SOFTS

1. Auxiliary functions

1.1 Embedding

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DataEmbedding_inverted

 DataEmbedding_inverted (c_in, d_model, dropout=0.1)

Data Embedding

1.2 STAD (STar Aggregate Dispatch)

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STAD

 STAD (d_series, d_core)

STar Aggregate Dispatch Module

2. Model

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SOFTS

 SOFTS (h, input_size, n_series, futr_exog_list=None, hist_exog_list=None,
        stat_exog_list=None, exclude_insample_y=False,
        hidden_size:int=512, d_core:int=512, e_layers:int=2,
        d_ff:int=2048, dropout:float=0.1, use_norm:bool=True, loss=MAE(),
        valid_loss=None, max_steps:int=1000, learning_rate:float=0.001,
        num_lr_decays:int=-1, early_stop_patience_steps:int=-1,
        val_check_steps:int=100, batch_size:int=32,
        valid_batch_size:Optional[int]=None, windows_batch_size=32,
        inference_windows_batch_size=32, start_padding_enabled=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)

*SOFTS

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].
n_series: int, number of time-series.
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, whether to exclude the target variable from the input.

hidden_size: int, dimension of the model.
d_core: int, dimension of core in STAD.
e_layers: int, number of encoder layers.
d_ff: int, dimension of fully-connected layer.
dropout: float, dropout rate.
use_norm: bool, whether to normalize or not.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module=loss, instantiated valid loss class from losses collection.
max_steps: int=1000, maximum number of training steps.
learning_rate: float=1e-3, Learning rate between (0, 1).
num_lr_decays: int=-1, 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=32, number of windows to sample in each training batch, default uses all.
inference_windows_batch_size: int=32, 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.
random_seed: int=1, random_seed for pytorch initializer and numpy generators.
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.

References
Lu Han, Xu-Yang Chen, Han-Jia Ye, De-Chuan Zhan. “SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion”*

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SOFTS.fit

 SOFTS.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:
dataset: NeuralForecast’s TimeSeriesDataset, see documentation.
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.
*

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SOFTS.predict

 SOFTS.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, see documentation.
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.*

3. Usage example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import SOFTS
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MASE
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 = SOFTS(h=12,
              input_size=24,
              n_series=2,
              hidden_size=256,
              d_core=256,
              e_layers=2,
              d_ff=64,
              dropout=0.1,
              use_norm=True,
              loss=MASE(seasonality=4),
              early_stop_patience_steps=3,
              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['SOFTS'], 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()