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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 Figure 1. Autoformer Architecture. Figure 1. Autoformer Architecture.

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1. Autoformer

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Autoformer

Autoformer(
    h,
    input_size,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    exclude_insample_y=False,
    decoder_input_size_multiplier=0.5,
    hidden_size=128,
    dropout=0.05,
    factor=3,
    n_head=4,
    conv_hidden_size=32,
    activation="gelu",
    encoder_layers=2,
    decoder_layers=1,
    MovingAvg_window=25,
    loss=MAE(),
    valid_loss=None,
    max_steps=5000,
    learning_rate=0.0001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=1024,
    inference_windows_batch_size=1024,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="identity",
    random_seed=1,
    drop_last_loader=False,
    alias=None,
    optimizer=None,
    optimizer_kwargs=None,
    lr_scheduler=None,
    lr_scheduler_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)
Bases: BaseModel 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:
NameTypeDescriptionDefault
hintforecast horizon.required
input_sizeintmaximum sequence length for truncated train backpropagation. Default -1 uses all history.required
futr_exog_liststr listfuture exogenous columns.None
hist_exog_liststr listhistoric exogenous columns.None
stat_exog_liststr liststatic exogenous columns.None
exclude_insample_yboolthe model skips the autoregressive features y[t-input_size:t] if True.False
decoder_input_size_multiplierfloat.0.5
hidden_sizeintunits of embeddings and encoders.128
n_headintcontrols number of multi-head’s attention.4
dropoutfloatdropout throughout Autoformer architecture.0.05
factorintProbsparse attention factor.3
conv_hidden_sizeintchannels of the convolutional encoder.32
activationstractivation from [‘ReLU’, ‘Softplus’, ‘Tanh’, ‘SELU’, ‘LeakyReLU’, ‘PReLU’, ‘Sigmoid’, ‘GELU’].‘gelu’
encoder_layersintnumber of layers for the TCN encoder.2
decoder_layersintnumber of layers for the MLP decoder.1
MovingAvg_windowintwindow size for the moving average filter.25
lossPyTorch moduleinstantiated train loss class from losses collection.MAE()
valid_lossPyTorch moduleinstantiated validation loss class from losses collection.None
max_stepsintmaximum number of training steps.5000
learning_ratefloatLearning rate between (0, 1).0.0001
num_lr_decaysintNumber of learning rate decays, evenly distributed across max_steps.-1
early_stop_patience_stepsintNumber of validation iterations before early stopping.-1
val_check_stepsintNumber of training steps between every validation loss check.100
batch_sizeintnumber of different series in each batch.32
valid_batch_sizeintnumber of different series in each validation and test batch, if None uses batch_size.None
windows_batch_sizeintnumber of windows to sample in each training batch, default uses all.1024
inference_windows_batch_sizeintnumber of windows to sample in each inference batch.1024
start_padding_enabledboolif True, the model will pad the time series with zeros at the beginning, by input size.False
training_data_availability_thresholdUnion[float, List[float]]minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).0.0
step_sizeintstep size between each window of temporal data.1
scaler_typestrtype of scaler for temporal inputs normalization see temporal scalers.‘identity’
random_seedintrandom_seed for pytorch initializer and numpy generators.1
drop_last_loaderboolif True TimeSeriesDataLoader drops last non-full batch.False
aliasstroptional, Custom name of the model.None
optimizerSubclass of ‘torch.optim.Optimizer’optional, user specified optimizer instead of the default choice (Adam).None
optimizer_kwargsdictoptional, list of parameters used by the user specified optimizer.None
lr_schedulerSubclass of ‘torch.optim.lr_scheduler.LRScheduler’optional, user specified lr_scheduler instead of the default choice (StepLR).None
lr_scheduler_kwargsdictoptional, list of parameters used by the user specified lr_scheduler.None
dataloader_kwargsdictoptional, list of parameters passed into the PyTorch Lightning dataloader by the TimeSeriesDataLoader.None
**trainer_kwargsintkeyword trainer arguments inherited from PyTorch Lighning’s trainer.

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Autoformer.fit

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:
NameTypeDescriptionDefault
datasetTimeSeriesDatasetNeuralForecast’s TimeSeriesDataset, see documentation.required
val_sizeintValidation size for temporal cross-validation.0
random_seedintRandom seed for pytorch initializer and numpy generators, overwrites model.init’s.None
test_sizeintTest size for temporal cross-validation.0
Returns:
TypeDescription
None

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Autoformer.predict

predict(
    dataset,
    test_size=None,
    step_size=1,
    random_seed=None,
    quantiles=None,
    h=None,
    explainer_config=None,
    **data_module_kwargs
)
Predict. Neural network prediction with PL’s Trainer execution of predict_step. Parameters:
NameTypeDescriptionDefault
datasetTimeSeriesDatasetNeuralForecast’s TimeSeriesDataset, see documentation.required
test_sizeintTest size for temporal cross-validation.None
step_sizeintStep size between each window.1
random_seedintRandom seed for pytorch initializer and numpy generators, overwrites model.init’s.None
quantileslistTarget quantiles to predict.None
hintPrediction horizon, if None, uses the model’s fitted horizon. Defaults to None.None
explainer_configdictconfiguration for explanations.None
**data_module_kwargsdictPL’s TimeSeriesDataModule args, see documentation.
Returns:
TypeDescription
None

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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='ME'
)
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()

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2. Auxiliary functions

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Decoder

Decoder(layers, norm_layer=None, projection=None)
Bases: Module 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",
)
Bases: Module Autoformer decoder layer with the progressive decomposition architecture

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Encoder

Encoder(attn_layers, conv_layers=None, norm_layer=None)
Bases: Module Autoformer encoder

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EncoderLayer

EncoderLayer(
    attention,
    hidden_size,
    conv_hidden_size=None,
    MovingAvg=25,
    dropout=0.1,
    activation="relu",
)
Bases: Module Autoformer encoder layer with the progressive decomposition architecture

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LayerNorm

LayerNorm(channels)
Bases: Module Special designed layernorm for the seasonal part

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AutoCorrelationLayer

AutoCorrelationLayer(
    correlation, hidden_size, n_head, d_keys=None, d_values=None
)
Bases: Module Auto Correlation Layer

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AutoCorrelation

AutoCorrelation(
    mask_flag=True,
    factor=1,
    scale=None,
    attention_dropout=0.1,
    output_attention=False,
)
Bases: Module 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.