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|
Formal representation of a smooth seasonal effect model.
Inherits From: StructuralTimeSeries
tfp.substrates.numpy.sts.SmoothSeasonal(
period,
frequency_multipliers,
allow_drift=True,
drift_scale_prior=None,
initial_state_prior=None,
observed_time_series=None,
name=None
)
The smooth seasonal model uses a set of trigonometric terms in order to
capture a recurring pattern whereby adjacent (in time) effects are
similar. The model uses frequencies calculated via:
frequencies[j] = 2. * pi * frequency_multipliers[j] / period
and then posits two latent states for each frequency. The two latent states
associated with frequency j drift over time via:
effect[t] = (effect[t - 1] * cos(frequencies[j]) +
auxiliary[t - 1] * sin(frequencies[j]) +
Normal(0., drift_scale))
auxiliary[t] = (-effect[t - 1] * sin(frequencies[j]) +
auxiliary[t - 1] * cos(frequencies[j]) +
Normal(0., drift_scale))
where effect is the smooth seasonal effect and auxiliary only appears as a
matter of construction. The interpretation of auxiliary is thus not
particularly important.
Examples
A smooth seasonal effect model representing smooth weekly seasonality on daily data:
component = SmoothSeasonal(
period=7,
frequency_multipliers=[1, 2, 3],
initial_state_prior=tfd.MultivariateNormalDiag(scale_diag=tf.ones([6])),
)
Args | |
|---|---|
period
|
positive scalar float Tensor giving the number of timesteps
required for the longest cyclic effect to repeat.
|
frequency_multipliers
|
One-dimensional float Tensor listing the
frequencies (cyclic components) included in the model, as multipliers of
the base/fundamental frequency 2. * pi / period. Each component is
specified by the number of times it repeats per period, and adds two
latent dimensions to the model. A smooth seasonal model that can
represent any periodic function is given by frequency_multipliers = [1,
2, ..., floor(period / 2)]. However, it is often desirable to enforce a
smoothness assumption (and reduce the computational burden) by dropping
some of the higher frequencies.
|
allow_drift
|
optional Python bool specifying whether the seasonal
effects can drift over time. Setting this to False
removes the drift_scale parameter from the model. This is
mathematically equivalent to
drift_scale_prior = tfd.Deterministic(0.), but removing drift
directly is preferred because it avoids the use of a degenerate prior.
Default value: True.
|
drift_scale_prior
|
optional tfd.Distribution instance specifying a prior
on the drift_scale parameter. If None, a heuristic default prior is
constructed based on the provided observed_time_series.
Default value: None.
|
initial_state_prior
|
instance of tfd.MultivariateNormal representing
the prior distribution on the latent states. Must have event shape
[2 * len(frequency_multipliers)]. If None, a heuristic default prior
is constructed based on the provided observed_time_series.
|
observed_time_series
|
optional float Tensor of shape
batch_shape + [T, 1] (omitting the trailing unit dimension is also
supported when T > 1), specifying an observed time series. Any NaNs
are interpreted as missing observations; missingness may be also be
explicitly specified by passing a tfp.sts.MaskedTimeSeries instance.
Any priors not explicitly set will be given default values according to
the scale of the observed time series (or batch of time series).
Default value: None.
|
name
|
the name of this model component. Default value: 'SmoothSeasonal'. |
Methods
batch_shape_tensor
batch_shape_tensor()
Runtime batch shape of models represented by this component.
| Returns | |
|---|---|
batch_shape
|
int Tensor giving the broadcast batch shape of
all model parameters. This should match the batch shape of
derived state space models, i.e.,
self.make_state_space_model(...).batch_shape_tensor().
|
copy
copy(
**override_parameters_kwargs
)
Creates a deep copy.
| Args | |
|---|---|
**override_parameters_kwargs
|
String/value dictionary of initialization arguments to override with new values. |
| Returns | |
|---|---|
copy
|
A new instance of type(self) initialized from the union
of self.init_parameters and override_parameters_kwargs, i.e.,
dict(self.init_parameters, **override_parameters_kwargs).
|
get_parameter
get_parameter(
parameter_name
)
Returns the parameter with the given name, or a KeyError.
joint_distribution
joint_distribution(
observed_time_series=None,
num_timesteps=None,
trajectories_shape=(),
initial_step=0,
mask=None,
experimental_parallelize=False
)
Constructs the joint distribution over parameters and observed values.
| Args | |
|---|---|
observed_time_series
|
Optional observed time series to model, as a
Tensor or tfp.sts.MaskedTimeSeries instance having shape
concat([batch_shape, trajectories_shape, num_timesteps, 1]). If
an observed time series is provided, the num_timesteps,
trajectories_shape, and mask arguments are ignored, and
an unnormalized (pinned) distribution over parameter values is returned.
Default value: None.
|
num_timesteps
|
scalar int Tensor number of timesteps to model. This
must be specified either directly or by passing an
observed_time_series.
Default value: 0.
|
trajectories_shape
|
int Tensor shape of sampled trajectories
for each set of parameter values. Ignored if an observed_time_series
is passed.
Default value: ().
|
initial_step
|
Optional scalar int Tensor specifying the starting
timestep.
Default value: 0.
|
mask
|
Optional bool Tensor having shape
concat([batch_shape, trajectories_shape, num_timesteps]), in which
True entries indicate that the series value at the corresponding step
is missing and should be ignored. This argument should be passed only
if observed_time_series is not specified or does not already contain
a missingness mask; it is an error to pass both this
argument and an observed_time_series value containing a missingness
mask.
Default value: None.
|
experimental_parallelize
|
If True, use parallel message passing
algorithms from tfp.experimental.parallel_filter to perform time
series operations in O(log num_timesteps) sequential steps. The
overall FLOP and memory cost may be larger than for the sequential
implementations by a constant factor.
Default value: False.
|
| Returns | |
|---|---|
joint_distribution
|
joint distribution of model parameters and
observed trajectories. If no observed_time_series was specified, this
is an instance of tfd.JointDistributionNamedAutoBatched with a
random variable for each model parameter (with names and order matching
self.parameters), plus a final random variable observed_time_series
representing a trajectory(ies) conditioned on the parameters. If
observed_time_series was specified, the return value is given by
joint_distribution.experimental_pin(
observed_time_series=observed_time_series) where joint_distribution
is as just described, so it defines an unnormalized posterior
distribution over the parameters.
|
Example:
The joint distribution can generate prior samples of parameters and trajectories:
from matplotlib import pylab as plt
import tensorflow_probability as tfp; tfp = tfp.substrates.numpy
# Sample and plot 100 trajectories from the prior.
model = tfp.sts.LocalLinearTrend()
prior_samples = model.joint_distribution(num_timesteps=200).sample([100])
plt.plot(
tf.linalg.matrix_transpose(prior_samples['observed_time_series'][..., 0]))
It also integrates with TFP inference APIs, providing a more flexible alternative to the STS-specific fitting utilities.
jd = model.joint_distribution(observed_time_series)
# Variational inference.
surrogate_posterior = (
tfp.experimental.vi.build_factored_surrogate_posterior(
event_shape=jd.event_shape,
bijector=jd.experimental_default_event_space_bijector()))
losses = tfp.vi.fit_surrogate_posterior(
target_log_prob_fn=jd.unnormalized_log_prob,
surrogate_posterior=surrogate_posterior,
optimizer=tf.optimizers.Adam(0.1),
num_steps=200)
parameter_samples = surrogate_posterior.sample(50)
# No U-Turn Sampler.
samples, kernel_results = tfp.experimental.mcmc.windowed_adaptive_nuts(
n_draws=500, joint_dist=dist)
joint_log_prob
joint_log_prob(
observed_time_series
)
Build the joint density log p(params) + log p(y|params) as a callable.
| Args | |
|---|---|
observed_time_series
|
Observed Tensor trajectories of shape
sample_shape + batch_shape + [num_timesteps, 1] (the trailing
1 dimension is optional if num_timesteps > 1), where
batch_shape should match self.batch_shape (the broadcast batch
shape of all priors on parameters for this structural time series
model). Any NaNs are interpreted as missing observations; missingness
may be also be explicitly specified by passing a
tfp.sts.MaskedTimeSeries instance.
|
| Returns | |
|---|---|
log_joint_fn
|
A function taking a Tensor argument for each model
parameter, in canonical order, and returning a Tensor log probability
of shape batch_shape. Note that, unlike tfp.Distributions
log_prob methods, the log_joint sums over the sample_shape from y,
so that sample_shape does not appear in the output log_prob. This
corresponds to viewing multiple samples in y as iid observations from a
single model, which is typically the desired behavior for parameter
inference.
|
make_state_space_model
make_state_space_model(
num_timesteps,
param_vals,
initial_state_prior=None,
initial_step=0,
**linear_gaussian_ssm_kwargs
)
Instantiate this model as a Distribution over specified num_timesteps.
| Args | |
|---|---|
num_timesteps
|
Python int number of timesteps to model.
|
param_vals
|
a list of Tensor parameter values in order corresponding to
self.parameters, or a dict mapping from parameter names to values.
|
initial_state_prior
|
an optional Distribution instance overriding the
default prior on the model's initial state. This is used in forecasting
("today's prior is yesterday's posterior").
|
initial_step
|
optional int specifying the initial timestep to model.
This is relevant when the model contains time-varying components,
e.g., holidays or seasonality.
|
**linear_gaussian_ssm_kwargs
|
Optional additional keyword arguments to
to the base tfd.LinearGaussianStateSpaceModel constructor.
|
| Returns | |
|---|---|
dist
|
a LinearGaussianStateSpaceModel Distribution object.
|
prior_sample
prior_sample(
num_timesteps,
initial_step=0,
params_sample_shape=(),
trajectories_sample_shape=(),
seed=None
)
Sample from the joint prior over model parameters and trajectories.
| Args | |
|---|---|
num_timesteps
|
Scalar int Tensor number of timesteps to model.
|
initial_step
|
Optional scalar int Tensor specifying the starting
timestep.
Default value: 0.
|
params_sample_shape
|
Number of possible worlds to sample iid from the
parameter prior, or more generally, Tensor int shape to fill with
iid samples.
Default value: [] (i.e., draw a single sample and don't expand the
shape).
|
trajectories_sample_shape
|
For each sampled set of parameters, number
of trajectories to sample, or more generally, Tensor int shape to
fill with iid samples.
Default value: [] (i.e., draw a single sample and don't expand the
shape).
|
seed
|
PRNG seed; see tfp.random.sanitize_seed for details.
Default value: None.
|
| Returns | |
|---|---|
trajectories
|
float Tensor of shape
trajectories_sample_shape + params_sample_shape + [num_timesteps, 1]
containing all sampled trajectories.
|
param_samples
|
list of sampled parameter value Tensors, in order
corresponding to self.parameters, each of shape
params_sample_shape + prior.batch_shape + prior.event_shape.
|
__add__
__add__(
other
)
Models the sum of the series from the two components.