The Long Short-Term Memory Recurrent Neural Network (LSTM), uses a multilayer LSTM encoder and an MLP decoder. It builds upon the LSTM-cell that improves the exploding and vanishing gradients of classic RNN’s. This network has been extensively used in sequential prediction tasks like language modeling, phonetic labeling, and forecasting. 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
-Jeffrey L. Elman (1990). “Finding Structure in Time”.
-Haşim Sak, Andrew Senior, Françoise Beaufays (2014). “Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition.”

source

​
LSTM

 LSTM (h:int, input_size:int=-1, inference_input_size:int=-1,
       encoder_n_layers:int=2, encoder_hidden_size:int=200,
       encoder_bias:bool=True, encoder_dropout:float=0.0,
       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=-1, early_stop_patience_steps:int=-1,
       val_check_steps:int=100, batch_size=32,
       valid_batch_size:Optional[int]=None, scaler_type:str='robust',
       random_seed=1, num_workers_loader=0, drop_last_loader=False,
       optimizer=None, optimizer_kwargs=None, **trainer_kwargs)

*LSTM

LSTM encoder, 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 all history.
inference_input_size: int, maximum sequence length for truncated inference. Default -1 uses all history.
encoder_n_layers: int=2, number of layers for the LSTM.
encoder_hidden_size: int=200, units for the LSTM’s hidden state size.
encoder_bias: bool=True, whether or not to use biases b_ih, b_hh within LSTM units.
encoder_dropout: float=0., dropout regularization applied to LSTM outputs.
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=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.
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.
*

​
LSTM.fit

 LSTM.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, 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.
test_size: int, test size for temporal cross-validation.
random_seed: int=None, random_seed for pytorch initializer and numpy generators, overwrites model.__init__’s.
*

​
LSTM.predict

 LSTM.predict (dataset, step_size=1, random_seed=None,
               **data_module_kwargs)

*Predict.

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

Parameters:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
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.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

​
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 LSTM
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

nf = NeuralForecast(
    models=[LSTM(h=12, input_size=-1,
                 loss=DistributionLoss(distribution='Normal', level=[80, 90]),
                 scaler_type='robust',
                 encoder_n_layers=2,
                 encoder_hidden_size=128,
                 context_size=10,
                 decoder_hidden_size=128,
                 decoder_layers=2,
                 max_steps=200,
                 futr_exog_list=['y_[lag12]'],
                 #hist_exog_list=['y_[lag12]'],
                 stat_exog_list=['airline1'],
                 )
    ],
    freq='M'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic)
Y_hat_df = nf.predict(futr_df=Y_test_df)

Y_hat_df = Y_hat_df.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['LSTM'], c='purple', label='mean')
plt.plot(plot_df['ds'], plot_df['LSTM-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['LSTM-lo-90'][-12:].values, 
                 y2=plot_df['LSTM-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()
GRUDilated RNN