> ## 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.
> StemGNN: Spectral Temporal Graph Neural Network for multivariate forecasting. Learns temporal dependencies and inter-series correlations in spectral domain.
# StemGNN
The Spectral Temporal Graph Neural Network
([`StemGNN`](./models.stemgnn.html#stemgnn))
is a Graph-based multivariate time-series forecasting model.
[`StemGNN`](./models.stemgnn.html#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”.](https://proceedings.neurips.cc/paper/2020/hash/cdf6581cb7aca4b7e19ef136c6e601a5-Abstract.html)
*Figure 1. StemGNN.*
## 1. StemGNN
### `StemGNN`
```python theme={null}
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_monitor="ptl/val_loss",
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](#neuralforecast.common._base_model.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](#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* |
| `n_series` | [int](#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](#int) | number of stacks in the model. | 2 |
| `multi_layer` | [int](#int) | multiplier for FC hidden size on StemGNN blocks. | 5 |
| `dropout_rate` | [float](#float) | dropout rate. | 0.5 |
| `leaky_rate` | [float](#float) | alpha for LeakyReLU layer on Latent Correlation layer. | 0.2 |
| `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 windows 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. | 32 |
| `inference_windows_batch_size` | [int](#int) | number of windows to sample in each inference batch, -1 uses all. | 32 |
| `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). | 'robust' |
| `random_seed` | [int](#int) | random\_seed for pytorch initializer and numpy generators. | 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 |
| `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). | {} |
#### `StemGNN.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 | |
#### `StemGNN.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 Examples
Train model and forecast future values with `predict` method.
```python theme={null}
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) # 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.
```python theme={null}
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`
```python theme={null}
GLU(input_channel, output_channel)
```
Bases: [Module](#torch.nn.Module)
GLU
### `StockBlockLayer`
```python theme={null}
StockBlockLayer(time_step, unit, multi_layer, stack_cnt=0)
```
Bases: [Module](#torch.nn.Module)
StockBlockLayer