XLinear

XLinear: A MLP-based model for multivariate forecasting with exogenous features.

XLinear is a MLP-based model for multivariate time series forecasting that uses gating mechanisms for temporal and cross-channel interactions. The architecture consists of temporal gating with a global token to capture global temporal patterns, followed by cross-channel gating to model dependencies between different time series.

References

• Xinyang, C., et al. “XLinear: A Lightweight and Accurate MLP-Based Model for Long-Term Time Series Forecasting with Exogenous Inputs”

Figure 1. Architecture of XLinear

XLinear

XLinear

XLinear(
    h,
    input_size,
    n_series,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    exclude_insample_y=False,
    hidden_size=128,
    temporal_ff=256,
    channel_ff=8,
    temporal_dropout=0.0,
    channel_dropout=0.0,
    embed_dropout=0.0,
    head_dropout=0.0,
    use_norm=True,
    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=32,
    inference_windows_batch_size=32,
    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

XLinear

XLinear is a linear-based model for multivariate time series forecasting that uses gating mechanisms for temporal and cross-channel interactions. The architecture consists of temporal gating with a global token to capture global temporal patterns, followed by cross-channel gating to model dependencies between different time series.

Parameters:

Name	Type	Description	Default
h	int	Forecast horizon.	required
input_size	int	Input size, y=[1,2,3,4] input_size=2 -> lags=[1,2].	required
n_series	int	Number of time series.	required
stat_exog_list	str list	Static exogenous columns.	None
hist_exog_list	str list	Historic exogenous columns.	None
futr_exog_list	str list	Future exogenous columns.	None
hidden_size	int	Dimension of the model embedding.	128
temporal_ff	int	Dimension of temporal feedforward layer in gating block.	256
channel_ff	int	Dimension of cross-channel feedforward layer in gating block.	8
temporal_dropout	float	Dropout rate for temporal gating.	0.0
channel_dropout	float	Dropout rate for cross-channel gating.	0.0
embed_dropout	float	Dropout rate for embedding projection.	0.0
head_dropout	float	Dropout rate for output head.	0.0
use_norm	bool	Whether to use RevIN normalization.	True
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 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.	32
inference_windows_batch_size	int	Number of windows to sample in each inference batch, -1 uses all.	32
start_padding_enabled	bool	If True, the model will pad the time series with zeros at the beginning.	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 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.	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.	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	keyword	trainer arguments inherited from PyTorch Lighning’s trainer.

XLinear.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

XLinear.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 XLinear
from neuralforecast.losses.pytorch import MAE
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 = XLinear(h=12, 
            input_size=24,
            n_series=2,
            stat_exog_list=['airline1'],
            hist_exog_list=["y_[lag12]"],
            futr_exog_list=['trend'],            
            loss = MAE(),
            scaler_type='robust',
            learning_rate=1e-3,
            max_steps=200,
            val_check_steps=10,
            early_stop_patience_steps=2)

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

# Plot predictions
Y_hat_df = forecasts.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['XLinear'], c='blue', label='median')
plt.grid()
plt.legend()
plt.plot()