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Decompose an observed time series into contributions from each component.
tfp.sts.decompose_by_component( model, observed_time_series, parameter_samples )
This method decomposes a time series according to the posterior represention of a structural time series model. In particular, it:
- Computes the posterior marginal mean and covariances over the additive model's latent space.
- Decomposes the latent posterior into the marginal blocks for each model component.
- Maps the per-component latent posteriors back through each component's observation model, to generate the time series modeled by that component.
model: An instance of
tfp.sts.Sumrepresenting a structural time series model.
batch_shape + [num_timesteps, 1](omitting the trailing unit dimension is also supported when
num_timesteps > 1), specifying an observed time series. May optionally be an instance of
tfp.sts.MaskedTimeSeries, which includes a mask
Tensorto specify timesteps with missing observations.
Tensorsrepresenting posterior samples of model parameters, with shapes
[concat([ [num_posterior_draws], param.prior.batch_shape, param.prior.event_shape]) for param in model.parameters]. This may optionally also be a map (Python
dict) of parameter names to
collections.OrderedDictinstance mapping component StructuralTimeSeries instances (elements of
tfd.Distributioninstances representing the posterior marginal distributions on the process modeled by each component. Each distribution has batch shape matching that of
posterior_covs, and event shape of
Suppose we've built a model and fit it to data:
day_of_week = tfp.sts.Seasonal( num_seasons=7, observed_time_series=observed_time_series, name='day_of_week') local_linear_trend = tfp.sts.LocalLinearTrend( observed_time_series=observed_time_series, name='local_linear_trend') model = tfp.sts.Sum(components=[day_of_week, local_linear_trend], observed_time_series=observed_time_series) num_steps_forecast = 50 samples, kernel_results = tfp.sts.fit_with_hmc(model, observed_time_series)
To extract the contributions of individual components, pass the time series
and sampled parameters into
component_dists = decompose_by_component( model, observed_time_series=observed_time_series, parameter_samples=samples) # Component mean and stddev have shape `[len(observed_time_series)]`. day_of_week_effect_mean = component_dists[day_of_week].mean() day_of_week_effect_stddev = component_dists[day_of_week].stddev()
Using the component distributions, we can visualize the uncertainty for each component:
from matplotlib import pylab as plt num_components = len(component_dists) xs = np.arange(len(observed_time_series)) fig = plt.figure(figsize=(12, 3 * num_components)) for i, (component, component_dist) in enumerate(component_dists.items()): # If in graph mode, replace `.numpy()` with `.eval()` or `sess.run()`. component_mean = component_dist.mean().numpy() component_stddev = component_dist.stddev().numpy() ax = fig.add_subplot(num_components, 1, 1 + i) ax.plot(xs, component_mean, lw=2) ax.fill_between(xs, component_mean - 2 * component_stddev, component_mean + 2 * component_stddev, alpha=0.5) ax.set_title(component.name)