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


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Decoder

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

Autoformer decoder


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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


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Encoder

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

Autoformer encoder


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EncoderLayer

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

Autoformer encoder layer with the progressive decomposition architecture


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SeriesDecomp

 SeriesDecomp (kernel_size)

Series decomposition block


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MovingAvg

 MovingAvg (kernel_size, stride)

Moving average block to highlight the trend of time series


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LayerNorm

 LayerNorm (channels)

Special designed layernorm for the seasonal part


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AutoCorrelationLayer

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

*Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes::

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call :meth:to, etc.

.. note:: As per the example above, an __init__() call to the parent class must be made before assignment on the child.

:ivar training: Boolean represents whether this module is in training or evaluation mode. :vartype training: bool*


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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


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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, **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.
**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 numpy as np
import pandas as pd
import pytorch_lightning as pl
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import MLP
from neuralforecast.losses.pytorch import MQLoss, DistributionLoss
from neuralforecast.tsdataset import TimeSeriesDataset
from neuralforecast.utils import AirPassengers, 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()