tfp.sts.Sum

Sum of structural time series components.

Inherits From: StructuralTimeSeries

Used in the notebooks

Used in the tutorials

This class enables compositional specification of a structural time series model from basic components. Given a list of component models, it represents an additive model, i.e., a model of time series that may be decomposed into a sum of terms corresponding to the component models.

Formally, the additive model represents a random process g[t] = f1[t] + f2[t] + ... + fN[t] + eps[t], where the f's are the random processes represented by the components, and eps[t] ~ Normal(loc=0, scale=observation_noise_scale) is an observation noise term. See the AdditiveStateSpaceModel documentation for mathematical details.

This model inherits the parameters (with priors) of its components, and adds an observation_noise_scale parameter governing the level of noise in the observed time series.

Examples

To construct a model combining a local linear trend with a day-of-week effect:

  local_trend = tfp.sts.LocalLinearTrend(
      observed_time_series=observed_time_series,
      name='local_trend')
  day_of_week_effect = tfp.sts.Seasonal(
      num_seasons=7,
      observed_time_series=observed_time_series,
      name='day_of_week_effect')
  additive_model = tfp.sts.Sum(
      components=[local_trend, day_of_week_effect],
      observed_time_series=observed_time_series)

  print([p.name for p in additive_model.parameters])
  # => `[observation_noise_scale,
  #      local_trend_level_scale,
  #      local_trend_slope_scale,
  #      day_of_week_effect_drift_scale`]

  print(local_trend.latent_size,
        seasonal.latent_size,
        additive_model.latent_size)
  # => `2`, `7`, `9`

components Python list of one or more StructuralTimeSeries instances. These must have unique names.
constant_offset optional scalar float Tensor, or batch of scalars, specifying a constant value added to the sum of outputs from the component models. This allows the components to model the shifted series observed_time_series - constant_offset. If None, this is set to the mean of the provided observed_time_series. Default value: None.
observation_noise_scale_prior optional tfd.Distribution instance specifying a prior on observation_noise_scale. 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. This is used to set the constant offset, if not provided, and to construct a default heuristic observation_noise_scale_prior if not provided. May optionally be an instance of tfp.sts.MaskedTimeSeries, which includes a mask Tensor to specify timesteps with missing observations. Default value: None.
name Python str name of this model component; used as name_scope for ops created by this class. Default value: 'Sum'.

ValueError if components do not have unique names.

batch_shape Static batch shape of models represented by this component.
components List of component StructuralTimeSeries models.
components_by_name OrderedDict mapping component names to components.
constant_offset Constant value subtracted from observed data.
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

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

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_component_state_space_models

View source

Build an ordered list of Distribution instances for component models.

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_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
component_ssms a Python list of LinearGaussianStateSpaceModel Distribution objects, in order corresponding to self.components.

make_state_space_model

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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

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.