def test_matches_locallineartrend(self):
"""SemiLocalLinearTrend with trivial AR process is a LocalLinearTrend."""
level_scale = self._build_placeholder(0.5)
slope_scale = self._build_placeholder(0.5)
initial_level = self._build_placeholder(3.)
initial_slope = self._build_placeholder(-2.)
num_timesteps = 5
y = self._build_placeholder([1.0, 2.5, 4.3, 6.1, 7.8])
semilocal_ssm = SemiLocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=level_scale,
slope_scale=slope_scale,
slope_mean=self._build_placeholder(0.),
autoregressive_coef=self._build_placeholder(1.),
initial_state_prior=tfd.MultivariateNormalDiag(
loc=[initial_level, initial_slope],
scale_diag=self._build_placeholder([1., 1.])))
local_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=level_scale,
slope_scale=slope_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=[initial_level, initial_slope],
scale_diag=self._build_placeholder([1., 1.])))
semilocal_lp = semilocal_ssm.log_prob(y[:, tf.newaxis])
local_lp = local_ssm.log_prob(y[:, tf.newaxis])
self.assertAllClose(self.evaluate(semilocal_lp),
self.evaluate(local_lp))
semilocal_mean = semilocal_ssm.mean()
local_mean = local_ssm.mean()
self.assertAllClose(self.evaluate(semilocal_mean),
self.evaluate(local_mean))
semilocal_variance = semilocal_ssm.variance()
local_variance = local_ssm.variance()
self.assertAllClose(self.evaluate(semilocal_variance),
self.evaluate(local_variance))
def test_stats(self):
# Build a model with expected initial loc 0 and slope 1.
level_scale = self._build_placeholder(1.0)
slope_scale = self._build_placeholder(1.0)
initial_state_prior = tfd.MultivariateNormalDiag(
loc=self._build_placeholder([0, 1.]),
scale_diag=self._build_placeholder([1., 1.]))
ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=10,
level_scale=level_scale,
slope_scale=slope_scale,
initial_state_prior=initial_state_prior)
# In expectation, the process grows linearly.
mean = self.evaluate(ssm.mean())
self.assertAllClose(mean, np.arange(0, 10)[:, np.newaxis])
# slope variance at time T is linear: T * slope_scale
expected_variance = [1, 3, 8, 18, 35, 61, 98, 148, 213, 295]
variance = self.evaluate(ssm.variance())
self.assertAllClose(variance, np.array(expected_variance)[:, np.newaxis])
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))