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.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 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.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 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.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 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 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 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.global_variables_initializer().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() lr.update_weights(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.global_variables_initializer().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() lr.update_weights(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) 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 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 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.global_variables_initializer().run() prediction = lr.predictions(examples) loss = lr.regularized_loss(examples) train_op = lr.minimize() for _ in range(_MAX_ITERATIONS): train_op.run() lr.update_weights(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 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 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() lr.update_weights(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 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 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 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, 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) train_op = lr.minimize() for _ in range(_MAX_ITERATIONS): train_op.run() lr.update_weights(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.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 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, 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) train_op = lr.minimize() for _ in range(_MAX_ITERATIONS): train_op.run() lr.update_weights(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(0.0, lr.approximate_duality_gap().eval(), rtol=2e-2, atol=1e-2)
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, 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) train_op = lr.minimize() for _ in range(_MAX_ITERATIONS): train_op.run() lr.update_weights(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] 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, 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() # 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 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, 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) train_op = lr.minimize() for _ in range(_MAX_ITERATIONS): train_op.run() lr.update_weights(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( 0.0, lr.approximate_duality_gap().eval(), rtol=2e-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=1.0, 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 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 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 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 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, 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() # 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=1.0, symmetric_l1_regularization=0, loss_type='smooth_hinge_loss') model = SdcaModel(examples, variables, options) tf.initialize_all_variables().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). The minimization leads to w1=w3=1/3 and w2=w4=-1/3. This gives # an unregularized hinge loss of 0.33 and a 0.11 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.assertAllClose([-0.67, 0.67], predictions.eval(), atol=0.05) self.assertAllEqual([0, 1], binary_predictions.eval()) self.assertAllClose(0.33, unregularized_loss.eval(), atol=0.02) self.assertAllClose(0.44, regularized_loss.eval(), atol=0.02)
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) variables_lib.global_variables_initializer().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() lr.update_weights(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 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) 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 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 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)