TiDE

Time-series Dense Encoder (TiDE) is a MLP-based univariate time-series forecasting model. TiDE uses Multi-layer Perceptrons (MLPs) in an encoder-decoder model for long-term time-series forecasting. In addition, this model can handle exogenous inputs.

1. Auxiliary Functions

1.1 MLP residual

An MLP block with a residual connection.

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MLPResidual

 MLPResidual (input_dim, hidden_size, output_dim, dropout, layernorm)

MLPResidual

2. Model

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TiDE

 TiDE (h, input_size, hidden_size=512, decoder_output_dim=32,
       temporal_decoder_dim=128, dropout=0.3, layernorm=True,
       num_encoder_layers=1, num_decoder_layers=1, temporal_width=4,
       futr_exog_list=None, hist_exog_list=None, stat_exog_list=None,
       exclude_insample_y=False, 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=1024,
       inference_windows_batch_size=1024, 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)

*TiDE

Time-series Dense Encoder (TiDE) is a MLP-based univariate time-series forecasting model. TiDE uses Multi-layer Perceptrons (MLPs) in an encoder-decoder model for long-term time-series forecasting.

Parameters:
h: int, forecast horizon.
input_size: int, considered autorregresive inputs (lags), y=[1,2,3,4] input_size=2 -> lags=[1,2].
hidden_size: int=1024, number of units for the dense MLPs.
decoder_output_dim: int=32, number of units for the output of the decoder.
temporal_decoder_dim: int=128, number of units for the hidden sizeof the temporal decoder.
dropout: float=0.0, dropout rate between (0, 1) .
layernorm: bool=True, if True uses Layer Normalization on the MLP residual block outputs.
num_encoder_layers: int=1, number of encoder layers.
num_decoder_layers: int=1, number of decoder layers.
temporal_width: int=4, lower temporal projected dimension.
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 historic exogenous data.
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.
windows_batch_size: int=1024, number of windows to sample in each training batch, default uses all.
inference_windows_batch_size: int=1024, 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:
- Das, Abhimanyu, Weihao Kong, Andrew Leach, Shaan Mathur, Rajat Sen, and Rose Yu (2024). “Long-term Forecasting with TiDE: Time-series Dense Encoder.”*

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TiDE.fit

 TiDE.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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TiDE.predict

 TiDE.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 Examples

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import TiDE
from neuralforecast.losses.pytorch import GMM
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

fcst = NeuralForecast(
    models=[
            TiDE(h=12,
                input_size=24,
                loss=GMM(n_components=7, return_params=True, level=[80,90], weighted=True),
                max_steps=100,
                scaler_type='standard',
                futr_exog_list=['y_[lag12]'],
                hist_exog_list=None,
                stat_exog_list=['airline1'],
                ),     
    ],
    freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic)
forecasts = fcst.predict(futr_df=Y_test_df)

# Plot quantile 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['TiDE-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['TiDE-lo-90'][-12:].values,
                 y2=plot_df['TiDE-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()