def test_velocity(self):
# no decay:
lt = LocalTrend(id='test', decay_velocity=False)
lt.add_measure('measure')
design = Design(processes=[lt], measures=['measure'])
batch_vel = design.for_batch(2, 1)
# check F:
self.assertListEqual(list1=batch_vel.F(0)[0].tolist(), list2=[[1., 1.], [0., 1.]])
state_mean = Tensor([[1.], [-.5]])
for i in range(3):
state_mean = torch.mm(batch_vel.F(0)[0], state_mean)
self.assertEqual(state_mean[0].item(), 1 - .5 * (i + 1.))
self.assertEqual(state_mean[1].item(), -.5)
# with decay:
lt = LocalTrend(id='test', decay_velocity=(.50, 1.00))
lt.add_measure('measure')
design = Design(processes=[lt], measures=['measure'])
batch_vel = design.for_batch(2, 1)
self.assertLess(batch_vel.F(0)[0][1, 1], 1.0)
self.assertGreater(batch_vel.F(0)[0][1, 1], 0.5)
decay = design.processes['test'].decayed_transitions['velocity'].get_value()
self.assertEqual(decay, batch_vel.F(0)[0][1, 1])
state_mean = Tensor([[0.], [1.0]])
for i in range(3):
state_mean = torch.mm(batch_vel.F(0)[0], state_mean)
self.assertEqual(decay ** (i + 1), state_mean[1].item())
def test_discrete_seasons(self):
# test seasons without durations
season = Season(id='day_of_week',
seasonal_period=7,
season_duration=1,
season_start='2018-01-01',
dt_unit='D')
season.add_measure('measure')
# need to include start_datetimes since included above
with self.assertRaises(ValueError) as cm:
season.for_batch(1, 1)
self.assertEqual(
cm.exception.args[0],
'Must pass `start_datetimes` to process `day_of_week`.')
design = Design(processes=[season], measures=['measure'])
process_kwargs = {
'day_of_week': {
'start_datetimes': array([datetime64('2018-01-01')])
}
}
batch_season = design.for_batch(1, 1, process_kwargs=process_kwargs)
# test transitions manually:
state_mean = torch.arange(0.0, 7.0)[:, None]
state_mean[0] = -state_mean[1:].sum()
for i in range(10):
state_mean_last = state_mean
state_mean = torch.mm(batch_season.F(0)[0], state_mean)
self.assertTrue((state_mean[1:] == state_mean_last[:-1]).all())
self.assertListEqual(
batch_season.H(0)[0].tolist(),
[[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
def test_design_h_batch_process(self):
#
vel_1 = LocalTrend(id='vel_1')
vel_1.add_measure('measure_1')
vel_2 = LocalTrend(id='vel_2')
vel_2.add_measure('measure_2')
vel_common = LocalTrend(id='vel_common')
vel_common.add_measure('measure_1')
vel_common.ses_to_measures[('measure_1',
'position')] = lambda: Tensor([1.0, 0.0])
vel_common.add_measure('measure_2')
vel_common.ses_to_measures[('measure_2',
'position')] = lambda: Tensor([0.0, 1.0])
design = Design(processes=[vel_1, vel_2, vel_common],
measures=['measure_1', 'measure_2'])
batch_design = design.for_batch(num_groups=2, num_timesteps=1)
design_H = batch_design.H(0)
self.assertListEqual(list1=design_H[0].tolist(),
list2=[[1.0, 0.0, 0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 1.0, 0.0, 0.0, 0.0]])
self.assertListEqual(list1=design_H[1].tolist(),
list2=[[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0, 1.0, 0.0]])
def test_fourier_season2(self):
season = FourierSeason2(id='season', seasonal_period=24, K=2, decay=False, dt_unit=None)
season.add_measure('measure')
design = Design(processes=[season], measures=['measure'])
for_batch = design.for_batch(1, 24 * 2)
positions = []
state = torch.randn(5)
for i in range(for_batch.num_timesteps):
state = for_batch.F(i)[0].matmul(state)
positions.append(round(state[-1].item() * 100) / 100.)
self.assertListEqual(positions[0:24], positions[-24:])
def test_tbats_season(self):
K = 3
season = TBATS(id='season', seasonal_period=24, K=K, decay=False, dt_unit=None)
season.add_measure('measure')
design = Design(processes=[season], measures=['measure'])
for_batch = design.for_batch(1, 24 * 7)
positions = []
state = torch.randn(int(K * 2))
for i in range(for_batch.num_timesteps):
state = for_batch.F(i)[0].matmul(state)
pos = for_batch.H(i)[0].matmul(state)
positions.append(round(pos.item() * 100) / 100.)
self.assertListEqual(positions[0:24], positions[-24:])
def test_design_h_batch_process(self):
#
vel_1 = LocalTrend(id='vel_1')
vel_1.add_measure('measure_1')
vel_2 = LocalTrend(id='vel_2')
vel_2.add_measure('measure_2')
vel_common = LocalTrend(id='vel_common')
vel_common.add_measure('measure_1')
vel_common._set_measure('measure_1', 'position', 1., force=True)
vel_common.add_measure('measure_2')
vel_common._set_measure('measure_2', 'position', 5., force=True)
design = Design(processes=[vel_1, vel_2, vel_common],
measures=['measure_1', 'measure_2'])
batch_design = design.for_batch(num_groups=1, num_timesteps=1)
design_H = batch_design.H(0)
self.assertListEqual(list1=design_H[0].tolist(),
list2=[[1.0, 0.0, 0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 1.0, 0.0, 5.0, 0.0]])
def test_discrete_seasons(self):
# test seasons without durations
season = Season(
id='day_of_week', seasonal_period=7, season_duration=1, dt_unit='D'
)
season.add_measure('measure')
# need to include start_datetimes since included above
with self.assertRaises(TypeError) as cm:
season.for_batch(1, 1)
self.assertIn('Missing argument `start_datetimes`', cm.exception.args[0])
design = Design(processes=[season], measures=['measure'])
batch_season = design.for_batch(1, 1, start_datetimes=np.array([np.datetime64('2018-01-01')]))
# test transitions manually:
state_mean = torch.arange(0.0, 7.0)[:, None]
state_mean[0] = -state_mean[1:].sum()
for i in range(10):
state_mean_last = state_mean
state_mean = torch.mm(batch_season.F(0)[0], state_mean)
self.assertTrue((state_mean[1:] == state_mean_last[:-1]).all())
self.assertListEqual(batch_season.H(0)[0].tolist(), [[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
class KalmanFilter(torch.nn.Module):
def __init__(self,
measures: Sequence[str],
processes: Sequence[Process],
device: Optional[torch.device] = None,
**kwargs):
super().__init__()
self.design: Design = None
self._init_design(measures=measures,
processes=processes,
device=device,
**kwargs)
# parameters from design:
self.design_parameters = ParameterList()
for param in self.design.parameters():
self.design_parameters.append(param)
# the StateBelief family, implemented by property (default gaussian)
self._family = None
self.to(device=self.design.device)
def _init_design(self, *args, **kwargs) -> None:
self.design = Design(*args, **kwargs)
@property
def measure_size(self) -> int:
return self.design.measure_size
@property
def family(self) -> TypeVar('Gaussian'):
if self._family is None:
self._family = Gaussian
return self._family
def predict_initial_state(self,
design_for_batch: DesignForBatch) -> 'Gaussian':
return self.family(
means=design_for_batch.initial_mean,
covs=design_for_batch.initial_covariance,
# we consider this a one-step-ahead prediction, so last measured one step ago:
last_measured=torch.ones(design_for_batch.num_groups,
dtype=torch.int))
def design_for_batch(self, num_groups: int, num_timesteps: int,
**kwargs) -> DesignForBatch:
return self.design.for_batch(num_groups=num_groups,
num_timesteps=num_timesteps,
**kwargs)
# noinspection PyShadowingBuiltins
def forward(self,
input: Tensor,
initial_state: Optional[StateBelief] = None,
progress: Union[tqdm, bool] = False,
**kwargs) -> StateBeliefOverTime:
"""
:param input: The multivariate time-series to be fit by the kalman-filter. A Tensor where the first dimension
represents the groups, the second dimension represents the time-points, and the third dimension represents the
measures.
:param initial_state: If a StateBelief, this is used as the prediction for time=0; if None then each process
generates initial values.
:param progress: Should progress-bar be generated?
:param kwargs: Other kwargs that will be passed to the `design_for_batch` method.
:return: A StateBeliefOverTime consisting of one-step-ahead predictions.
"""
num_groups, num_timesteps, num_measures = input.shape
if num_measures != self.measure_size:
raise ValueError(
f"This KalmanFilter has {self.measure_size} measurement-dimensions; but the input shape is "
f"{(num_groups, num_timesteps, num_measures)} (last dim should == measure-size)."
)
design_for_batch = self.design_for_batch(num_groups=num_groups,
num_timesteps=num_timesteps,
**kwargs)
# initial state of the system:
if initial_state is None:
state_prediction = self.predict_initial_state(design_for_batch)
else:
state_prediction = initial_state
progress = progress or identity
if progress is True:
progress = tqdm
iterator = progress(range(num_timesteps))
# generate one-step-ahead predictions:
state_predictions = []
for t in iterator:
if t > 0:
# take state-prediction of previous t (now t-1), correct it according to what was actually measured at at t-1
state_belief = state_prediction.update(obs=input[:, t - 1, :])
# predict the state for t, from information from t-1
# F at t-1 is transition *from* t-1 *to* t
F = design_for_batch.F(t - 1)
Q = design_for_batch.Q(t - 1)
state_prediction = state_belief.predict(F=F, Q=Q)
# compute how state-prediction at t translates into measurement-prediction at t
H = design_for_batch.H(t)
R = design_for_batch.R(t)
state_prediction.compute_measurement(H=H, R=R)
# append to output:
state_predictions.append(state_prediction)
return self.family.concatenate_over_time(
state_beliefs=state_predictions, design=self.design)
def smooth(self, states: StateBeliefOverTime):
raise NotImplementedError
def simulate(self,
states: Union[StateBeliefOverTime, StateBelief],
horizon: int,
num_iter: int,
progress: bool = False,
from_times: Sequence[int] = None,
state_to_measured: Optional[Callable] = None,
white_noise: Optional[Tuple[Tensor, Tensor]] = None,
ntry_diag_incr: int = 1000,
**kwargs) -> List[Tensor]:
assert horizon > 0
# forecast-from time:
if from_times is None:
if isinstance(states, StateBelief):
initial_state = states
else:
# a StateBeliefOverTime was passed, but no from_times, so just pick the last one
initial_state = states.last_prediction()
else:
# from_times will be used to pick the slice
initial_state = states.get_state_belief(from_times)
initial_state = initial_state.__class__(
means=initial_state.means.repeat((num_iter, 1)),
covs=initial_state.covs.repeat((num_iter, 1, 1)),
last_measured=initial_state.last_measured.repeat(num_iter))
design_for_batch = self.design_for_batch(
num_groups=initial_state.num_groups,
num_timesteps=horizon,
**kwargs)
if white_noise is None:
process_wn, measure_wn = None, None
else:
process_wn, measure_wn = white_noise
trajectories = initial_state.simulate_state_trajectories(
design_for_batch=design_for_batch,
progress=progress,
ntry_diag_incr=ntry_diag_incr,
eps=process_wn)
if state_to_measured is None:
sim = trajectories.measurement_distribution.deterministic_sample(
eps=measure_wn)
else:
sim = state_to_measured(trajectories)
return torch.chunk(sim, num_iter)
def forecast(self,
states: Union[StateBeliefOverTime, StateBelief],
horizon: int,
from_times: Optional[Sequence[int]] = None,
progress: bool = False,
**kwargs) -> StateBeliefOverTime:
assert horizon > 0
# forecast-from time:
if from_times is None:
if isinstance(states, StateBelief):
state_prediction = states
else:
# a StateBeliefOverTime was passed, but no from_times, so just pick the last one
state_prediction = states.last_prediction()
else:
# from_times will be used to pick the slice
state_prediction = states.get_state_belief(from_times)
design_for_batch = self.design_for_batch(
num_groups=state_prediction.num_groups,
num_timesteps=horizon,
**kwargs)
progress = progress or identity
if progress is True:
progress = tqdm
iterator = progress(range(design_for_batch.num_timesteps))
forecasts = []
for t in iterator:
if t > 0:
# predict the state for t, from information from t-1
# F at t-1 is transition *from* t-1 *to* t
F = design_for_batch.F(t - 1)
Q = design_for_batch.Q(t - 1)
state_prediction = state_prediction.predict(F=F, Q=Q)
# compute how state-prediction at t translates into measurement-prediction at t
H = design_for_batch.H(t)
R = design_for_batch.R(t)
state_prediction.compute_measurement(H=H, R=R)
# append to output:
forecasts.append(state_prediction)
return self.family.concatenate_over_time(state_beliefs=forecasts,
design=self.design)