def test_multivariate_observations(self):
# since STS components are scalar by design, we manually construct
# a multivariate-output model to verify that the additive SSM handles
# this case.
num_timesteps = 5
observation_size = 2
multivariate_ssm = self._dummy_model(num_timesteps=num_timesteps,
observation_size=observation_size)
# Note it would not work to specify observation_noise_scale here;
# multivariate observations need to derive the (multivariate)
# observation noise distribution from their components.
combined_ssm = AdditiveStateSpaceModel(
[multivariate_ssm, multivariate_ssm])
y = combined_ssm.sample()
expected_event_shape = [num_timesteps, observation_size]
if self.use_static_shape:
self.assertAllEqual(combined_ssm.event_shape.as_list(),
expected_event_shape)
self.assertAllEqual(y.shape.as_list()[-2:], expected_event_shape)
else:
self.assertAllEqual(
self.evaluate(combined_ssm.event_shape_tensor()),
expected_event_shape)
self.assertAllEqual(
self.evaluate(tf.shape(input=y))[-2:], expected_event_shape)
def test_broadcasting_batch_shape(self):
seed = test_util.test_seed(sampler_type='stateless')
# Build three SSMs with broadcast batch shape.
ssm1 = self._dummy_model(batch_shape=[2])
ssm2 = self._dummy_model(batch_shape=[3, 2])
ssm3 = self._dummy_model(batch_shape=[1, 2])
additive_ssm = AdditiveStateSpaceModel(
component_ssms=[ssm1, ssm2, ssm3])
y = additive_ssm.sample(seed=seed)
broadcast_batch_shape = [3, 2]
if self.use_static_shape:
self.assertAllEqual(
tensorshape_util.as_list(additive_ssm.batch_shape),
broadcast_batch_shape)
self.assertAllEqual(
tensorshape_util.as_list(y.shape)[:-2], broadcast_batch_shape)
else:
self.assertAllEqual(
self.evaluate(additive_ssm.batch_shape_tensor()),
broadcast_batch_shape)
self.assertAllEqual(
self.evaluate(tf.shape(y))[:-2], broadcast_batch_shape)
def test_mismatched_observation_size_error(self):
ssm1 = self._dummy_model(observation_size=1)
ssm2 = self._dummy_model(observation_size=2)
with self.assertRaisesWithPredicateMatch(Exception, ''):
# In the static case, the constructor should raise an exception.
additive_ssm = AdditiveStateSpaceModel(component_ssms=[ssm1, ssm2])
# In the dynamic case, the exception is raised at runtime.
_ = self.evaluate(additive_ssm.sample())
def test_mismatched_num_timesteps_error(self):
ssm1 = self._dummy_model(num_timesteps=10)
ssm2 = self._dummy_model(num_timesteps=8)
with self.assertRaisesWithPredicateMatch(ValueError,
'same number of timesteps'):
# In the static case, the constructor should raise an exception.
additive_ssm = AdditiveStateSpaceModel(component_ssms=[ssm1, ssm2])
# In the dynamic case, the exception is raised at runtime.
_ = self.evaluate(additive_ssm.sample())
def test_batch_shape(self):
batch_shape = [3, 2]
ssm = self._dummy_model(batch_shape=batch_shape)
additive_ssm = AdditiveStateSpaceModel([ssm, ssm])
y = additive_ssm.sample()
if self.use_static_shape:
self.assertAllEqual(additive_ssm.batch_shape.as_list(), batch_shape)
self.assertAllEqual(y.shape.as_list()[:-2], batch_shape)
else:
self.assertAllEqual(self.evaluate(additive_ssm.batch_shape_tensor()),
batch_shape)
self.assertAllEqual(self.evaluate(tf.shape(y))[:-2], batch_shape)
def test_dynamic_num_timesteps(self):
# Verify that num_timesteps is set statically when at least one component
# (not necessarily the first) has static num_timesteps.
num_timesteps = 4
dynamic_timesteps_component = self._dummy_model(
num_timesteps=tf.placeholder_with_default(input=num_timesteps,
shape=None))
static_timesteps_component = self._dummy_model(
num_timesteps=num_timesteps)
additive_ssm = AdditiveStateSpaceModel([dynamic_timesteps_component,
dynamic_timesteps_component])
self.assertEqual(self.evaluate(additive_ssm.num_timesteps), num_timesteps)
additive_ssm = AdditiveStateSpaceModel([dynamic_timesteps_component,
static_timesteps_component])
self.assertEqual(additive_ssm.num_timesteps, num_timesteps)
def test_batch_shape(self):
batch_shape = [3, 2]
seed = test_util.test_seed(sampler_type='stateless')
ssm = self._dummy_model(batch_shape=batch_shape)
additive_ssm = AdditiveStateSpaceModel([ssm, ssm])
y = additive_ssm.sample(seed=seed)
if self.use_static_shape:
self.assertAllEqual(
tensorshape_util.as_list(additive_ssm.batch_shape),
batch_shape)
self.assertAllEqual(
tensorshape_util.as_list(y.shape)[:-2], batch_shape)
else:
self.assertAllEqual(
self.evaluate(additive_ssm.batch_shape_tensor()), batch_shape)
self.assertAllEqual(self.evaluate(tf.shape(y))[:-2], batch_shape)
def test_broadcasting_correctness(self):
# This test verifies that broadcasting of component parameters works as
# expected. We construct a SSM with no batch shape, and test that when we
# add it to another SSM of batch shape [3], we get the same model
# as if we had explicitly broadcast the parameters of the first SSM before
# adding.
num_timesteps = 5
transition_matrix = np.random.randn(2, 2)
transition_noise_diag = np.exp(np.random.randn(2))
observation_matrix = np.random.randn(1, 2)
observation_noise_diag = np.exp(np.random.randn(1))
initial_state_prior_diag = np.exp(np.random.randn(2))
# First build the model in which we let AdditiveSSM do the broadcasting.
batchless_ssm = tfd.LinearGaussianStateSpaceModel(
num_timesteps=num_timesteps,
transition_matrix=self._build_placeholder(transition_matrix),
transition_noise=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(transition_noise_diag)),
observation_matrix=self._build_placeholder(observation_matrix),
observation_noise=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(observation_noise_diag)),
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(initial_state_prior_diag))
)
another_ssm = self._dummy_model(num_timesteps=num_timesteps,
latent_size=4,
batch_shape=[3])
broadcast_additive_ssm = AdditiveStateSpaceModel(
[batchless_ssm, another_ssm])
# Next try doing our own broadcasting explicitly.
broadcast_vector = np.ones([3, 1])
broadcast_matrix = np.ones([3, 1, 1])
batch_ssm = tfd.LinearGaussianStateSpaceModel(
num_timesteps=num_timesteps,
transition_matrix=self._build_placeholder(
transition_matrix * broadcast_matrix),
transition_noise=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(
transition_noise_diag * broadcast_vector)),
observation_matrix=self._build_placeholder(
observation_matrix * broadcast_matrix),
observation_noise=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(
observation_noise_diag * broadcast_vector)),
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(
initial_state_prior_diag * broadcast_vector)))
manual_additive_ssm = AdditiveStateSpaceModel([batch_ssm, another_ssm])
# Both additive SSMs define the same model, so they should give the same
# log_probs.
y = self.evaluate(broadcast_additive_ssm.sample(seed=42))
self.assertAllEqual(self.evaluate(broadcast_additive_ssm.log_prob(y)),
self.evaluate(manual_additive_ssm.log_prob(y)))
def test_identity(self):
# Test that an additive SSM with a single component defines the same
# distribution as the component model.
y = self._build_placeholder([1.0, 2.5, 4.3, 6.1, 7.8])
local_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=5,
level_scale=0.3,
slope_scale=0.6,
observation_noise_scale=0.1,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder([1., 1.])))
additive_ssm = AdditiveStateSpaceModel([local_ssm])
local_lp = local_ssm.log_prob(y[:, np.newaxis])
additive_lp = additive_ssm.log_prob(y[:, np.newaxis])
self.assertAllClose(self.evaluate(local_lp), self.evaluate(additive_lp))
def test_broadcasting_batch_shape(self):
# Build three SSMs with broadcast batch shape.
ssm1 = self._dummy_model(batch_shape=[2])
ssm2 = self._dummy_model(batch_shape=[3, 2])
ssm3 = self._dummy_model(batch_shape=[1, 2])
additive_ssm = AdditiveStateSpaceModel(
component_ssms=[ssm1, ssm2, ssm3])
y = additive_ssm.sample()
broadcast_batch_shape = [3, 2]
if self.use_static_shape:
self.assertAllEqual(additive_ssm.batch_shape.as_list(),
broadcast_batch_shape)
self.assertAllEqual(y.shape.as_list()[:-2], broadcast_batch_shape)
else:
self.assertAllEqual(
self.evaluate(additive_ssm.batch_shape_tensor()),
broadcast_batch_shape)
self.assertAllEqual(
self.evaluate(tf.shape(input=y))[:-2], broadcast_batch_shape)
def test_batch_shape_ignores_component_state_priors(self):
# If we pass an initial_state_prior directly to an AdditiveSSM, overriding
# the initial state priors of component models, the overall batch shape
# should no longer depend on the (overridden) component priors.
# This ensures that we produce correct shapes in forecasting, where the
# shapes may have changed to include dimensions corresponding to posterior
# draws.
# Create a component model with no batch shape *except* in the initial state
# prior.
latent_size = 2
ssm = self._dummy_model(latent_size=latent_size,
batch_shape=[],
initial_state_prior_batch_shape=[5, 5])
# If we override the initial state prior with an unbatched prior, the
# resulting AdditiveSSM should not have batch dimensions.
unbatched_initial_state_prior = tfd.MultivariateNormalDiag(
scale_diag=self._build_placeholder(np.ones([latent_size])))
additive_ssm = AdditiveStateSpaceModel(
[ssm], initial_state_prior=unbatched_initial_state_prior)
self.assertAllEqual(self.evaluate(additive_ssm.batch_shape_tensor()),
[])
def test_sum_of_local_linear_trends(self):
# We know analytically that the sum of two local linear trends is
# another local linear trend, with means and variances scaled
# accordingly, so the additive model should match this behavior.
level_scale = 0.5
slope_scale = 1.1
initial_level = 3.
initial_slope = -2.
observation_noise_scale = 0.
num_timesteps = 5
y = self._build_placeholder([1.0, 2.5, 4.3, 6.1, 7.8])
# Combine two local linear trend models, one a full model, the other
# with just a moving mean (zero slope).
local_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=level_scale,
slope_scale=slope_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=self._build_placeholder([initial_level, initial_slope]),
scale_diag=self._build_placeholder([1., 1.])))
second_level_scale = 0.3
second_initial_level = 1.1
moving_level_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=second_level_scale,
slope_scale=0.,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=self._build_placeholder([second_initial_level, 0.]),
scale_diag=self._build_placeholder([1., 0.])))
additive_ssm = AdditiveStateSpaceModel(
[local_ssm, moving_level_ssm],
observation_noise_scale=observation_noise_scale)
# Build the analytical sum of the two processes.
target_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=np.float32(
np.sqrt(level_scale**2 + second_level_scale**2)),
slope_scale=np.float32(slope_scale),
observation_noise_scale=observation_noise_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=self._build_placeholder(
[initial_level + second_initial_level,
initial_slope + 0.]),
scale_diag=self._build_placeholder(np.sqrt([2., 1.]))))
# Test that both models behave equivalently.
additive_mean = additive_ssm.mean()
target_mean = target_ssm.mean()
self.assertAllClose(self.evaluate(additive_mean),
self.evaluate(target_mean))
additive_variance = additive_ssm.variance()
target_variance = target_ssm.variance()
self.assertAllClose(self.evaluate(additive_variance),
self.evaluate(target_variance))
additive_lp = additive_ssm.log_prob(y[:, np.newaxis])
target_lp = target_ssm.log_prob(y[:, np.newaxis])
self.assertAllClose(self.evaluate(additive_lp),
self.evaluate(target_lp))
def test_nesting_additive_ssms(self):
ssm1 = self._dummy_model(batch_shape=[1, 2])
ssm2 = self._dummy_model(batch_shape=[3, 2])
observation_noise_scale = 0.1
additive_ssm = AdditiveStateSpaceModel(
[ssm1, ssm2], observation_noise_scale=observation_noise_scale)
nested_additive_ssm = AdditiveStateSpaceModel(
[AdditiveStateSpaceModel([ssm1]),
AdditiveStateSpaceModel([ssm2])],
observation_noise_scale=observation_noise_scale)
# Test that both models behave equivalently.
y = self.evaluate(nested_additive_ssm.sample())
additive_lp = additive_ssm.log_prob(y)
nested_additive_lp = nested_additive_ssm.log_prob(y)
self.assertAllClose(self.evaluate(additive_lp),
self.evaluate(nested_additive_lp))
additive_mean = additive_ssm.mean()
nested_additive_mean = nested_additive_ssm.mean()
self.assertAllClose(self.evaluate(additive_mean),
self.evaluate(nested_additive_mean))
additive_variance = additive_ssm.variance()
nested_additive_variance = nested_additive_ssm.variance()
self.assertAllClose(self.evaluate(additive_variance),
self.evaluate(nested_additive_variance))
def test_constant_offset(self):
offset_ = 1.23456
offset = self._build_placeholder(offset_)
ssm = self._dummy_model()
additive_ssm = AdditiveStateSpaceModel([ssm])
additive_ssm_with_offset = AdditiveStateSpaceModel(
[ssm], constant_offset=offset)
additive_ssm_with_offset_and_explicit_scale = AdditiveStateSpaceModel(
[ssm],
constant_offset=offset,
observation_noise_scale=(
ssm.get_observation_noise_for_timestep(0).stddev()[..., 0]))
mean_, offset_mean_, offset_with_scale_mean_ = self.evaluate(
(additive_ssm.mean(), additive_ssm_with_offset.mean(),
additive_ssm_with_offset_and_explicit_scale.mean()))
print(mean_.shape, offset_mean_.shape, offset_with_scale_mean_.shape)
self.assertAllClose(mean_, offset_mean_ - offset_)
self.assertAllClose(mean_, offset_with_scale_mean_ - offset_)
# Offset should not affect the stddev.
stddev_, offset_stddev_, offset_with_scale_stddev_ = self.evaluate(
(additive_ssm.stddev(), additive_ssm_with_offset.stddev(),
additive_ssm_with_offset_and_explicit_scale.stddev()))
self.assertAllClose(stddev_, offset_stddev_)
self.assertAllClose(stddev_, offset_with_scale_stddev_)
def test_mismatched_dtype_error(self):
ssm1 = self._dummy_model(dtype=self.dtype)
ssm2 = self._dummy_model(dtype=np.float16)
with self.assertRaisesRegexp(Exception, 'dtype'):
_ = AdditiveStateSpaceModel(component_ssms=[ssm1, ssm2])
def test_constant_offset(self, is_scalar=True):
offset_ = np.array(3.1415) if is_scalar else np.array(
[3., 1., 4., 1., 5.])
offset = self._build_placeholder(offset_)
ssm = self._dummy_model()
additive_ssm = AdditiveStateSpaceModel([ssm])
additive_ssm_with_offset = AdditiveStateSpaceModel(
[ssm], constant_offset=offset)
additive_ssm_with_offset_and_explicit_scale = AdditiveStateSpaceModel(
[ssm],
constant_offset=offset,
observation_noise_scale=(
ssm.get_observation_noise_for_timestep(0).stddev()[..., 0]))
mean_, offset_mean_, offset_with_scale_mean_ = self.evaluate(
(additive_ssm.mean(), additive_ssm_with_offset.mean(),
additive_ssm_with_offset_and_explicit_scale.mean()))
self.assertAllClose(mean_, offset_mean_ - offset_[..., tf.newaxis])
self.assertAllClose(mean_,
offset_with_scale_mean_ - offset_[..., tf.newaxis])
# Offset should not affect the stddev.
stddev_, offset_stddev_, offset_with_scale_stddev_ = self.evaluate(
(additive_ssm.stddev(), additive_ssm_with_offset.stddev(),
additive_ssm_with_offset_and_explicit_scale.stddev()))
self.assertAllClose(stddev_, offset_stddev_)
self.assertAllClose(stddev_, offset_with_scale_stddev_)
