def testEqualsAutoregressive(self):
# An ARMA(p, 0) process is just an AR(p) processes
num_timesteps = 10
observed_time_series = self._build_placeholder(
np.random.randn(num_timesteps, 1))
level_scale = self._build_placeholder(0.1)
# We'll test an AR1 process, and also (just for kicks) that the trivial
# embedding as an AR2 process gives the same model.
coefficients_order1 = np.array([1.]).astype(self.dtype)
coefficients_order2 = np.array([1., 1.]).astype(self.dtype)
ar1_ssm = AutoregressiveStateSpaceModel(
num_timesteps=num_timesteps,
coefficients=coefficients_order1,
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale]))
ar2_ssm = AutoregressiveStateSpaceModel(
num_timesteps=num_timesteps,
coefficients=coefficients_order2,
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale, 1.]))
arma1_ssm = AutoregressiveMovingAverageStateSpaceModel(
num_timesteps=num_timesteps,
ar_coefficients=coefficients_order1,
ma_coefficients=np.array([0.]).astype(self.dtype),
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale, 1.]))
arma2_ssm = AutoregressiveMovingAverageStateSpaceModel(
num_timesteps=num_timesteps,
ar_coefficients=coefficients_order2,
ma_coefficients=np.array([0.]).astype(self.dtype),
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale, 1.]))
ar1_lp, arma1_lp, ar2_lp, arma2_lp = (
ar1_ssm.log_prob(observed_time_series),
arma1_ssm.log_prob(observed_time_series),
ar2_ssm.log_prob(observed_time_series),
arma2_ssm.log_prob(observed_time_series))
self.assertAllClose(ar1_lp, arma1_lp)
self.assertAllClose(ar2_lp, arma2_lp)
def testEqualsLocalLevel(self):
# An AR1 process with coef 1 is just a random walk, equivalent to a local
# level model. Test that both models define the same distribution
# (log-prob).
num_timesteps = 10
observed_time_series = self._build_placeholder(
np.random.randn(num_timesteps, 1))
level_scale = self._build_placeholder(0.1)
# We'll test an AR1 process, and also (just for kicks) that the trivial
# embedding as an AR2 process gives the same model.
coefficients_order1 = np.array([1.]).astype(self.dtype)
coefficients_order2 = np.array([1., 0.]).astype(self.dtype)
ar1_ssm = AutoregressiveStateSpaceModel(
num_timesteps=num_timesteps,
coefficients=coefficients_order1,
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale]))
ar2_ssm = AutoregressiveStateSpaceModel(
num_timesteps=num_timesteps,
coefficients=coefficients_order2,
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale, 1.]))
local_level_ssm = LocalLevelStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale]))
ar1_lp, ar2_lp, ll_lp = self.evaluate(
(ar1_ssm.log_prob(observed_time_series),
ar2_ssm.log_prob(observed_time_series),
local_level_ssm.log_prob(observed_time_series)))
self.assertAllClose(ar1_lp, ll_lp)
self.assertAllClose(ar2_lp, ll_lp)
def testLogprobCorrectness(self):
# Compare the state-space model's log-prob to an explicit implementation.
num_timesteps = 10
observed_time_series_ = np.random.randn(num_timesteps)
coefficients_ = np.array([.7, -.1]).astype(self.dtype)
level_scale_ = 1.0
observed_time_series = self._build_placeholder(observed_time_series_)
level_scale = self._build_placeholder(level_scale_)
expected_logp = ar_explicit_logp(observed_time_series_, coefficients_,
level_scale_)
ssm = AutoregressiveStateSpaceModel(
num_timesteps=num_timesteps,
coefficients=coefficients_,
level_scale=level_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
scale_diag=[level_scale, 0.]))
lp = ssm.log_prob(observed_time_series[..., tf.newaxis])
self.assertAllClose(self.evaluate(lp), expected_logp)