def test_slope_mean_and_variance(self):
"""Check that slope follows `slope_mean` and has stationary variance."""
level_scale = 0.1
slope_scale = 0.2
initial_level = 3.
initial_slope = 0.
slope_mean = -2.
initial_level = 3.
autoregressive_coef = 0.9
num_timesteps = 50
# Stationary distribution of an AR1 process, from
# (https://en.wikipedia.org/wiki/Autoregressive_model#Example:_An_AR(1)_process) # pylint: disable=line-too-long
stationary_slope_variance = slope_scale**2 / (1. -
autoregressive_coef**2)
# Initialize the slope prior at the stationary variance.
initial_state_prior = tfd.MultivariateNormalDiag(
loc=self._build_placeholder([initial_level, initial_slope]),
scale_diag=self._build_placeholder(
[1., np.sqrt(stationary_slope_variance)]))
semilocal_ssm = SemiLocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=self._build_placeholder(level_scale),
slope_scale=self._build_placeholder(slope_scale),
slope_mean=self._build_placeholder(slope_mean),
autoregressive_coef=self._build_placeholder(autoregressive_coef),
initial_state_prior=initial_state_prior)
# The slope of the mean should converge to `slope_mean` (as opposed to
# staying fixed at `initial_slope` as in a LocalLinearTrend).
mean_ = self.evaluate(semilocal_ssm.mean()[..., 0])
final_slope = mean_[num_timesteps - 1] - mean_[num_timesteps - 2]
self.assertAllClose(final_slope, slope_mean, atol=0.05)
# The variance in latent `slope` should converge to the stationary
# distribution of an AR1 process:
latent_covs, _ = semilocal_ssm._joint_covariances()
actual_slope_variances = tf.linalg.diag_part(latent_covs)[:, 1]
converged_slope_variance = actual_slope_variances[-1]
self.assertAllClose(self.evaluate(converged_slope_variance),
stationary_slope_variance,
atol=1e-4)
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))