tfp.sts.AutoregressiveIntegratedMovingAverage

tfp.sts.AutoregressiveIntegratedMovingAverage( ar_order, ma_order, integration_degree=0, ar_coefficients_prior=None, ma_coefficients_prior=None, level_drift_prior=None, level_scale_prior=None, initial_state_prior=None, ar_coefficient_constraining_bijector=None, ma_coefficient_constraining_bijector=None, observed_time_series=None, name=None ) 

level[t + 1] = ( level_drift + noise[t + 1] + sum(ar_coefficients * levels[t : t - order : -1]) + sum(ma_coefficients * noise[t : t - order : -1])) noise[t + 1] ~ Normal(0., scale=level_scale) ``` where `noise` is an iid noise process. An integrated ([ARIMA]( https://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average)) process corresponds to an ARMA model of the `integration_degree`th-order differences of a sequence, or equivalently, taking `integration_degree` cumulative sums of an underlying ARMA process. <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2"><h2 class="add-link">Args</h2></th></tr> <tr> <td> `ar_order`<a id="ar_order"></a> </td> <td> scalar Python positive `int` specifying the order of the autoregressive process (`p` in `ARIMA(p, d, q)`). </td> </tr><tr> <td> `ma_order`<a id="ma_order"></a> </td> <td> scalar Python positive `int` specifying the order of the moving-average process (`q` in `ARIMA(p, d, q)`). </td> </tr><tr> <td> `integration_degree`<a id="integration_degree"></a> </td> <td> scalar Python positive `int` specifying the number of times to integrate an ARMA process. (`d` in `ARIMA(p, d, q)`). Default value: `0`. </td> </tr><tr> <td> `ar_coefficients_prior`<a id="ar_coefficients_prior"></a> </td> <td> optional `tfd.Distribution` instance specifying a prior on the `ar_coefficients` parameter. If `None`, a default standard normal (`tfd.MultivariateNormalDiag(scale_diag=tf.ones([ar_order]))`) prior is used. Default value: `None`. </td> </tr><tr> <td> `ma_coefficients_prior`<a id="ma_coefficients_prior"></a> </td> <td> optional `tfd.Distribution` instance specifying a prior on the `ma_coefficients` parameter. If `None`, a default standard normal (`tfd.MultivariateNormalDiag(scale_diag=tf.ones([ma_order]))`) prior is used. Default value: `None`. </td> </tr><tr> <td> `level_drift_prior`<a id="level_drift_prior"></a> </td> <td> optional `tfd.Distribution` instance specifying a prior on the `level_drift` parameter. If `None`, the parameter is not inferred and is instead fixed to zero. Default value: `None`. </td> </tr><tr> <td> `level_scale_prior`<a id="level_scale_prior"></a> </td> <td> 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`. </td> </tr><tr> <td> `initial_state_prior`<a id="initial_state_prior"></a> </td> <td> optional `tfd.Distribution` instance specifying a prior on the initial state, corresponding to the values of the process at a set of size `order` of imagined timesteps before the initial step. If `None`, a heuristic default prior is constructed based on the provided `observed_time_series`. Default value: `None`. </td> </tr><tr> <td> `ar_coefficient_constraining_bijector`<a id="ar_coefficient_constraining_bijector"></a> </td> <td> optional `tfb.Bijector` instance representing a constraining mapping for the autoregressive coefficients. For example, `tfb.Tanh()` constrains the coefficients to lie in `(-1, 1)`, while `tfb.Softplus()` constrains them to be positive, and `tfb.Identity()` implies no constraint. If `None`, the default behavior constrains the coefficients to lie in `(-1, 1)` using a `Tanh` bijector. Default value: `None`. </td> </tr><tr> <td> `ma_coefficient_constraining_bijector`<a id="ma_coefficient_constraining_bijector"></a> </td> <td> optional `tfb.Bijector` instance representing a constraining mapping for the moving average coefficients. For example, `tfb.Tanh()` constrains the coefficients to lie in `(-1, 1)`, while `tfb.Softplus()` constrains them to be positive, and `tfb.Identity()` implies no constraint. If `None`, the default behavior is to apply no constraint. Default value: `None`. </td> </tr><tr> <td> `observed_time_series`<a id="observed_time_series"></a> </td> <td> 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 `NaN`s are interpreted as missing observations; missingness may be also be explicitly specified by passing a <a href="../../tfp/sts/MaskedTimeSeries"><code>tfp.sts.MaskedTimeSeries</code></a> instance. Any priors not explicitly set will be given default values according to the scale of the observed time series (or batch of time series). Default value: `None`. </td> </tr><tr> <td> `name`<a id="name"></a> </td> <td> the name of this model component. Default value: 'ARIMA'. </td> </tr> </table> <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2"><h2 class="add-link">Attributes</h2></th></tr> <tr> <td> `batch_shape`<a id="batch_shape"></a> </td> <td> Static batch shape of models represented by this component. </td> </tr><tr> <td> `init_parameters`<a id="init_parameters"></a> </td> <td> Parameters used to instantiate this `StructuralTimeSeries`. </td> </tr><tr> <td> `initial_state_prior`<a id="initial_state_prior"></a> </td> <td> </td> </tr><tr> <td> `integration_degree`<a id="integration_degree"></a> </td> <td> </td> </tr><tr> <td> `latent_size`<a id="latent_size"></a> </td> <td> Python `int` dimensionality of the latent space in this model. </td> </tr><tr> <td> `name`<a id="name"></a> </td> <td> Name of this model component. </td> </tr><tr> <td> `parameters`<a id="parameters"></a> </td> <td> List of Parameter(name, prior, bijector) namedtuples for this model. </td> </tr> </table> ## Methods <h3 id="batch_shape_tensor"><code>batch_shape_tensor</code></h3> <a target="_blank" class="external" href="https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/sts/structural_time_series.py#L121-L134">View source</a> <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link"> <code>batch_shape_tensor() </code></pre> Runtime batch shape of models represented by this component. <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2">Returns</th></tr> <tr> <td> `batch_shape` </td> <td> `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()`. </td> </tr> </table> <h3 id="copy"><code>copy</code></h3> <a target="_blank" class="external" href="https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/sts/structural_time_series.py#L179-L194">View source</a> <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link"> <code>copy( **override_parameters_kwargs ) </code></pre> Creates a deep copy. Note: the copy distribution may continue to depend on the original initialization arguments. <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2">Args</th></tr> <tr> <td> `**override_parameters_kwargs` </td> <td> String/value dictionary of initialization arguments to override with new values. </td> </tr> </table> <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2">Returns</th></tr> <tr> <td> `copy` </td> <td> A new instance of `type(self)` initialized from the union of self.init_parameters and override_parameters_kwargs, i.e., `dict(self.init_parameters, **override_parameters_kwargs)`. </td> </tr> </table> <h3 id="get_parameter"><code>get_parameter</code></h3> <a target="_blank" class="external" href="https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/sts/structural_time_series.py#L86-L92">View source</a> <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link"> <code>get_parameter( parameter_name ) </code></pre> Returns the parameter with the given name, or a KeyError. <h3 id="joint_distribution"><code>joint_distribution</code></h3> <a target="_blank" class="external" href="https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/sts/structural_time_series.py#L263-L406">View source</a> <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link"> <code>joint_distribution( observed_time_series=None, num_timesteps=None, trajectories_shape=(), initial_step=0, mask=None, experimental_parallelize=False ) </code></pre> Constructs the joint distribution over parameters and observed values. <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2">Args</th></tr> <tr> <td> `observed_time_series` </td> <td> Optional observed time series to model, as a `Tensor` or <a href="../../tfp/sts/MaskedTimeSeries"><code>tfp.sts.MaskedTimeSeries</code></a> instance having shape `concat([batch_shape, trajectories_shape, num_timesteps, 1])`. If an observed time series is provided, the `num_timesteps`, `trajectories_shape`, and `mask` arguments are ignored, and an unnormalized (pinned) distribution over parameter values is returned. Default value: `None`. </td> </tr><tr> <td> `num_timesteps` </td> <td> scalar `int` `Tensor` number of timesteps to model. This must be specified either directly or by passing an `observed_time_series`. Default value: `0`. </td> </tr><tr> <td> `trajectories_shape` </td> <td> `int` `Tensor` shape of sampled trajectories for each set of parameter values. Ignored if an `observed_time_series` is passed. Default value: `()`. </td> </tr><tr> <td> `initial_step` </td> <td> Optional scalar `int` `Tensor` specifying the starting timestep. Default value: `0`. </td> </tr><tr> <td> `mask` </td> <td> Optional `bool` `Tensor` having shape `concat([batch_shape, trajectories_shape, num_timesteps])`, in which `True` entries indicate that the series value at the corresponding step is missing and should be ignored. This argument should be passed only if `observed_time_series` is not specified or does not already contain a missingness mask; it is an error to pass both this argument and an `observed_time_series` value containing a missingness mask. Default value: `None`. </td> </tr><tr> <td> `experimental_parallelize` </td> <td> If `True`, use parallel message passing algorithms from <a href="../../tfp/experimental/parallel_filter"><code>tfp.experimental.parallel_filter</code></a> to perform time series operations in `O(log num_timesteps)` sequential steps. The overall FLOP and memory cost may be larger than for the sequential implementations by a constant factor. Default value: `False`. </td> </tr> </table> <!-- Tabular view --> <table class="responsive fixed orange"> <colgroup><col width="214px"><col></colgroup> <tr><th colspan="2">Returns</th></tr> <tr> <td> `joint_distribution` </td> <td> joint distribution of model parameters and observed trajectories. If no `observed_time_series` was specified, this is an instance of `tfd.JointDistributionNamedAutoBatched` with a random variable for each model parameter (with names and order matching `self.parameters`), plus a final random variable `observed_time_series` representing a trajectory(ies) conditioned on the parameters. If `observed_time_series` was specified, the return value is given by `joint_distribution.experimental_pin( observed_time_series=observed_time_series)` where `joint_distribution` is as just described, so it defines an unnormalized posterior distribution over the parameters. </td> </tr> </table> #### Example: The joint distribution can generate prior samples of parameters and trajectories: ```python from matplotlib import pylab as plt import tensorflow_probability as tfp # Sample and plot 100 trajectories from the prior. model = tfp.sts.LocalLinearTrend() prior_samples = model.joint_distribution(num_timesteps=200).sample([100]) plt.plot( tf.linalg.matrix_transpose(prior_samples['observed_time_series'][..., 0])) 

jd = model.joint_distribution(observed_time_series) # Variational inference. surrogate_posterior = ( tfp.experimental.vi.build_factored_surrogate_posterior( event_shape=jd.event_shape, bijector=jd.experimental_default_event_space_bijector())) losses = tfp.vi.fit_surrogate_posterior( target_log_prob_fn=jd.unnormalized_log_prob, surrogate_posterior=surrogate_posterior, optimizer=tf.optimizers.Adam(0.1), num_steps=200) parameter_samples = surrogate_posterior.sample(50) # No U-Turn Sampler. samples, kernel_results = tfp.experimental.mcmc.windowed_adaptive_nuts( n_draws=500, joint_dist=dist) 

joint_log_prob( observed_time_series ) 

make_state_space_model( num_timesteps, param_vals, initial_state_prior=None, initial_step=0, **linear_gaussian_ssm_kwargs ) 

prior_sample( num_timesteps, initial_step=0, params_sample_shape=(), trajectories_sample_shape=(), seed=None ) 

__add__( other )