tfp.sts.SemiLocalLinearTrend

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Class SemiLocalLinearTrend

Formal representation of a semi-local linear trend model.

Inherits From: StructuralTimeSeries

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.

__init__

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__init__(
    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
)

Specify a semi-local linear trend model.

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'.

Properties

batch_shape

Static batch shape of models represented by this component.

Returns:

• batch_shape: A tf.TensorShape 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. It may be partially defined or unknown.

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

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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

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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

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make_state_space_model(
    num_timesteps,
    param_vals=None,
    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

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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: .
• 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: .
• 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.