Formal representation of a semi-local linear trend model.
Inherits From: StructuralTimeSeries
tfp.sts.SemiLocalLinearTrend(
level_scale_prior=None, slope_mean_prior=None, slope_scale_prior=None,
autoregressive_coef_prior=None, initial_level_prior=None,
initial_slope_prior=None, observed_time_series=None,
constrain_ar_coef_stationary=True, constrain_ar_coef_positive=False, name=None
)
Like the LocalLinearTrend model, a semi-local linear trend posits a
latent level and slope, with the level component updated according to
the current slope plus a random walk:
level[t] = level[t-1] + slope[t-1] + Normal(0., level_scale)
The slope component in a SemiLocalLinearTrend model evolves according to
a first-order autoregressive (AR1) process with potentially nonzero mean:
slope[t] = (slope_mean +
autoregressive_coef * (slope[t-1] - slope_mean) +
Normal(0., slope_scale))
Unlike the random walk used in LocalLinearTrend, a stationary
AR1 process (coefficient in (-1, 1)) maintains bounded variance over time,
so a SemiLocalLinearTrend model will often produce more reasonable
uncertainties when forecasting over long timescales.
Args |
|---|
level_scale_prior
|
optional tfd.Distribution instance specifying a prior
on the level_scale parameter. If None, a heuristic default prior is
constructed based on the provided observed_time_series.
Default value: None.
|
slope_mean_prior
|
optional tfd.Distribution instance specifying a prior
on the slope_mean parameter. If None, a heuristic default prior is
constructed based on the provided observed_time_series.
Default value: None.
|
slope_scale_prior
|
optional tfd.Distribution instance specifying a prior
on the slope_scale parameter. If None, a heuristic default prior is
constructed based on the provided observed_time_series.
Default value: None.
|
autoregressive_coef_prior
|
optional tfd.Distribution instance specifying
a prior on the autoregressive_coef parameter. If None, the default
prior is a standard Normal(0., 1.). Note that the prior may be
implicitly truncated by constrain_ar_coef_stationary and/or
constrain_ar_coef_positive.
Default value: None.
|
initial_level_prior
|
optional tfd.Distribution instance specifying a
prior on the initial level. If None, a heuristic default prior is
constructed based on the provided observed_time_series.
Default value: None.
|
initial_slope_prior
|
optional tfd.Distribution instance specifying a
prior on the initial slope. If None, a heuristic default prior is
constructed based on the provided observed_time_series.
Default value: None.
|
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 priors not explicitly set will be given default values according to
the scale of the observed time series (or batch of time series). May
optionally be an instance of tfp.sts.MaskedTimeSeries, which includes
a mask Tensor to specify timesteps with missing observations.
Default value: None.
|
constrain_ar_coef_stationary
|
if True, perform inference using a
parameterization that restricts autoregressive_coef to the interval
(-1, 1), or (0, 1) if force_positive_ar_coef is also True,
corresponding to stationary processes. This will implicitly truncates
the support of autoregressive_coef_prior.
Default value: True.
|
constrain_ar_coef_positive
|
if True, perform inference using a
parameterization that restricts autoregressive_coef to be positive,
or in (0, 1) if constrain_ar_coef_stationary is also True. This
will implicitly truncate the support of autoregressive_coef_prior.
Default value: False.
|
name
|
the name of this model component.
Default value: 'SemiLocalLinearTrend'.
|
Attributes |
|---|
batch_shape
|
Static batch shape of models represented by this component.
|
initial_state_prior
|
Prior distribution on the initial latent state (level and scale).
|
latent_size
|
Python int dimensionality of the latent space in this model.
|
name
|
Name of this model component.
|
parameters
|
List of Parameter(name, prior, bijector) namedtuples for this model.
|
Methods
batch_shape_tensor
View source
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().
|
joint_log_prob
View source
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). May optionally be an instance of tfp.sts.MaskedTimeSeries,
which includes a mask Tensor to specify timesteps with missing
observations.
|
| 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
View source
make_state_space_model(
num_timesteps, param_vals, initial_state_prior=None, initial_step=0
)
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.
|
| Returns |
|---|
dist
|
a LinearGaussianStateSpaceModel Distribution object.
|
prior_sample
View source
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
|
Python int random seed.
|
| 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.
|
View source on GitHub