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 c[t+1:t+H]\mathbf{c}_{[t+1:t+H]}, that are decoded and adapted into y^[t+1:t+H],[q]\mathbf{\hat{y}}_{[t+1:t+H],[q]} through MLPs.

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

source

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DilatedRNN

 DilatedRNN (h:int, input_size:int=-1, inference_input_size:int=-1,
             cell_type:str='LSTM', dilations:List[List[int]]=[[1, 2], [4,
             8]], encoder_hidden_size:int=200, context_size:int=10,
             decoder_hidden_size:int=200, decoder_layers:int=2,
             futr_exog_list=None, hist_exog_list=None,
             stat_exog_list=None, 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, step_size:int=1,
             scaler_type:str='robust', random_seed:int=1,
             num_workers_loader:int=0, drop_last_loader:bool=False,
             optimizer=None, optimizer_kwargs=None, **trainer_kwargs)

*DilatedRNN

Parameters:
h: int, forecast horizon.
input_size: int, maximum sequence length for truncated train backpropagation. Default -1 uses all history.
inference_input_size: int, maximum sequence length for truncated inference. Default -1 uses all 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.
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.
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.
num_workers_loader: int=os.cpu_count(), workers to be used by TimeSeriesDataLoader.
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.
**trainer_kwargs: int, keyword trainer arguments inherited from PyTorch Lighning’s trainer.
*

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Usage Example

import numpy as np
import pandas as pd
import pytorch_lightning as pl
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import DilatedRNN
from neuralforecast.losses.pytorch import MQLoss, DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.tsdataset import TimeSeriesDataset, TimeSeriesLoader

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='M'
)
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()
LSTMTCN