The iTransformer model simply takes the Transformer architecture but it applies the attention and feed-forward network on the inverted dimensions. This means that time points of each individual series are embedded into tokens. That way, the attention mechanisms learn multivariate correlation and the feed-forward network learns non-linear relationships.

References - Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, Mingsheng Long. “iTransformer: Inverted Transformers Are Effective for Time Series Forecasting”

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1. Auxiliary functions

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1.1 Attention

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FullAttention

 FullAttention (mask_flag=True, factor=5, scale=None,
                attention_dropout=0.1, output_attention=False)

FullAttention

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TriangularCausalMask

 TriangularCausalMask (B, L, device='cpu')

TriangularCausalMask

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1.2 Inverted embedding

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DataEmbedding_inverted

 DataEmbedding_inverted (c_in, hidden_size, dropout=0.1)

DataEmbedding_inverted

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2. Model

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iTransformer

 iTransformer (h, input_size, n_series, futr_exog_list=None,
               hist_exog_list=None, stat_exog_list=None,
               hidden_size:int=512, n_heads:int=8, e_layers:int=2,
               d_layers:int=1, d_ff:int=2048, factor:int=1,
               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, step_size:int=1,
               scaler_type:str='identity', random_seed:int=1,
               num_workers_loader:int=0, drop_last_loader:bool=False,
               optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
               lr_scheduler_kwargs=None, **trainer_kwargs)

*iTransformer

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.
hidden_size: int, dimension of the model.
n_heads: int, number of heads.
e_layers: int, number of encoder layers.
d_layers: int, number of decoder layers.
d_ff: int, dimension of fully-connected layer.
factor: int, attention factor.
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.
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.
num_workers_loader: int=os.cpu_count(), workers to be used by TimeSeriesDataLoader.
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.
**trainer_kwargs: int, keyword trainer arguments inherited from PyTorch Lighning’s trainer.

References
- Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, Mingsheng Long. “iTransformer: Inverted Transformers Are Effective for Time Series Forecasting”*

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iTransformer.fit

 iTransformer.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.
test_size: int, test size for temporal cross-validation.
*

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iTransformer.predict

 iTransformer.predict (dataset, test_size=None, step_size=1,
                       random_seed=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.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

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3. Usage example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import iTransformer
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MSE

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 = iTransformer(h=12,
                     input_size=24,
                     n_series=2,
                     hidden_size=128,
                     n_heads=2,
                     e_layers=2,
                     d_layers=1,
                     d_ff=4,
                     factor=1,
                     dropout=0.1,
                     use_norm=True,
                     loss=MSE(),
                     valid_loss=MAE(),
                     early_stop_patience_steps=3,
                     batch_size=32)

fcst = NeuralForecast(models=[model], freq='M')
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['iTransformer'], 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()