tfp.sts.SemiLocalLinearTrend

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.

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.

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=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`

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 `Tensor`s, in order corresponding to `self.parameters`, each of shape `params_sample_shape + prior.batch_shape + prior.event_shape`.

tfp.sts.SemiLocalLinearTrend

Args

Attributes

Methods

batch_shape_tensor

joint_log_prob

make_state_space_model

prior_sample

`batch_shape_tensor`

`joint_log_prob`

`make_state_space_model`

`prior_sample`