> ## Documentation Index
> Fetch the complete documentation index at: https://nixtla-old-docs.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.
# Dilated RNN
The Dilated Recurrent Neural Network
([`DilatedRNN`](https://nixtlaverse.nixtla.io/neuralforecast/models.dilated_rnn.html#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`](https://nixtlaverse.nixtla.io/neuralforecast/models.dilated_rnn.html#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”.](https://arxiv.org/abs/1710.02224) -[Yao Qin, et al. “A
Dual-Stage Attention-Based recurrent neural network for time series
prediction”.](https://arxiv.org/abs/1704.02971) -[Kashif Rasul, et
al. “Zalando Research: PyTorch Dilated Recurrent Neural
Networks”.](https://arxiv.org/abs/1710.02224) Figure 1. Three layer DilatedRNN with
dilation 1, 2, 4.
***
source
### DilatedRNN
> ```text theme={null}
> 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](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`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](https://nixtla.github.io/neuralforecast/common.scalers.html).
`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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer). \*
***
### DilatedRNN.fit
> ```text theme={null}
> 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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
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`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`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
> ```text theme={null}
> 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`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`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](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*
## Usage Example
```python theme={null}
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]].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()
```
