NBEATSx

NBEATSx: Neural Basis Expansion Analysis with exogenous variables. MLP-based architecture with interpretable trend-seasonality blocks for forecasting.

The Neural Basis Expansion Analysis (NBEATS) is an MLP-based deep neural architecture with backward and forward residual links. The network has two variants: (1) in its interpretable configuration, NBEATS sequentially projects the signal into polynomials and harmonic basis to learn trend and seasonality components; (2) in its generic configuration, it substitutes the polynomial and harmonic basis for identity basis and larger network’s depth. The Neural Basis Expansion Analysis with Exogenous (NBEATSx), incorporates projections to exogenous temporal variables available at the time of the prediction.

This method proved state-of-the-art performance on the M3, M4, and Tourism Competition datasets, improving accuracy by 3% over the ESRNN M4 competition winner. For Electricity Price Forecasting tasks NBEATSx model improved accuracy by 20% and 5% over ESRNN and NBEATS, and 5% on task-specialized architectures.

References

• Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados, Yoshua Bengio (2019). “N-BEATS: Neural basis expansion analysis for interpretable time series forecasting”.

• Kin G. Olivares, Cristian Challu, Grzegorz Marcjasz, Rafał Weron, Artur Dubrawski (2021). “Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx”.

Figure 1. Neural Basis Expansion Analysis with Exogenous Variables.

NBEATSx

NBEATSx

NBEATSx(
    h,
    input_size,
    futr_exog_list=None,
    hist_exog_list=None,
    stat_exog_list=None,
    exclude_insample_y=False,
    n_harmonics=2,
    n_polynomials=2,
    stack_types=["identity", "trend", "seasonality"],
    n_blocks=[1, 1, 1],
    mlp_units=3 * [[512, 512]],
    dropout_prob_theta=0.0,
    activation="ReLU",
    shared_weights=False,
    loss=MAE(),
    valid_loss=None,
    max_steps=1000,
    learning_rate=0.001,
    num_lr_decays=3,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=1024,
    inference_windows_batch_size=-1,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="identity",
    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

NBEATSx

The Neural Basis Expansion Analysis with Exogenous variables (NBEATSx) is a simple and effective deep learning architecture. It is built with a deep stack of MLPs with doubly residual connections. The NBEATSx architecture includes additional exogenous blocks, extending NBEATS capabilities and interpretability. With its interpretable version, NBEATSx decomposes its predictions on seasonality, trend, and exogenous effects.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
input_size	int	autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].	required
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	the model skips the autoregressive features y[t-input_size:t] if True.	False
n_harmonics	int	Number of harmonic oscillations in the SeasonalityBasis [cos(i * t/n_harmonics), sin(i * t/n_harmonics)]. Note that it will only be used if ‘seasonality’ is in stack_types.	2
n_polynomials	int	Number of polynomial terms for TrendBasis [1,t,…,t^n_poly]. Note that it will only be used if ‘trend’ is in stack_types.	2
stack_types	List[str]	List of stack types. Subset from [‘seasonality’, ‘trend’, ‘identity’, ‘exogenous’].	[‘identity’, ‘trend’, ‘seasonality’]
n_blocks	List[int]	Number of blocks for each stack. Note that len(n_blocks) = len(stack_types).	[1, 1, 1]
mlp_units	List[List[int]]	Structure of hidden layers for each stack type. Each internal list should contain the number of units of each hidden layer. Note that len(n_hidden) = len(stack_types).	3 * [[512, 512]]
dropout_prob_theta	float	Float between (0, 1). Dropout for N-BEATS basis.	0.0
activation	str	activation from [‘ReLU’, ‘Softplus’, ‘Tanh’, ‘SELU’, ‘LeakyReLU’, ‘PReLU’, ‘Sigmoid’].	’ReLU’
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.	3
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 different series in each batch.	32
valid_batch_size	int	number of different series in each validation and test batch, if None uses batch_size.	None
windows_batch_size	int	number of windows to sample in each training batch, default uses all.	1024
inference_windows_batch_size	int	number of windows to sample in each inference batch, -1 uses all.	-1
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.	‘identity’
random_seed	int	random seed initialization for replicability.	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.

NBEATSx.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

NBEATSx.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 NBEATSx
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

model = NBEATSx(h=12, input_size=24,
                loss=MQLoss(level=[80, 90]),
                scaler_type='robust',
                dropout_prob_theta=0.5,
                stat_exog_list=['airline1'],
                futr_exog_list=['trend'],
                stack_types = ["identity", "trend", "seasonality", "exogenous"],
                n_blocks = [1,1,1,1],
                max_steps=200,
                val_check_steps=10,
                early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='ME'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
Y_hat_df = nf.predict(futr_df=Y_test_df)

# Plot quantile predictions
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['NBEATSx-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['NBEATSx-lo-90'][-12:].values, 
                 y2=plot_df['NBEATSx-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()