LSTM

LSTM: Long Short-Term Memory network for sequential forecasting. Multilayer encoder-decoder architecture that addresses vanishing gradients in time series.

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 $\mathbf{c}_{[t+1:t+H]}$, 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

• 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.”

Figure 1. Long Short-Term Memory Cell.

1. LSTM

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:

Name	Type	Description	Default
h	int	forecast horizon.	required
input_size	int	maximum sequence length for truncated train backpropagation. Default -1 uses 3 * horizon	-1
inference_input_size	int	maximum sequence length for truncated inference. Default None uses input_size history.	None
h_train	int	maximum sequence length for truncated train backpropagation. Default 1.	1
encoder_n_layers	int	number of layers for the LSTM.	2
encoder_hidden_size	int	units for the LSTM’s hidden state size.	128
encoder_bias	bool	whether or not to use biases b_ih, b_hh within LSTM units.	True
encoder_dropout	float	dropout regularization applied to LSTM outputs.	0.0
context_size	deprecated	deprecated.	None
decoder_hidden_size	int	size of hidden layer for the MLP decoder.	128
decoder_layers	int	number of layers for the MLP decoder.	2
futr_exog_list	str list	future exogenous columns.	None
hist_exog_list	str list	historic exogenous columns.	None
stat_exog_list	str list	static exogenous columns.	None
exclude_insample_y	bool	whether to exclude the target variable from the input.	False
recurrent	bool	whether to produce forecasts recursively (True) or direct (False).	False
loss	PyTorch module	instantiated train loss class from losses collection.	MAE()
valid_loss	PyTorch module	instantiated valid loss class from losses collection.	None
max_steps	int	maximum number of training steps.	1000
learning_rate	float	Learning rate between (0, 1).	0.001
num_lr_decays	int	Number of learning rate decays, evenly distributed across max_steps.	-1
early_stop_patience_steps	int	Number of validation iterations before early stopping.	-1
val_check_steps	int	Number of training steps between every validation loss check.	100
batch_size	int	number of differentseries in each batch.	32
valid_batch_size	int	number of different series in each validation and test batch.	None
windows_batch_size	int	number of windows to sample in each training batch, default uses all.	128
inference_windows_batch_size	int	number of windows to sample in each inference batch, -1 uses all.	1024
start_padding_enabled	bool	if True, the model will pad the time series with zeros at the beginning, by input size.	False
training_data_availability_threshold	Union[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_size	int	step size between each window of temporal data.	1
scaler_type	str	type of scaler for temporal inputs normalization see temporal scalers.	‘robust’
random_seed	int	random_seed for pytorch initializer and numpy generators.	1
drop_last_loader	bool	if True TimeSeriesDataLoader drops last non-full batch.	False
alias	str	optional, Custom name of the model.	None
optimizer	Subclass of ‘torch.optim.Optimizer’	optional, user specified optimizer instead of the default choice (Adam).	None
optimizer_kwargs	dict	optional, list of parameters used by the user specified optimizer.	None
lr_scheduler	Subclass of ‘torch.optim.lr_scheduler.LRScheduler’	optional, user specified lr_scheduler instead of the default choice (StepLR).	None
lr_scheduler_kwargs	dict	optional, list of parameters used by the user specified lr_scheduler.	None
dataloader_kwargs	dict	optional, list of parameters passed into the PyTorch Lightning dataloader by the TimeSeriesDataLoader.	None
**trainer_kwargs	int	keyword trainer arguments inherited from PyTorch Lighning’s trainer.

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:

Name	Type	Description	Default
dataset	TimeSeriesDataset	NeuralForecast’s TimeSeriesDataset, see documentation.	required
val_size	int	Validation size for temporal cross-validation.	0
random_seed	int	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	None
test_size	int	Test size for temporal cross-validation.	0

Returns:

Type	Description
None

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:

Name	Type	Description	Default
dataset	TimeSeriesDataset	NeuralForecast’s TimeSeriesDataset, see documentation.	required
test_size	int	Test size for temporal cross-validation.	None
step_size	int	Step size between each window.	1
random_seed	int	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	None
quantiles	list	Target quantiles to predict.	None
h	int	Prediction horizon, if None, uses the model’s fitted horizon. Defaults to None.	None
explainer_config	dict	configuration for explanations.	None
**data_module_kwargs	dict	PL’s TimeSeriesDataModule args, see documentation.

Returns:

Type	Description
None

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()