Autoformer

The Autoformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.

The architecture has the following distinctive features: - In-built progressive decomposition in trend and seasonal compontents based on a moving average filter. - Auto-Correlation mechanism that discovers the period-based dependencies by calculating the autocorrelation and aggregating similar sub-series based on the periodicity. - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The Autoformer model utilizes a three-component approach to define its embedding: - It employs encoded autoregressive features obtained from a convolution network. - Absolute positional embeddings obtained from calendar features are utilized.

References
- Wu, Haixu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. “Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting”

​

1. Auxiliary Functions

​

Decoder

 Decoder (layers, norm_layer=None, projection=None)

Autoformer decoder

​

DecoderLayer

 DecoderLayer (self_attention, cross_attention, hidden_size, c_out,
               conv_hidden_size=None, MovingAvg=25, dropout=0.1,
               activation='relu')

Autoformer decoder layer with the progressive decomposition architecture

​

Encoder

 Encoder (attn_layers, conv_layers=None, norm_layer=None)

Autoformer encoder

​

EncoderLayer

 EncoderLayer (attention, hidden_size, conv_hidden_size=None,
               MovingAvg=25, dropout=0.1, activation='relu')

Autoformer encoder layer with the progressive decomposition architecture

​

LayerNorm

 LayerNorm (channels)

Special designed layernorm for the seasonal part

​

AutoCorrelationLayer

 AutoCorrelationLayer (correlation, hidden_size, n_head, d_keys=None,
                       d_values=None)

Auto Correlation Layer

​

AutoCorrelation

 AutoCorrelation (mask_flag=True, factor=1, scale=None,
                  attention_dropout=0.1, output_attention=False)

AutoCorrelation Mechanism with the following two phases: (1) period-based dependencies discovery (2) time delay aggregation This block can replace the self-attention family mechanism seamlessly.

​

2. Autoformer

​

Autoformer

 Autoformer (h:int, input_size:int, stat_exog_list=None,
             hist_exog_list=None, futr_exog_list=None,
             exclude_insample_y=False,
             decoder_input_size_multiplier:float=0.5, hidden_size:int=128,
             dropout:float=0.05, factor:int=3, n_head:int=4,
             conv_hidden_size:int=32, activation:str='gelu',
             encoder_layers:int=2, decoder_layers:int=1,
             MovingAvg_window:int=25, loss=MAE(), valid_loss=None,
             max_steps:int=5000, learning_rate:float=0.0001,
             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,
             num_workers_loader:int=0, drop_last_loader:bool=False,
             optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
             lr_scheduler_kwargs=None, dataloader_kwargs=None,
             **trainer_kwargs)

*Autoformer

The Autoformer model tackles the challenge of finding reliable dependencies on intricate temporal patterns of long-horizon forecasting.

The architecture has the following distinctive features: - In-built progressive decomposition in trend and seasonal compontents based on a moving average filter. - Auto-Correlation mechanism that discovers the period-based dependencies by calculating the autocorrelation and aggregating similar sub-series based on the periodicity. - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The Autoformer model utilizes a three-component approach to define its embedding: - It employs encoded autoregressive features obtained from a convolution network. - Absolute positional embeddings obtained from calendar features are utilized.

Parameters:
h: int, forecast horizon.
input_size: int, maximum sequence length for truncated train backpropagation. Default -1 uses all history.
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, the model skips the autoregressive features y[t-input_size:t] if True.
decoder_input_size_multiplier: float = 0.5, .
hidden_size: int=128, units of embeddings and encoders.
n_head: int=4, controls number of multi-head’s attention.
dropout: float (0, 1), dropout throughout Autoformer architecture.
factor: int=3, Probsparse attention factor.
conv_hidden_size: int=32, channels of the convolutional encoder.
activation: str=GELU, activation from [‘ReLU’, ‘Softplus’, ‘Tanh’, ‘SELU’, ‘LeakyReLU’, ‘PReLU’, ‘Sigmoid’, ‘GELU’].
encoder_layers: int=2, number of layers for the TCN encoder.
decoder_layers: int=1, number of layers for the MLP decoder.
distil: bool = True, wether the Autoformer decoder uses bottlenecks.
loss: PyTorch module, instantiated train 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=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.
start_padding_enabled: bool=False, if True, the model will pad the time series with zeros at the beginning, by input size.
scaler_type: str=‘robust’, 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.
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*<br/>
- [Wu, Haixu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. "Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting"](https://proceedings.neurips.cc/paper/2021/hash/bcc0d400288793e8bdcd7c19a8ac0c2b-Abstract.html)<br/>*

​

Autoformer.fit

 Autoformer.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.
*

​

Autoformer.predict

 Autoformer.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.
random_seed: int=None, random_seed for pytorch initializer and numpy generators, overwrites model.__init__’s.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

​

Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import Autoformer
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic, augment_calendar_df

AirPassengersPanel, calendar_cols = augment_calendar_df(df=AirPassengersPanel, freq='M')

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

model = Autoformer(h=12,
                 input_size=24,
                 hidden_size = 16,
                 conv_hidden_size = 32,
                 n_head=2,
                 loss=MAE(),
                 futr_exog_list=calendar_cols,
                 scaler_type='robust',
                 learning_rate=1e-3,
                 max_steps=300,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='M'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = nf.predict(futr_df=Y_test_df)

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])

if model.loss.is_distribution_output:
    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['Autoformer-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['Autoformer-lo-90'][-12:].values, 
                    y2=plot_df['Autoformer-hi-90'][-12:].values,
                    alpha=0.4, label='level 90')
    plt.grid()
    plt.legend()
    plt.plot()
else:
    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['Autoformer'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()