> ## Documentation Index
> Fetch the complete documentation index at: https://nixtla-old-docs.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.
# NBEATSx
The Neural Basis Expansion Analysis
([`NBEATS`](https://nixtlaverse.nixtla.io/neuralforecast/models.nbeats.html#nbeats))
is an
[`MLP`](https://nixtlaverse.nixtla.io/neuralforecast/models.mlp.html#mlp)-based
deep neural architecture with backward and forward residual links. The
network has two variants: (1) in its interpretable configuration,
[`NBEATS`](https://nixtlaverse.nixtla.io/neuralforecast/models.nbeats.html#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`](https://nixtlaverse.nixtla.io/neuralforecast/models.nbeatsx.html#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`](https://nixtlaverse.nixtla.io/neuralforecast/models.nbeatsx.html#nbeatsx)
model improved accuracy by 20% and 5% over `ESRNN` and
[`NBEATS`](https://nixtlaverse.nixtla.io/neuralforecast/models.nbeats.html#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”.](https://arxiv.org/abs/1905.10437) -[Kin G. Olivares,
Cristian Challu, Grzegorz Marcjasz, Rafał Weron, Artur Dubrawski (2021).
“Neural basis expansion analysis with exogenous variables: Forecasting
electricity prices with NBEATSx”.](https://arxiv.org/abs/2104.05522) Figure 1. Neural Basis Expansion Analysis
with Exogenous Variables.
***
source
### NBEATSx
> ```text theme={null}
> 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:list=['identity', 'trend',
> 'seasonality'], n_blocks:list=[1, 1, 1], mlp_units:list=[[512,
> 512], [512, 512], [512, 512]], dropout_prob_theta=0.0,
> activation='ReLU', shared_weights=False, loss=MAE(),
> valid_loss=None, max_steps:int=1000, learning_rate:float=0.001,
> num_lr_decays:int=3, early_stop_patience_steps:int=-1,
> val_check_steps:int=100, batch_size=32,
> valid_batch_size:Optional[int]=None,
> windows_batch_size:int=1024,
> inference_windows_batch_size:int=-1,
> start_padding_enabled:bool=False, step_size:int=1,
> scaler_type:str='identity', random_seed:int=1,
> drop_last_loader:bool=False, alias:Optional[str]=None,
> optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
> lr_scheduler_kwargs=None, dataloader_kwargs=None,
> **trainer_kwargs)
> ```
\*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:** `h`: int, Forecast horizon. `input_size`: int,
autorregresive inputs size, y=\[1,2,3,4] input\_size=2 ->
y\_\[t-2:t]=\[1,2]. `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, the model skips the autoregressive
features y\[t-input\_size:t] if True. `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`. `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`. `stack_types`:
List\[str], List of stack types. Subset from \[‘seasonality’, ‘trend’,
‘identity’, ‘exogenous’]. `n_blocks`: List\[int], Number of blocks
for each stack. Note that len(n\_blocks) = len(stack\_types).
`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).
`dropout_prob_theta`: float, Float between (0, 1). Dropout for N-BEATS
basis. `activation`: str, activation from \[‘ReLU’, ‘Softplus’,
‘Tanh’, ‘SELU’, ‘LeakyReLU’, ‘PReLU’, ‘Sigmoid’]. `loss`: PyTorch
module, instantiated train loss class from [losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`max_steps`: int=1000, maximum number of training steps.
`learning_rate`: float=1e-3, Learning rate between (0, 1).
`num_lr_decays`: int=3, 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 different
series in each batch. `valid_batch_size`: int=None, number of
different series in each validation and test batch, if None uses
batch\_size. `windows_batch_size`: int=1024, number of windows to
sample in each training batch, default uses all.
`inference_windows_batch_size`: int=-1, 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=‘identity’, type of
scaler for temporal inputs normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).
`random_seed`: int, random seed initialization for replicability.
`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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
**References:** -[Kin G. Olivares, Cristian Challu, Grzegorz
Marcjasz, Rafał Weron, Artur Dubrawski (2021). “Neural basis expansion
analysis with exogenous variables: Forecasting electricity prices with
NBEATSx”.](https://arxiv.org/abs/2104.05522)\*
***
### NBEATSx.fit
> ```text theme={null}
> NBEATSx.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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
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`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`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. \*
***
### NBEATSx.predict
> ```text theme={null}
> NBEATSx.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`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`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](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*
## Usage Example
```python theme={null}
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]].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()
```
