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Elman proposed this classic recurrent neural network (RNN) in 1990, where each layer uses the following recurrent transformation: htl=Activation([yt,xt(h),x(s)]Wih⊺+bih+ht−1lWhh⊺+bhh)\mathbf{h}^{l}_{t} = \mathrm{Activation}([\mathbf{y}_{t},\mathbf{x}^{(h)}_{t},\mathbf{x}^{(s)}] W^{\intercal}_{ih} + b_{ih} + \mathbf{h}^{l}_{t-1} W^{\intercal}_{hh} + b_{hh}) where htl\mathbf{h}^{l}_{t}, is the hidden state of RNN layer ll 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. The available activations are tanh, and relu. 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. References
-Jeffrey L. Elman (1990). “Finding Structure in Time”.
-Cho, K., van Merrienboer, B., Gülcehre, C., Bougares, F., Schwenk, H., & Bengio, Y. (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation.
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RNN

 RNN (h:int, input_size:int=-1, inference_input_size:Optional[int]=None,
      h_train:int=1, encoder_n_layers:int=2, encoder_hidden_size:int=128,
      encoder_activation:str='tanh', encoder_bias:bool=True,
      encoder_dropout:float=0.0, context_size:Optional[int]=None,
      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, recurrent=False, loss=MAE(),
      valid_loss=None, max_steps:int=1000, learning_rate:float=0.001,
      num_lr_decays:int=-1, 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=1,
      drop_last_loader=False, alias:Optional[str]=None, optimizer=None,
      optimizer_kwargs=None, lr_scheduler=None, lr_scheduler_kwargs=None,
      dataloader_kwargs=None, **trainer_kwargs)
*RNN Multi Layer Elman RNN (RNN), with MLP decoder. The network has tanh or relu non-linearities, it is trained using ADAM stochastic gradient descent. The network accepts static, historic and future exogenous data. 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.
h_train: int, maximum sequence length for truncated train backpropagation. Default 1.
encoder_n_layers: int=2, number of layers for the RNN.
encoder_hidden_size: int=200, units for the RNN’s hidden state size.
encoder_activation: str=tanh, type of RNN activation from tanh or relu.
encoder_bias: bool=True, whether or not to use biases b_ih, b_hh within RNN units.
encoder_dropout: float=0., dropout regularization applied to RNN outputs.
context_size: deprecated.
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, whether to exclude the target variable from the historic exogenous data.
recurrent: bool=False, whether to produce forecasts recursively (True) or direct (False).
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=1000, maximum number of training steps.
learning_rate: float=1e-3, Learning rate between (0, 1).
num_lr_decays: int=-1, Number of learning rate decays, evenly distributed across max_steps.
early_stop_patience_steps: int=-1, Number of validation iterations before early stopping.
val_check_steps: int=100, Number of training steps between every validation loss check.
batch_size: int=32, number of differentseries 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.
*

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RNN.fit

 RNN.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.
*

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RNN.predict

 RNN.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.*

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Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import RNN
from neuralforecast.losses.pytorch import MQLoss
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=[RNN(h=12,
                input_size=24,
                inference_input_size=24,
                loss=MQLoss(level=[80, 90]),
                valid_loss=MQLoss(level=[80, 90]),
                scaler_type='standard',
                encoder_n_layers=2,
                encoder_hidden_size=128,
                decoder_hidden_size=128,
                decoder_layers=2,
                max_steps=200,
                futr_exog_list=['y_[lag12]'],
                stat_exog_list=['airline1'],
                )
    ],
    freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
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['RNN-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['RNN-lo-90'][-12:].values, 
                 y2=plot_df['RNN-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()