
# This gives an unregularized loss of .3167 and .3366 with regularization.
train_op = model.minimize()
for _ in range(_MAX_ITERATIONS):
train_op.run()
model.update_weights(train_op).run()
self.assertAllClose([0.0196, 1.9965], predictions.eval(), atol=1e-4)
self.assertAllClose(0.3167, unregularized_loss.eval(), atol=1e-4)
self.assertAllClose(0.3366, regularized_loss.eval(), atol=1e-4)
self.assertAllClose(0., approximate_duality_gap.eval(), atol=1e-6)
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)
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()
# 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 testLinearDenseFeatures(self):
with self._single_threaded_test_session():
examples = dict(
sparse_features=[],
dense_features=[tf.convert_to_tensor(
[-2.0, 0.0],
dtype=tf.float32), tf.convert_to_tensor(
[0.0, 2.0],
dtype=tf.float32)],
example_weights=[1.0, 1.0],
example_labels=[-10.0, 14.0],
example_ids=['%d' % i for i in xrange(2)])
variables = dict(sparse_features_weights=[],
dense_features_weights=[tf.Variable(tf.zeros(
[1],
dtype=tf.float32)), tf.Variable(tf.zeros(
[1],
dtype=tf.float32))],
dual=tf.Variable(tf.zeros(
[2],
dtype=tf.float32)),
primal_loss=tf.Variable(tf.zeros(
[],
dtype=tf.float64)))
options = dict(symmetric_l2_regularization=1,
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 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],
prediction.eval(),
rtol=0.01)
loss = lr.regularized_loss(examples)
self.assertAllClose(
(4.0 + 7.84 + 16.0 + 31.36) / 2,
loss.eval(),
rtol=0.01)
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.test_session(use_gpu=False):
# Only use examples 0 and 2
examples = make_example_dict(example_protos, example_weights)
variables = make_variable_dict(examples, 1, 1)
options = dict(symmetric_l2_regularization=0.25,
symmetric_l1_regularization=0,
loss_type='logistic_loss')
tf.initialize_all_variables().run()
lr = SdcaModel(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())
self.assertAllClose(0.526336, loss.eval())
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 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=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())
for _ in xrange(5):
lr.minimize().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(), rtol=0.11)
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)
