Dilated RNN

The Dilated Recurrent Neural Network (DilatedRNN) addresses common challenges of modeling long sequences like vanishing gradients, computational efficiency, and improved model flexibility to model complex relationships while maintaining its parsimony. The DilatedRNN builds a deep stack of RNN layers using skip conditions on the temporal and the network’s depth dimensions. The temporal dilated recurrent skip connections offer the capability to focus on multi-resolution inputs.The predictions are obtained by transforming the hidden states into contexts $\mathbf{c}_{[t+1:t+H]}$, that are decoded and adapted into $\mathbf{\hat{y}}_{[t+1:t+H],[q]}$ through MLPs.

where $\mathbf{h}_{t}$, is the hidden state for time $t$, $\mathbf{y}_{t}$ is the input at time $t$ and $\mathbf{h}_{t-1}$ is the hidden state of the previous layer at $t-1$, $\mathbf{x}^{(s)}$ are static exogenous inputs, $\mathbf{x}^{(h)}_{t}$ historic exogenous, $\mathbf{x}^{(f)}_{[:t+H]}$ are future exogenous available at the time of the prediction.

References
-Shiyu Chang, et al. “Dilated Recurrent Neural Networks”.
-Yao Qin, et al. “A Dual-Stage Attention-Based recurrent neural network for time series prediction”.
-Kashif Rasul, et al. “Zalando Research: PyTorch Dilated Recurrent Neural Networks”.

​

DilatedRNN

 DilatedRNN (h:int, input_size:int=-1,
             inference_input_size:Optional[int]=None,
             cell_type:str='LSTM', dilations:List[List[int]]=[[1, 2], [4,
             8]], encoder_hidden_size:int=128, context_size:int=10,
             decoder_hidden_size:int=128, decoder_layers:int=2,
             futr_exog_list=None, hist_exog_list=None,
             stat_exog_list=None, exclude_insample_y=False, loss=MAE(),
             valid_loss=None, max_steps:int=1000,
             learning_rate:float=0.001, num_lr_decays:int=3,
             early_stop_patience_steps:int=-1, val_check_steps:int=100,
             batch_size=32, valid_batch_size:Optional[int]=None,
             windows_batch_size=128, inference_windows_batch_size=1024,
             start_padding_enabled=False, step_size:int=1,
             scaler_type:str='robust', random_seed:int=1,
             drop_last_loader:bool=False, alias:Optional[str]=None,
             optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
             lr_scheduler_kwargs=None, dataloader_kwargs=None,
             **trainer_kwargs)

*DilatedRNN

Parameters:
h: int, forecast horizon.
input_size: int, maximum sequence length for truncated train backpropagation. Default -1 uses 3 * horizon
inference_input_size: int, maximum sequence length for truncated inference. Default None uses input_size history.
cell_type: str, type of RNN cell to use. Options: ‘GRU’, ‘RNN’, ‘LSTM’, ‘ResLSTM’, ‘AttentiveLSTM’.
dilations: int list, dilations betweem layers.
encoder_hidden_size: int=200, units for the RNN’s hidden state size.
context_size: int=10, size of context vector for each timestamp on the forecasting window.
decoder_hidden_size: int=200, size of hidden layer for the MLP decoder.
decoder_layers: int=2, number of layers for the MLP decoder.
futr_exog_list: str list, future exogenous columns.
hist_exog_list: str list, historic exogenous columns.
stat_exog_list: str list, static exogenous columns.
exclude_insample_y: bool=False, the model skips the autoregressive features y[t-input_size:t] if True.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module=loss, instantiated valid loss class from losses collection.
max_steps: int, maximum number of training steps.
learning_rate: float, Learning rate between (0, 1).
num_lr_decays: int, Number of learning rate decays, evenly distributed across max_steps.
early_stop_patience_steps: int, Number of validation iterations before early stopping.
val_check_steps: int, Number of training steps between every validation loss check.
batch_size: int=32, number of different series in each batch.
valid_batch_size: int=None, number of different series in each validation and test batch.
windows_batch_size: int=128, number of windows to sample in each training batch, default uses all.
inference_windows_batch_size: int=1024, number of windows to sample in each inference batch, -1 uses all.
start_padding_enabled: bool=False, if True, the model will pad the time series with zeros at the beginning, by input size.

step_size: int=1, step size between each window of temporal data.
scaler_type: str=‘robust’, type of scaler for temporal inputs normalization see temporal scalers.
random_seed: int=1, random_seed for pytorch initializer and numpy generators.
drop_last_loader: bool=False, if True TimeSeriesDataLoader drops last non-full batch.
alias: str, optional, Custom name of the model.
optimizer: Subclass of ‘torch.optim.Optimizer’, optional, user specified optimizer instead of the default choice (Adam).
optimizer_kwargs: dict, optional, list of parameters used by the user specified optimizer.
lr_scheduler: Subclass of ‘torch.optim.lr_scheduler.LRScheduler’, optional, user specified lr_scheduler instead of the default choice (StepLR).
lr_scheduler_kwargs: dict, optional, list of parameters used by the user specified lr_scheduler.
dataloader_kwargs: dict, optional, list of parameters passed into the PyTorch Lightning dataloader by the TimeSeriesDataLoader.
**trainer_kwargs: int, keyword trainer arguments inherited from PyTorch Lighning’s trainer.
*

​

DilatedRNN.fit

 DilatedRNN.fit (dataset, val_size=0, test_size=0, random_seed=None,
                 distributed_config=None)

*Fit.

The fit method, optimizes the neural network’s weights using the initialization parameters (learning_rate, windows_batch_size, …) and the loss function as defined during the initialization. Within fit we use a PyTorch Lightning Trainer that inherits the initialization’s self.trainer_kwargs, to customize its inputs, see PL’s trainer arguments.

The method is designed to be compatible with SKLearn-like classes and in particular to be compatible with the StatsForecast library.

By default the model is not saving training checkpoints to protect disk memory, to get them change enable_checkpointing=True in __init__.

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
val_size: int, validation size for temporal cross-validation.
random_seed: int=None, random_seed for pytorch initializer and numpy generators, overwrites model.__init__’s.
test_size: int, test size for temporal cross-validation.
*

​

DilatedRNN.predict

 DilatedRNN.predict (dataset, test_size=None, step_size=1,
                     random_seed=None, quantiles=None,
                     **data_module_kwargs)

*Predict.

Neural network prediction with PL’s Trainer execution of predict_step.

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
test_size: int=None, test size for temporal cross-validation.
step_size: int=1, Step size between each window.
random_seed: int=None, random_seed for pytorch initializer and numpy generators, overwrites model.__init__’s.
quantiles: list of floats, optional (default=None), target quantiles to predict.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

​

Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import DilatedRNN
from neuralforecast.losses.pytorch import DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]] # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

fcst = NeuralForecast(
    models=[DilatedRNN(h=12,
                       input_size=-1,
                       loss=DistributionLoss(distribution='Normal', level=[80, 90]),
                       scaler_type='robust',
                       encoder_hidden_size=100,
                       max_steps=200,
                       futr_exog_list=['y_[lag12]'],
                       hist_exog_list=None,
                       stat_exog_list=['airline1'],
    )
    ],
    freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic)
forecasts = fcst.predict(futr_df=Y_test_df)

Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])

plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['DilatedRNN-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['DilatedRNN-lo-90'][-12:].values, 
                 y2=plot_df['DilatedRNN-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()