FEDformer

The FEDformer 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 components based on a moving average filter. - Frequency Enhanced Block and Frequency Enhanced Attention to perform attention in the sparse representation on basis such as Fourier transform. - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The FEDformer 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
- Zhou, Tian, Ziqing Ma, Qingsong Wen, Xue Wang, Liang Sun, and Rong Jin.. “FEDformer: Frequency enhanced decomposed transformer for long-term series forecasting”

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1. Auxiliary functions

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AutoCorrelationLayer

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

Auto Correlation Layer

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LayerNorm

 LayerNorm (channels)

Special designed layernorm for the seasonal part

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Decoder

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

FEDformer 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')

FEDformer decoder layer with the progressive decomposition architecture

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Encoder

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

FEDformer encoder

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EncoderLayer

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

FEDformer encoder layer with the progressive decomposition architecture

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FourierCrossAttention

 FourierCrossAttention (in_channels, out_channels, seq_len_q, seq_len_kv,
                        modes=64, mode_select_method='random',
                        activation='tanh', policy=0)

Fourier Cross Attention layer

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FourierBlock

 FourierBlock (in_channels, out_channels, seq_len, modes=0,
               mode_select_method='random')

Fourier block

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get_frequency_modes

 get_frequency_modes (seq_len, modes=64, mode_select_method='random')

Get modes on frequency domain: ‘random’ for sampling randomly ‘else’ for sampling the lowest modes;

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2. Model

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FEDformer

 FEDformer (h:int, input_size:int, stat_exog_list=None,
            hist_exog_list=None, futr_exog_list=None,
            decoder_input_size_multiplier:float=0.5,
            version:str='Fourier', modes:int=64, mode_select:str='random',
            hidden_size:int=128, dropout:float=0.05, n_head:int=8,
            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,
            start_padding_enabled=False, val_check_steps:int=100,
            batch_size:int=32, valid_batch_size:Optional[int]=None,
            windows_batch_size=1024, inference_windows_batch_size=1024,
            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)

*FEDformer

The FEDformer 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 components based on a moving average filter. - Frequency Enhanced Block and Frequency Enhanced Attention to perform attention in the sparse representation on basis such as Fourier transform. - Classic encoder-decoder proposed by Vaswani et al. (2017) with a multi-head attention mechanism.

The FEDformer 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.
decoder_input_size_multiplier: float = 0.5, .
version: str = ‘Fourier’, version of the model.
modes: int = 64, number of modes for the Fourier block.
mode_select: str = ‘random’, method to select the modes for the Fourier block.
hidden_size: int=128, units of embeddings and encoders.
dropout: float (0, 1), dropout throughout Autoformer architecture.
n_head: int=8, controls number of multi-head’s attention.
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.
MovingAvg_window: int=25, window size for the moving average filter.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module, instantiated validation 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.
*

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import FEDformer
from neuralforecast.utils import AirPassengersPanel, 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 = FEDformer(h=12,
                 input_size=24,
                 modes=64,
                 hidden_size=64,
                 conv_hidden_size=128,
                 n_head=8,
                 loss=MAE(),
                 futr_exog_list=calendar_cols,
                 scaler_type='robust',
                 learning_rate=1e-3,
                 max_steps=500,
                 batch_size=2,
                 windows_batch_size=32,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='M',
)
nf.fit(df=Y_train_df, static_df=None, 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['FEDformer-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['FEDformer-lo-90'][-12:].values, 
                    y2=plot_df['FEDformer-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['FEDformer'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()