official/nlp/modeling/layers/gaussian_process_test.py
# Copyright 2024 The TensorFlow Authors. All Rights Reserved.
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"""Tests for Gaussian process functions."""
import os
import shutil
from absl.testing import parameterized
import numpy as np
import tensorflow as tf, tf_keras
from official.nlp.modeling.layers import gaussian_process
def exact_gaussian_kernel(x1, x2):
"""Computes exact Gaussian kernel value(s) for tensors x1 and x2."""
x1_squared = tf.reduce_sum(tf.square(x1), list(range(1, len(x1.shape))))
x2_squared = tf.reduce_sum(tf.square(x2), list(range(1, len(x2.shape))))
square = (x1_squared[:, tf.newaxis] + x2_squared[tf.newaxis, :] -
2 * tf.matmul(x1, x2, transpose_b=True))
return tf.math.exp(-square / 2.)
def _generate_normal_data(num_sample, num_dim, loc):
"""Generates random data sampled from i.i.d. normal distribution."""
return np.random.normal(
size=(num_sample, num_dim), loc=loc, scale=1. / np.sqrt(num_dim))
def _generate_rbf_data(x_data, orthogonal=True):
"""Generates high-dim data that is the eigen components of a RBF kernel."""
k_rbf = exact_gaussian_kernel(x_data, x_data)
x_orth, x_diag, _ = np.linalg.svd(k_rbf)
if orthogonal:
return x_orth
return np.diag(np.sqrt(x_diag)).dot(x_orth.T)
def _make_minibatch_iterator(data_numpy, batch_size, num_epoch):
"""Makes a tf.data.Dataset for given batch size and num epoches."""
dataset = tf.data.Dataset.from_tensor_slices(data_numpy)
dataset = dataset.repeat(num_epoch).batch(batch_size)
return iter(dataset)
def _compute_posterior_kernel(x_tr, x_ts, kernel_func, ridge_penalty):
"""Computes the posterior covariance matrix of a Gaussian process."""
num_sample = x_tr.shape[0]
k_tt_inv = tf.linalg.inv(
kernel_func(x_tr, x_tr) + ridge_penalty * np.eye(num_sample))
k_ts = kernel_func(x_tr, x_ts)
k_ss = kernel_func(x_ts, x_ts)
return k_ss - tf.matmul(k_ts, tf.matmul(k_tt_inv, k_ts), transpose_a=True)
class GaussianProcessTest(tf.test.TestCase, parameterized.TestCase):
def setUp(self):
super(GaussianProcessTest, self).setUp()
self.num_data_dim = 10
self.num_inducing = 1024
self.num_train_sample = 1024
self.num_test_sample = 256
self.prec_tolerance = {'atol': 1e-3, 'rtol': 5e-2}
self.cov_tolerance = {'atol': 5e-2, 'rtol': 2.}
self.rbf_kern_func = exact_gaussian_kernel
self.x_tr = _generate_normal_data(
self.num_train_sample, self.num_data_dim, loc=0.)
self.x_ts = _generate_normal_data(
self.num_test_sample, self.num_data_dim, loc=1.)
def test_layer_build(self):
"""Tests if layer.built=True after building."""
rfgp_model = gaussian_process.RandomFeatureGaussianProcess(units=1)
rfgp_model.build(input_shape=self.x_tr.shape)
self.assertTrue(rfgp_model.built)
@parameterized.named_parameters(('rbf_data', False),
('orthogonal_data', True))
def test_laplace_covariance_minibatch(self, generate_orthogonal_data):
"""Tests if model correctly learns population-lvel precision matrix."""
batch_size = 50
epochs = 1000
x_data = _generate_rbf_data(self.x_ts, generate_orthogonal_data)
data_iterator = _make_minibatch_iterator(x_data, batch_size, epochs)
# Estimates precision matrix using minibatch.
cov_estimator = gaussian_process.LaplaceRandomFeatureCovariance(
momentum=0.999, ridge_penalty=0)
for minibatch_data in data_iterator:
_ = cov_estimator(minibatch_data, training=True)
# Evaluation
prec_mat_expected = x_data.T.dot(x_data)
prec_mat_computed = (
cov_estimator.precision_matrix.numpy() * self.num_test_sample)
np.testing.assert_allclose(prec_mat_computed, prec_mat_expected,
**self.prec_tolerance)
def test_random_feature_prior_approximation(self):
"""Tests random feature GP's ability in approximating exact GP prior."""
num_inducing = 10240
rfgp_model = gaussian_process.RandomFeatureGaussianProcess(
units=1,
num_inducing=num_inducing,
normalize_input=False,
gp_kernel_type='gaussian',
return_random_features=True)
# Extract random features.
_, _, gp_feature = rfgp_model(self.x_tr, training=True)
gp_feature_np = gp_feature.numpy()
prior_kernel_computed = gp_feature_np.dot(gp_feature_np.T)
prior_kernel_expected = self.rbf_kern_func(self.x_tr, self.x_tr)
np.testing.assert_allclose(prior_kernel_computed, prior_kernel_expected,
**self.cov_tolerance)
def test_random_feature_posterior_approximation(self):
"""Tests random feature GP's ability in approximating exact GP posterior."""
# Set momentum = 0.5 so posterior precision matrix is 0.5 * (I + K).
gp_cov_momentum = 0.5
gp_cov_ridge_penalty = 1.
num_inducing = 1024
rfgp_model = gaussian_process.RandomFeatureGaussianProcess(
units=1,
num_inducing=num_inducing,
normalize_input=False,
gp_kernel_type='gaussian',
gp_cov_momentum=gp_cov_momentum,
gp_cov_ridge_penalty=gp_cov_ridge_penalty)
# Computes posterior covariance on test data.
_, _ = rfgp_model(self.x_tr, training=True)
_, gp_cov_ts = rfgp_model(self.x_ts, training=False)
# Scale up covariance estimate since prec matrix is down-scaled by momentum.
post_kernel_computed = gp_cov_ts * gp_cov_momentum
post_kernel_expected = _compute_posterior_kernel(self.x_tr, self.x_ts,
self.rbf_kern_func,
gp_cov_ridge_penalty)
np.testing.assert_allclose(post_kernel_computed, post_kernel_expected,
**self.cov_tolerance)
def test_random_feature_linear_kernel(self):
"""Tests if linear kernel indeed leads to an identity mapping."""
# Specify linear kernel
gp_kernel_type = 'linear'
normalize_input = False
scale_random_features = False
use_custom_random_features = True
rfgp_model = gaussian_process.RandomFeatureGaussianProcess(
units=1,
normalize_input=normalize_input,
gp_kernel_type=gp_kernel_type,
scale_random_features=scale_random_features,
use_custom_random_features=use_custom_random_features,
return_random_features=True)
_, _, gp_feature = rfgp_model(self.x_tr, training=True)
# Check if linear kernel leads to identity mapping.
np.testing.assert_allclose(gp_feature, self.x_tr, **self.prec_tolerance)
def test_no_matrix_update_during_test(self):
"""Tests if the precision matrix is not updated during testing."""
rfgp_model = gaussian_process.RandomFeatureGaussianProcess(units=1)
# Training.
_, gp_covmat_null = rfgp_model(self.x_tr, training=True)
precision_mat_before_test = rfgp_model._gp_cov_layer.precision_matrix
# Testing.
_ = rfgp_model(self.x_ts, training=False)
precision_mat_after_test = rfgp_model._gp_cov_layer.precision_matrix
self.assertAllClose(
gp_covmat_null, tf.eye(self.num_train_sample), atol=1e-4)
self.assertAllClose(
precision_mat_before_test, precision_mat_after_test, atol=1e-4)
def test_state_saving_and_loading(self):
"""Tests if the loaded model returns same results."""
input_data = np.random.random((1, 2))
rfgp_model = gaussian_process.RandomFeatureGaussianProcess(units=1)
inputs = tf_keras.Input((2,), batch_size=1)
outputs = rfgp_model(inputs)
model = tf_keras.Model(inputs, outputs)
gp_output, gp_covmat = model.predict(input_data)
# Save and then load the model.
temp_dir = self.get_temp_dir()
self.addCleanup(shutil.rmtree, temp_dir)
saved_model_dir = os.path.join(temp_dir, 'rfgp_model')
model.save(saved_model_dir)
new_model = tf_keras.models.load_model(saved_model_dir)
gp_output_new, gp_covmat_new = new_model.predict(input_data)
self.assertAllClose(gp_output, gp_output_new, atol=1e-4)
self.assertAllClose(gp_covmat, gp_covmat_new, atol=1e-4)
class MeanFieldLogitsTest(tf.test.TestCase):
def testMeanFieldLogitsLikelihood(self):
"""Tests if scaling is correct under different likelihood."""
batch_size = 10
num_classes = 12
variance = 1.5
mean_field_factor = 2.
rng = np.random.RandomState(0)
tf.random.set_seed(1)
logits = rng.randn(batch_size, num_classes)
covmat = tf.linalg.diag([variance] * batch_size)
logits_logistic = gaussian_process.mean_field_logits(
logits, covmat, mean_field_factor=mean_field_factor)
self.assertAllClose(logits_logistic, logits / 2., atol=1e-4)
def testMeanFieldLogitsTemperatureScaling(self):
"""Tests using mean_field_logits as temperature scaling method."""
batch_size = 10
num_classes = 12
rng = np.random.RandomState(0)
tf.random.set_seed(1)
logits = rng.randn(batch_size, num_classes)
# Test if there's no change to logits when mean_field_factor < 0.
logits_no_change = gaussian_process.mean_field_logits(
logits, covariance_matrix=None, mean_field_factor=-1)
# Test if mean_field_logits functions as a temperature scaling method when
# mean_field_factor > 0, with temperature = sqrt(1. + mean_field_factor).
logits_scale_by_two = gaussian_process.mean_field_logits(
logits, covariance_matrix=None, mean_field_factor=3.)
self.assertAllClose(logits_no_change, logits, atol=1e-4)
self.assertAllClose(logits_scale_by_two, logits / 2., atol=1e-4)
if __name__ == '__main__':
tf.test.main()