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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 Figure 1. Long Short-Term Memory Cell. Figure 1. Long Short-Term Memory Cell.

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1. LSTM

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LSTM

LSTM(
    h,
    input_size=-1,
    inference_input_size=None,
    h_train=1,
    encoder_n_layers=2,
    encoder_hidden_size=128,
    encoder_bias=True,
    encoder_dropout=0.0,
    context_size=None,
    decoder_hidden_size=128,
    decoder_layers=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=1000,
    learning_rate=0.001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=128,
    inference_windows_batch_size=1024,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="robust",
    random_seed=1,
    drop_last_loader=False,
    alias=None,
    optimizer=None,
    optimizer_kwargs=None,
    lr_scheduler=None,
    lr_scheduler_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)
Bases: BaseModel 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:
NameTypeDescriptionDefault
hintforecast horizon.required
input_sizeintmaximum sequence length for truncated train backpropagation. Default -1 uses 3 * horizon-1
inference_input_sizeintmaximum sequence length for truncated inference. Default None uses input_size history.None
h_trainintmaximum sequence length for truncated train backpropagation. Default 1.1
encoder_n_layersintnumber of layers for the LSTM.2
encoder_hidden_sizeintunits for the LSTM’s hidden state size.128
encoder_biasboolwhether or not to use biases b_ih, b_hh within LSTM units.True
encoder_dropoutfloatdropout regularization applied to LSTM outputs.0.0
context_sizedeprecateddeprecated.None
decoder_hidden_sizeintsize of hidden layer for the MLP decoder.128
decoder_layersintnumber of layers for the MLP decoder.2
futr_exog_liststr listfuture exogenous columns.None
hist_exog_liststr listhistoric exogenous columns.None
stat_exog_liststr liststatic exogenous columns.None
exclude_insample_yboolwhether to exclude the target variable from the input.False
recurrentboolwhether to produce forecasts recursively (True) or direct (False).False
lossPyTorch moduleinstantiated train loss class from losses collection.MAE()
valid_lossPyTorch moduleinstantiated valid loss class from losses collection.None
max_stepsintmaximum number of training steps.1000
learning_ratefloatLearning rate between (0, 1).0.001
num_lr_decaysintNumber of learning rate decays, evenly distributed across max_steps.-1
early_stop_patience_stepsintNumber of validation iterations before early stopping.-1
val_check_stepsintNumber of training steps between every validation loss check.100
batch_sizeintnumber of differentseries in each batch.32
valid_batch_sizeintnumber of different series in each validation and test batch.None
windows_batch_sizeintnumber of windows to sample in each training batch, default uses all.128
inference_windows_batch_sizeintnumber of windows to sample in each inference batch, -1 uses all.1024
start_padding_enabledboolif True, the model will pad the time series with zeros at the beginning, by input size.False
training_data_availability_thresholdUnion[float, List[float]]minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).0.0
step_sizeintstep size between each window of temporal data.1
scaler_typestrtype of scaler for temporal inputs normalization see temporal scalers.‘robust’
random_seedintrandom_seed for pytorch initializer and numpy generators.1
drop_last_loaderboolif True TimeSeriesDataLoader drops last non-full batch.False
aliasstroptional, Custom name of the model.None
optimizerSubclass of ‘torch.optim.Optimizer’optional, user specified optimizer instead of the default choice (Adam).None
optimizer_kwargsdictoptional, list of parameters used by the user specified optimizer.None
lr_schedulerSubclass of ‘torch.optim.lr_scheduler.LRScheduler’optional, user specified lr_scheduler instead of the default choice (StepLR).None
lr_scheduler_kwargsdictoptional, list of parameters used by the user specified lr_scheduler.None
dataloader_kwargsdictoptional, list of parameters passed into the PyTorch Lightning dataloader by the TimeSeriesDataLoader.None
**trainer_kwargsintkeyword trainer arguments inherited from PyTorch Lighning’s trainer.

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LSTM.fit

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:
NameTypeDescriptionDefault
datasetTimeSeriesDatasetNeuralForecast’s TimeSeriesDataset, see documentation.required
val_sizeintValidation size for temporal cross-validation.0
random_seedintRandom seed for pytorch initializer and numpy generators, overwrites model.init’s.None
test_sizeintTest size for temporal cross-validation.0
Returns:
TypeDescription
None

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LSTM.predict

predict(
    dataset,
    test_size=None,
    step_size=1,
    random_seed=None,
    quantiles=None,
    h=None,
    explainer_config=None,
    **data_module_kwargs
)
Predict. Neural network prediction with PL’s Trainer execution of predict_step. Parameters:
NameTypeDescriptionDefault
datasetTimeSeriesDatasetNeuralForecast’s TimeSeriesDataset, see documentation.required
test_sizeintTest size for temporal cross-validation.None
step_sizeintStep size between each window.1
random_seedintRandom seed for pytorch initializer and numpy generators, overwrites model.init’s.None
quantileslistTarget quantiles to predict.None
hintPrediction horizon, if None, uses the model’s fitted horizon. Defaults to None.None
explainer_configdictconfiguration for explanations.None
**data_module_kwargsdictPL’s TimeSeriesDataModule args, see documentation.
Returns:
TypeDescription
None

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Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import LSTM
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

nf = NeuralForecast(
    models=[LSTM(h=12, 
                 input_size=8,
                 loss=DistributionLoss(distribution="Normal", level=[80, 90]),
                 scaler_type='robust',
                 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'],
                 recurrent=True,
                 h_train=1,
                 )
    ],
    freq='ME'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic)
Y_hat_df = nf.predict(futr_df=Y_test_df)

# Plots
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-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.grid()
plt.plot()