> ## Documentation Index
> Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt
> Use this file to discover all available pages before exploring further.
> NBEATSx: Neural Basis Expansion Analysis with exogenous variables. MLP-based architecture with interpretable trend-seasonality blocks for forecasting.
# NBEATSx
The Neural Basis Expansion Analysis
([`NBEATS`](./models.nbeats.html#nbeats))
is an
[`MLP`](./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`](./neuralforecast/models.nbeats.html#nbeats-2)
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`](./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`](./models.nbeatsx.html#nbeatsx)
model improved accuracy by 20% and 5% over `ESRNN` and
[`NBEATS`](./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.*
## NBEATSx
### `NBEATSx`
```python 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=["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_monitor="ptl/val_loss",
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](#neuralforecast.common._base_model.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](#int) | Forecast horizon. | *required* |
| `input_size` | [int](#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](#bool) | the model skips the autoregressive features y\[t-input\_size:t] if True. | False |
| `n_harmonics` | [int](#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](#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](#List)\[[str](#str)] | List of stack types. Subset from \['seasonality', 'trend', 'identity', 'exogenous']. | \['identity', 'trend', 'seasonality'] |
| `n_blocks` | [List](#List)\[[int](#int)] | Number of blocks for each stack. Note that len(n\_blocks) = len(stack\_types). | \[1, 1, 1] |
| `mlp_units` | [List](#List)\[[List](#List)\[[int](#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) | Float between (0, 1). Dropout for N-BEATS basis. | 0.0 |
| `activation` | [str](#str) | activation from \['ReLU', 'Softplus', 'Tanh', 'SELU', 'LeakyReLU', 'PReLU', 'Sigmoid']. | 'ReLU' |
| `loss` | PyTorch module | instantiated train loss class from [losses collection](./losses.pytorch.html). | [MAE](#neuralforecast.losses.pytorch.MAE)() |
| `valid_loss` | PyTorch module | instantiated valid loss class from [losses collection](./losses.pytorch.html). | None |
| `max_steps` | [int](#int) | maximum number of training steps. | 1000 |
| `learning_rate` | [float](#float) | Learning rate between (0, 1). | 0.001 |
| `num_lr_decays` | [int](#int) | Number of learning rate decays, evenly distributed across max\_steps. | 3 |
| `early_stop_patience_steps` | [int](#int) | Number of validation iterations before early stopping. | -1 |
| `val_monitor` | [str](#str) | metric to monitor for early stopping. Valid options: "ptl/val\_loss", "valid\_loss", "train\_loss". Default: "ptl/val\_loss". | 'ptl/val\_loss' |
| `val_check_steps` | [int](#int) | Number of training steps between every validation loss check. | 100 |
| `batch_size` | [int](#int) | number of different series in each batch. | 32 |
| `valid_batch_size` | [int](#int) | number of different series in each validation and test batch, if None uses batch\_size. | None |
| `windows_batch_size` | [int](#int) | number of windows to sample in each training batch, default uses all. | 1024 |
| `inference_windows_batch_size` | [int](#int) | number of windows to sample in each inference batch, -1 uses all. | -1 |
| `start_padding_enabled` | [bool](#bool) | if True, the model will pad the time series with zeros at the beginning, by input size. | False |
| `training_data_availability_threshold` | [Union](#Union)\[[float](#float), [List](#List)\[[float](#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](#int) | step size between each window of temporal data. | 1 |
| `scaler_type` | [str](#str) | type of scaler for temporal inputs normalization see [temporal scalers](https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/common/_scalers.py). | 'identity' |
| `random_seed` | [int](#int) | random seed initialization for replicability. | 1 |
| `drop_last_loader` | [bool](#bool) | if True `TimeSeriesDataLoader` drops last non-full batch. | False |
| `alias` | [str](#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](#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](#dict) | optional, list of parameters used by the user specified `lr_scheduler`. | None |
| `dataloader_kwargs` | [dict](#dict) | optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`. | None |
| `**trainer_kwargs` | [int](#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`
```python theme={null}
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:**
| Name | Type | Description | Default |
| ------------- | ---------------------------------------------------- | -------------------------------------------------------------------------------------- | ----------------- |
| `dataset` | [TimeSeriesDataset](#TimeSeriesDataset) | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `val_size` | [int](#int) | Validation size for temporal cross-validation. | 0 |
| `random_seed` | [int](#int) | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | None |
| `test_size` | [int](#int) | Test size for temporal cross-validation. | 0 |
**Returns:**
| Type | Description |
| ---- | ----------- |
| None | |
#### `NBEATSx.predict`
```python theme={null}
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](#TimeSeriesDataset) | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `test_size` | [int](#int) | Test size for temporal cross-validation. | None |
| `step_size` | [int](#int) | Step size between each window. | 1 |
| `random_seed` | [int](#int) | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | None |
| `quantiles` | [list](#list) | Target quantiles to predict. | None |
| `h` | [int](#int) | Prediction horizon, if None, uses the model's fitted horizon. Defaults to None. | None |
| `explainer_config` | [dict](#dict) | configuration for explanations. | None |
| `**data_module_kwargs` | [dict](#dict) | PL's TimeSeriesDataModule args, see [documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule). | {} |
**Returns:**
| Type | Description |
| ---- | ----------- |
| None | |
### 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()
```