def testVarianceAndCovarianceMatrix(self):
df = np.float64(4.)
amp = np.float64(.5)
len_scale = np.float64(.2)
jitter = np.float64(1e-4)
kernel = psd_kernels.ExponentiatedQuadratic(amp, len_scale)
index_points = np.expand_dims(np.random.uniform(-1., 1., 10), -1)
tp = tfd.StudentTProcess(
df=df,
kernel=kernel,
index_points=index_points,
jitter=jitter)
def _kernel_fn(x, y):
return amp ** 2 * np.exp(-.5 * (np.squeeze((x - y)**2)) / (len_scale**2))
expected_covariance = (
_kernel_fn(np.expand_dims(index_points, 0),
np.expand_dims(index_points, 1)) +
jitter * np.eye(10))
self.assertAllClose(expected_covariance,
self.evaluate(tp.covariance()))
self.assertAllClose(np.diag(expected_covariance),
self.evaluate(tp.variance()))
def testCopy(self):
# 5 random index points in R^2
index_points_1 = np.random.uniform(-4., 4., (5, 2)).astype(np.float32)
# 10 random index points in R^2
index_points_2 = np.random.uniform(-4., 4., (10, 2)).astype(np.float32)
# ==> shape = [6, 25, 2]
if not self.is_static:
index_points_1 = tf1.placeholder_with_default(index_points_1,
shape=None)
index_points_2 = tf1.placeholder_with_default(index_points_2,
shape=None)
mean_fn = lambda x: np.array([0.], np.float32)
kernel_1 = psd_kernels.ExponentiatedQuadratic()
kernel_2 = psd_kernels.ExpSinSquared()
tp1 = tfd.StudentTProcess(df=3.,
kernel=kernel_1,
index_points=index_points_1,
mean_fn=mean_fn,
jitter=1e-5,
validate_args=True)
tp2 = tp1.copy(df=4., index_points=index_points_2, kernel=kernel_2)
event_shape_1 = [5]
event_shape_2 = [10]
self.assertEqual(tp1.mean_fn, tp2.mean_fn)
self.assertIsInstance(tp1.kernel, psd_kernels.ExponentiatedQuadratic)
self.assertIsInstance(tp2.kernel, psd_kernels.ExpSinSquared)
if self.is_static or tf.executing_eagerly():
self.assertAllEqual(tp1.batch_shape, tp2.batch_shape)
self.assertAllEqual(tp1.event_shape, event_shape_1)
self.assertAllEqual(tp2.event_shape, event_shape_2)
self.assertEqual(self.evaluate(tp1.df), 3.)
self.assertEqual(self.evaluate(tp2.df), 4.)
self.assertAllEqual(tp2.index_points, index_points_2)
self.assertAllEqual(tp1.index_points, index_points_1)
self.assertAllEqual(tp2.index_points, index_points_2)
self.assertAllEqual(tf.get_static_value(tp1.jitter),
tf.get_static_value(tp2.jitter))
else:
self.assertAllEqual(self.evaluate(tp1.batch_shape_tensor()),
self.evaluate(tp2.batch_shape_tensor()))
self.assertAllEqual(self.evaluate(tp1.event_shape_tensor()),
event_shape_1)
self.assertAllEqual(self.evaluate(tp2.event_shape_tensor()),
event_shape_2)
self.assertEqual(self.evaluate(tp1.jitter),
self.evaluate(tp2.jitter))
self.assertEqual(self.evaluate(tp1.df), 3.)
self.assertEqual(self.evaluate(tp2.df), 4.)
self.assertAllEqual(self.evaluate(tp1.index_points),
index_points_1)
self.assertAllEqual(self.evaluate(tp2.index_points),
index_points_2)
def testMean(self):
mean_fn = lambda x: x[:, 0]**2
kernel = psd_kernels.ExponentiatedQuadratic()
index_points = np.expand_dims(np.random.uniform(-1., 1., 10), -1)
tp = tfd.StudentTProcess(
df=3., kernel=kernel, index_points=index_points, mean_fn=mean_fn)
expected_mean = mean_fn(index_points)
self.assertAllClose(expected_mean,
self.evaluate(tp.mean()))
def testShapes(self):
# 5x5 grid of index points in R^2 and flatten to 25x2
index_points = np.linspace(-4., 4., 5, dtype=np.float32)
index_points = np.stack(np.meshgrid(index_points, index_points), axis=-1)
index_points = np.reshape(index_points, [-1, 2])
# ==> shape = [25, 2]
# Kernel with batch_shape [2, 4, 1]
df = np.array(
[[3., 4., 5., 4.], [7.5, 8, 5., 5.]],
dtype=np.float32).reshape([2, 4, 1])
amplitude = np.array([1., 2.], np.float32).reshape([2, 1, 1])
length_scale = np.array([1., 2., 3., 4.], np.float32).reshape([1, 4, 1])
batched_index_points = np.stack([index_points]*6)
# ==> shape = [6, 25, 2]
if not self.is_static:
df = tf1.placeholder_with_default(df, shape=None)
amplitude = tf1.placeholder_with_default(amplitude, shape=None)
length_scale = tf1.placeholder_with_default(length_scale, shape=None)
batched_index_points = tf1.placeholder_with_default(
batched_index_points, shape=None)
kernel = psd_kernels.ExponentiatedQuadratic(amplitude, length_scale)
tp = tfd.StudentTProcess(
df, kernel, batched_index_points, jitter=1e-5, validate_args=True)
batch_shape = [2, 4, 6]
event_shape = [25]
sample_shape = [5, 3]
samples = tp.sample(sample_shape)
if self.is_static or tf.executing_eagerly():
self.assertAllEqual(tp.batch_shape_tensor(), batch_shape)
self.assertAllEqual(tp.event_shape_tensor(), event_shape)
self.assertAllEqual(samples.shape,
sample_shape + batch_shape + event_shape)
self.assertAllEqual(tp.batch_shape, batch_shape)
self.assertAllEqual(tp.event_shape, event_shape)
self.assertAllEqual(samples.shape,
sample_shape + batch_shape + event_shape)
self.assertAllEqual(tp.mean().shape, batch_shape + event_shape)
self.assertAllEqual(tp.variance().shape, batch_shape + event_shape)
else:
self.assertAllEqual(self.evaluate(tp.batch_shape_tensor()), batch_shape)
self.assertAllEqual(self.evaluate(tp.event_shape_tensor()), event_shape)
self.assertAllEqual(
self.evaluate(samples).shape,
sample_shape + batch_shape + event_shape)
self.assertIsNone(tensorshape_util.rank(samples.shape))
self.assertIsNone(tensorshape_util.rank(tp.batch_shape))
self.assertEqual(tensorshape_util.rank(tp.event_shape), 1)
self.assertIsNone(
tf.compat.dimension_value(tensorshape_util.dims(tp.event_shape)[0]))
self.assertAllEqual(
self.evaluate(tf.shape(tp.mean())), batch_shape + event_shape)
self.assertAllEqual(self.evaluate(
tf.shape(tp.variance())), batch_shape + event_shape)
def testMarginalHasCorrectTypes(self):
tp = tfd.StudentTProcess(df=3.,
kernel=psd_kernels.ExponentiatedQuadratic())
self.assertIsInstance(
tp.get_marginal_distribution(
index_points=np.ones([1, 1], dtype=np.float32)), tfd.StudentT)
self.assertIsInstance(
tp.get_marginal_distribution(
index_points=np.ones([10, 1], dtype=np.float32)),
tfd.MultivariateStudentTLinearOperator)
def testEmptyDataMatchesStPPrior(self):
df = np.float64(3.5)
amp = np.float64(.5)
len_scale = np.float64(.2)
index_points = np.random.uniform(-1., 1., (10, 1)).astype(np.float64)
# k_xx - k_xn @ (k_nn + sigma^2) @ k_nx + sigma^2
mean_fn = lambda x: x[:, 0]**2
kernel = psd_kernels.ExponentiatedQuadratic(amp, len_scale)
stp = tfd.StudentTProcess(df,
kernel,
index_points,
mean_fn=mean_fn,
validate_args=True)
stprm_nones = tfd.StudentTProcessRegressionModel(
df,
kernel=kernel,
index_points=index_points,
mean_fn=mean_fn,
validate_args=True)
stprm_zero_shapes = tfd.StudentTProcessRegressionModel(
df,
kernel=kernel,
index_points=index_points,
observation_index_points=tf.ones([0, 1], tf.float64),
observations=tf.ones([0], tf.float64),
mean_fn=mean_fn,
validate_args=True)
for stprm in [stprm_nones, stprm_zero_shapes]:
self.assertAllClose(self.evaluate(stp.mean()),
self.evaluate(stprm.mean()))
self.assertAllClose(self.evaluate(stp.covariance()),
self.evaluate(stprm.covariance()))
self.assertAllClose(self.evaluate(stp.variance()),
self.evaluate(stprm.variance()))
observations = np.random.uniform(-1., 1., 10).astype(np.float64)
self.assertAllClose(self.evaluate(stp.log_prob(observations)),
self.evaluate(stprm.log_prob(observations)))
def testLateBindingIndexPoints(self):
amp = np.float64(.5)
len_scale = np.float64(.2)
kernel = psd_kernels.ExponentiatedQuadratic(amp, len_scale)
mean_fn = lambda x: x[:, 0]**2
jitter = np.float64(1e-4)
tp = tfd.StudentTProcess(df=np.float64(3.),
kernel=kernel,
mean_fn=mean_fn,
jitter=jitter,
validate_args=True)
index_points = np.random.uniform(-1., 1., [10, 1]).astype(np.float64)
expected_mean = mean_fn(index_points)
self.assertAllClose(expected_mean,
self.evaluate(tp.mean(index_points=index_points)))
def _kernel_fn(x, y):
return amp**2 * np.exp(-.5 * (np.squeeze(
(x - y)**2)) / (len_scale**2))
expected_covariance = _kernel_fn(np.expand_dims(index_points, -3),
np.expand_dims(index_points, -2))
self.assertAllClose(
expected_covariance,
self.evaluate(tp.covariance(index_points=index_points)))
self.assertAllClose(
np.diag(expected_covariance),
self.evaluate(tp.variance(index_points=index_points)))
self.assertAllClose(
np.sqrt(np.diag(expected_covariance)),
self.evaluate(tp.stddev(index_points=index_points)))
# Calling mean with no index_points should raise an Error
with self.assertRaises(ValueError):
tp.mean()
def student_t_processes(draw,
kernel_name=None,
batch_shape=None,
event_dim=None,
feature_dim=None,
feature_ndims=None,
enable_vars=False):
# First draw a kernel.
k, _ = draw(
kernel_hps.base_kernels(
kernel_name=kernel_name,
batch_shape=batch_shape,
event_dim=event_dim,
feature_dim=feature_dim,
feature_ndims=feature_ndims,
# Disable variables
enable_vars=False))
compatible_batch_shape = draw(
tfp_hps.broadcast_compatible_shape(k.batch_shape))
index_points = draw(
kernel_hps.kernel_input(batch_shape=compatible_batch_shape,
example_ndims=1,
feature_dim=feature_dim,
feature_ndims=feature_ndims,
enable_vars=enable_vars,
name='index_points'))
params = draw(
broadcasting_params('StudentTProcess',
compatible_batch_shape,
event_dim=event_dim,
enable_vars=enable_vars))
stp = tfd.StudentTProcess(
kernel=k,
index_points=index_points,
# The Student-T Process can encounter cholesky decomposition errors,
# so use a large jitter to avoid that.
jitter=1e-1,
df=params['df'])
return stp
def student_t_processes(draw,
kernel_name=None,
batch_shape=None,
event_dim=None,
feature_dim=None,
feature_ndims=None,
enable_vars=False):
# First draw a kernel.
k, _ = draw(
kernel_hps.base_kernels(
kernel_name=kernel_name,
batch_shape=batch_shape,
event_dim=event_dim,
feature_dim=feature_dim,
feature_ndims=feature_ndims,
# Disable variables
enable_vars=False))
compatible_batch_shape = draw(
tfp_hps.broadcast_compatible_shape(k.batch_shape))
index_points = draw(
kernel_hps.kernel_input(batch_shape=compatible_batch_shape,
example_ndims=1,
feature_dim=feature_dim,
feature_ndims=feature_ndims,
enable_vars=enable_vars,
name='index_points'))
params = draw(
broadcasting_params('StudentTProcess',
compatible_batch_shape,
event_dim=event_dim,
enable_vars=enable_vars))
stp = tfd.StudentTProcess(
kernel=k,
index_points=index_points,
cholesky_fn=lambda x: marginal_fns.retrying_cholesky(x)[0],
df=params['df'],
observation_noise_variance=params['observation_noise_variance'])
return stp