StemGNN

StemGNN: Spectral Temporal Graph Neural Network for multivariate forecasting. Learns temporal dependencies and inter-series correlations in spectral domain.

The Spectral Temporal Graph Neural Network (StemGNN) is a Graph-based multivariate time-series forecasting model. StemGNN jointly learns temporal dependencies and inter-series correlations in the spectral domain, by combining Graph Fourier Transform (GFT) and Discrete Fourier Transform (DFT).

This method proved state-of-the-art performance on geo-temporal datasets such as Solar, METR-LA, and PEMS-BAY, and

References

• Defu Cao, Yujing Wang, Juanyong Duan, Ce Zhang, Xia Zhu, Congrui Huang, Yunhai Tong, Bixiong Xu, Jing Bai, Jie Tong, Qi Zhang (2020). “Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting”.

Figure 1. StemGNN.

1. StemGNN

StemGNN

StemGNN(
    h,
    input_size,
    n_series,
    futr_exog_list=None,
    hist_exog_list=None,
    stat_exog_list=None,
    exclude_insample_y=False,
    n_stacks=2,
    multi_layer=5,
    dropout_rate=0.5,
    leaky_rate=0.2,
    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=32,
    inference_windows_batch_size=32,
    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

StemGNN

The Spectral Temporal Graph Neural Network (StemGNN) is a Graph-based multivariate time-series forecasting model. StemGNN jointly learns temporal dependencies and inter-series correlations in the spectral domain, by combining Graph Fourier Transform (GFT) and Discrete Fourier Transform (DFT).

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
n_series	int	number of time-series.	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
n_stacks	int	number of stacks in the model.	2
multi_layer	int	multiplier for FC hidden size on StemGNN blocks.	5
dropout_rate	float	dropout rate.	0.5
leaky_rate	float	alpha for LeakyReLU layer on Latent Correlation layer.	0.2
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 windows 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.	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, 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
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.

StemGNN.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

StemGNN.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 Examples

Train model and forecast future values with predict method.

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import StemGNN
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MAE

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

model = StemGNN(h=12,
                input_size=24,
                n_series=2,
                scaler_type='standard',
                max_steps=500,
                early_stop_patience_steps=-1,
                val_check_steps=10,
                learning_rate=1e-3,
                loss=MAE(),
                valid_loss=MAE(),
                batch_size=32
                )

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
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
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['StemGNN'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

Using cross_validation to forecast multiple historic values.

fcst = NeuralForecast(models=[model], freq='M')
forecasts = fcst.cross_validation(df=AirPassengersPanel, static_df=AirPassengersStatic, n_windows=2, step_size=12)

# Plot predictions
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
Y_hat_df = forecasts.loc['Airline1']
Y_df = AirPassengersPanel[AirPassengersPanel['unique_id']=='Airline1']

plt.plot(Y_df['ds'], Y_df['y'], c='black', label='True')
plt.plot(Y_hat_df['ds'], Y_hat_df['StemGNN'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

2. Auxiliary functions

GLU

GLU(input_channel, output_channel)

Bases: Module

GLU

StockBlockLayer

StockBlockLayer(time_step, unit, multi_layer, stack_cnt=0)

Bases: Module

StockBlockLayer