View source on GitHub

Class ARModel

Auto-regressive model, both linear and non-linear.

Features to the model include time and values of input_window_size timesteps, and times for output_window_size timesteps. These are passed through a configurable prediction model, and then fed to a loss function (e.g. squared loss).

Note that this class can also be used to regress against time only by setting the input_window_size to zero.

Each periodicity in the periodicities arg is divided by the num_time_buckets into time buckets that are represented as features added to the model.

A good heuristic for picking an appropriate periodicity for a given data set would be the length of cycles in the data. For example, energy usage in a home is typically cyclic each day. If the time feature in a home energy usage dataset is in the unit of hours, then 24 would be an appropriate periodicity. Similarly, a good heuristic for num_time_buckets is how often the data is expected to change within the cycle. For the aforementioned home energy usage dataset and periodicity of 24, then 48 would be a reasonable value if usage is expected to change every half hour.

Each feature's value for a given example with time t is the difference between t and the start of the time bucket it falls under. If it doesn't fall under a feature's associated time bucket, then that feature's value is zero.

For example: if periodicities = (9, 12) and num_time_buckets = 3, then 6 features would be added to the model, 3 for periodicity 9 and 3 for periodicity 12.

For an example data point where t = 17: - It's in the 3rd time bucket for periodicity 9 (2nd period is 9-18 and 3rd time bucket is 15-18) - It's in the 2nd time bucket for periodicity 12 (2nd period is 12-24 and 2nd time bucket is between 16-20).

Therefore the 6 added features for this row with t = 17 would be:

Feature name (periodicity#_timebucket#), feature value

P9_T1, 0 # not in first time bucket P9_T2, 0 # not in second time bucket P9_T3, 2 # 17 - 15 since 15 is the start of the 3rd time bucket P12_T1, 0 # not in first time bucket P12_T2, 1 # 17 - 16 since 16 is the start of the 2nd time bucket P12_T3, 0 # not in third time bucket


View source


Constructs an auto-regressive model.


  • periodicities: periodicities of the input data, in the same units as the time feature (for example 24 if feeding hourly data with a daily periodicity, or 60 * 24 if feeding minute-level data with daily periodicity). Note this can be a single value or a list of values for multiple periodicities.
  • input_window_size: Number of past time steps of data to look at when doing the regression.
  • output_window_size: Number of future time steps to predict. Note that setting it to > 1 empirically seems to give a better fit.
  • num_features: number of input features per time step.
  • prediction_model_factory: A callable taking arguments num_features, input_window_size, and output_window_size and returning a tf.keras.Model. The Model's call() takes two arguments: an input window and an output window, and returns a dictionary of predictions. See FlatPredictionModel for an example. Example usage:
prediction_model_factory=functools.partial( FlatPredictionModel,

The default model computes predictions as a linear function of flattened input and output windows. * num_time_buckets: Number of buckets into which to divide (time % periodicity). This value multiplied by the number of periodicities is the number of time features added to the model. * loss: Loss function to use for training. Currently supported values are SQUARED_LOSS and NORMAL_LIKELIHOOD_LOSS. Note that for NORMAL_LIKELIHOOD_LOSS, we train the covariance term as well. For SQUARED_LOSS, the evaluation loss is reported based on un-scaled observations and predictions, while the training loss is computed on normalized data (if input statistics are available). * exogenous_feature_columns: A list of tf.feature_columns (for example tf.feature_column.embedding_column) corresponding to features which provide extra information to the model but are not part of the series to be predicted.



tf.feature_colums for features which are not predicted.



View source


Default loss definition with state replicated across a batch.

Time series passed to this model have a batch dimension, and each series in a batch can be operated on in parallel. This loss definition assumes that each element of the batch represents an independent sample conditioned on the same initial state (i.e. it is simply replicated across the batch). A batch size of one provides sequential operations on a single time series.

More complex processing may operate instead on get_start_state() and get_batch_loss() directly.


  • features: A dictionary (such as is produced by a chunker) with at minimum the following key/value pairs (others corresponding to the exogenous_feature_columns argument to __init__ may be included representing exogenous regressors): TrainEvalFeatures.TIMES: A [batch size x window size] integer Tensor with times for each observation. If there is no artificial chunking, the window size is simply the length of the time series. TrainEvalFeatures.VALUES: A [batch size x window size x num features] Tensor with values for each observation.
  • mode: The tf.estimator.ModeKeys mode to use (TRAIN, EVAL). For INFER, see predict().


A ModelOutputs object.


View source


Sample synthetic data from model parameters, with optional substitutions.

Returns number_of_series possible sequences of future values, sampled from the generative model with each conditioned on the previous. Samples are based on trained parameters, except for those parameters explicitly overridden in model_parameters.

For distributions over future observations, see predict().


  • number_of_series: Number of time series to create.
  • series_length: Length of each time series.
  • model_parameters: A dictionary mapping model parameters to values, which replace trained parameters when generating data.
  • seed: If specified, return deterministic time series according to this value.


A dictionary with keys TrainEvalFeatures.TIMES (mapping to an array with shape [number_of_series, series_length]) and TrainEvalFeatures.VALUES (mapping to an array with shape [number_of_series, series_length, num_features]).


View source


Computes predictions and a loss.


  • features: A dictionary (such as is produced by a chunker) with the following key/value pairs (shapes are given as required for training): TrainEvalFeatures.TIMES: A [batch size, self.window_size] integer Tensor with times for each observation. To train on longer sequences, the data should first be chunked. TrainEvalFeatures.VALUES: A [batch size, self.window_size, self.num_features] Tensor with values for each observation. When evaluating, TIMES and VALUES must have a window size of at least self.window_size, but it may be longer, in which case the last window_size - self.input_window_size times (or fewer if this is not divisible by self.output_window_size) will be evaluated on with non-overlapping output windows (and will have associated predictions). This is primarily to support qualitative evaluation/plotting, and is not a recommended way to compute evaluation losses (since there is no overlap in the output windows, which for window-based models is an undesirable bias).
  • mode: The tf.estimator.ModeKeys mode to use (TRAIN or EVAL).
  • state: Unused


A model.ModelOutputs object.


  • ValueError: If mode is not TRAIN or EVAL, or if static shape information is incorrect.


View source


Returns a tuple of state for the start of the time series.

For example, a mean and covariance. State should not have a batch dimension, and will often be TensorFlow Variables to be learned along with the rest of the model parameters.


View source


Define ops for the model, not depending on any previously defined ops.


  • input_statistics: A math_utils.InputStatistics object containing input statistics. If None, data-independent defaults are used, which may result in longer or unstable training.


View source


Create loss_op.


View source


Computes predictions multiple steps into the future.


  • features: A dictionary with the following key/value pairs: PredictionFeatures.TIMES: A [batch size, predict window size] integer Tensor of times, after the window of data indicated by STATE_TUPLE, to make predictions for. PredictionFeatures.STATE_TUPLE: A tuple of (times, values), times with shape [batch size, self.input_window_size], values with shape [batch size, self.input_window_size, self.num_features] representing a segment of the time series before TIMES. This data is used to start of the autoregressive computation. This should have data for at least self.input_window_size timesteps. And any exogenous features, with shapes prefixed by shape of TIMES.


A dictionary with keys, "mean", "covariance". The values are Tensors of shape [batch_size, predict window size, num_features] and correspond to the values passed in TIMES.


View source


Compute model predictions given input data.


  • times: A [batch size, self.window_size] integer Tensor, the first self.input_window_size times in each part of the batch indicating input features, and the last self.output_window_size times indicating prediction times.
  • values: A [batch size, self.input_window_size, self.num_features] Tensor with input features.
  • exogenous_regressors: A [batch size, self.window_size, self.exogenous_size] Tensor with exogenous features.


Tuple (predicted_mean, predicted_covariance), where each element is a Tensor with shape [batch size, self.output_window_size, self.num_features].


View source


Class Members

  • NORMAL_LIKELIHOOD_LOSS = 'normal_likelihood_loss'
  • SQUARED_LOSS = 'squared_loss'