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”

Figure 1. FEDformer Architecture.

1. FEDformer

`FEDformer`

FEDformer(
    h,
    input_size,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    decoder_input_size_multiplier=0.5,
    version="Fourier",
    modes=64,
    mode_select="random",
    hidden_size=128,
    dropout=0.05,
    n_head=8,
    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 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:

Name	Type	Description	Default
`h`	`int`	forecast horizon.	required
`input_size`	`int`	maximum sequence length for truncated train backpropagation.	required
`stat_exog_list`	`List[str]`	static exogenous columns.	`None`
`hist_exog_list`	`List[str]`	historic exogenous columns.	`None`
`futr_exog_list`	`List[str]`	future exogenous columns.	`None`
`decoder_input_size_multiplier`	`float`	multiplier for the input size of the decoder.	`0.5`
`version`	`str`	version of the model.	`‘Fourier’`
`modes`	`int`	number of modes for the Fourier block.	`64`
`mode_select`	`str`	method to select the modes for the Fourier block.	`‘random’`
`hidden_size`	`int`	units of embeddings and encoders.	`128`
`dropout`	`float`	dropout throughout Autoformer architecture.	`0.05`
`n_head`	`int`	controls number of multi-head’s attention.	`8`
`conv_hidden_size`	`int`	channels of the convolutional encoder.	`32`
`activation`	`str`	activation from [‘ReLU’, ‘Softplus’, ‘Tanh’, ‘SELU’, ‘LeakyReLU’, ‘PReLU’, ‘Sigmoid’, ‘GELU’].	`‘gelu’`
`encoder_layers`	`int`	number of layers for the TCN encoder.	`2`
`decoder_layers`	`int`	number of layers for the MLP decoder.	`1`
`MovingAvg_window`	`int`	window size for the moving average filter.	`25`
`loss`	`PyTorch module`	instantiated train loss class from losses collection.	`MAE()`
`valid_loss`	`PyTorch module`	instantiated validation loss class from losses collection.	`None`
`max_steps`	`int`	maximum number of training steps.	`5000`
`learning_rate`	`float`	Learning rate between (0, 1).	`0.0001`
`num_lr_decays`	`int`	Number of learning rate decays, evenly distributed across max_steps.	`-1`
`early_stop_patience_steps`	`int`	Number of validation iterations before early stopping.	`-1`
`val_check_steps`	`int`	Number of training steps between every validation loss check.	`100`
`batch_size`	`int`	number of different series in each batch.	`32`
`valid_batch_size`	`int`	number of different series in each validation and test batch, if None uses batch_size.	`None`
`windows_batch_size`	`int`	number of windows to sample in each training batch, default uses all.	`1024`
`inference_windows_batch_size`	`int`	number of windows to sample in each inference batch.	`1024`
`start_padding_enabled`	`bool`	if True, the model will pad the time series with zeros at the beginning, by input size.	`False`
`training_data_availability_threshold`	`Union[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_size`	`int`	step size between each window of temporal data.	`1`
`scaler_type`	`str`	type of scaler for temporal inputs normalization see temporal scalers.	`‘identity’`
`random_seed`	`int`	random_seed for pytorch initializer and numpy generators.	`1`
`drop_last_loader`	`bool`	if True `TimeSeriesDataLoader` drops last non-full batch.	`False`
`alias`	`str`	optional, Custom name of the model.	`None`
`optimizer`	`Subclass of ‘torch.optim.Optimizer’`	optional, user specified optimizer instead of the default choice (Adam).	`None`
`optimizer_kwargs`	`dict`	optional, list of parameters used by the user specified optimizer.	`None`
`lr_scheduler`	`Subclass of ‘torch.optim.lr_scheduler.LRScheduler’`	optional, user specified lr_scheduler instead of the default choice (StepLR).	`None`
`lr_scheduler_kwargs`	`dict`	optional, list of parameters used by the user specified lr_scheduler.	`None`
`dataloader_kwargs`	`dict`	optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`.	`None`
`**trainer_kwargs`	`int`	keyword trainer arguments inherited from PyTorch Lighning’s trainer.

`FEDformer.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:

Name	Type	Description	Default
`dataset`	`TimeSeriesDataset`	NeuralForecast’s `TimeSeriesDataset`, see documentation.	required
`val_size`	`int`	Validation size for temporal cross-validation.	`0`
`random_seed`	`int`	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	`None`
`test_size`	`int`	Test size for temporal cross-validation.	`0`

Returns:

Type	Description
None

`FEDformer.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:

Name	Type	Description	Default
`dataset`	`TimeSeriesDataset`	NeuralForecast’s `TimeSeriesDataset`, see documentation.	required
`test_size`	`int`	Test size for temporal cross-validation.	`None`
`step_size`	`int`	Step size between each window.	`1`
`random_seed`	`int`	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	`None`
`quantiles`	`list`	Target quantiles to predict.	`None`
`h`	`int`	Prediction horizon, if None, uses the model’s fitted horizon. Defaults to None.	`None`
`explainer_config`	`dict`	configuration for explanations.	`None`
`**data_module_kwargs`	`dict`	PL’s TimeSeriesDataModule args, see documentation.

Returns:

Type	Description
None

Usage Example

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='ME',
)
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()

2. Auxiliary functions

`AutoCorrelationLayer`

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

Bases: Module Auto Correlation Layer

`LayerNorm`

LayerNorm(channels)

Bases: Module Special designed layernorm for the seasonal part

`Decoder`

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

Bases: Module FEDformer decoder

`DecoderLayer`

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

Bases: Module FEDformer decoder layer with the progressive decomposition architecture

`Encoder`

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

Bases: Module FEDformer encoder

`EncoderLayer`

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

Bases: Module FEDformer encoder layer with the progressive decomposition architecture

`FourierCrossAttention`

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

Bases: Module Fourier Cross Attention layer

`FourierBlock`

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

Bases: Module Fourier block

`FourierBlock.compl_mul1d`

compl_mul1d(input, weights)

`FourierBlock.forward`

forward(q, k, v, mask)

`FourierBlock.index`

index = get_frequency_modes(
    seq_len, modes=modes, mode_select_method=mode_select_method
)

`FourierBlock.scale`

scale = 1 / (in_channels * out_channels)

`FourierBlock.weights1`

weights1 = nn.Parameter(
    self.scale
    * torch.rand(
        8,
        in_channels // 8,
        out_channels // 8,
        len(self.index),
        dtype=(torch.cfloat),
    )
)

`get_frequency_modes`

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

Getting Started

Capabilities

Tutorials

Use cases

API Reference

1. FEDformer

`FEDformer`

`FEDformer.fit`

`FEDformer.predict`

Usage Example

2. Auxiliary functions

`AutoCorrelationLayer`

`LayerNorm`

`Decoder`

`DecoderLayer`

`Encoder`

`EncoderLayer`

`FourierCrossAttention`

`FourierBlock`

`FourierBlock.compl_mul1d`

`FourierBlock.forward`

`FourierBlock.index`

`FourierBlock.scale`

`FourierBlock.weights1`

`get_frequency_modes`

Getting Started

Capabilities

Tutorials

Use cases

API Reference

​1. FEDformer

​FEDformer

​FEDformer.fit

​FEDformer.predict

​Usage Example

​2. Auxiliary functions

​AutoCorrelationLayer

​LayerNorm

​Decoder

​DecoderLayer

​Encoder

​EncoderLayer

​FourierCrossAttention

​FourierBlock

​FourierBlock.compl_mul1d

​FourierBlock.forward

​FourierBlock.index

​FourierBlock.scale

​FourierBlock.weights1

​get_frequency_modes

1. FEDformer

`FEDformer`

`FEDformer.fit`

`FEDformer.predict`

Usage Example

2. Auxiliary functions

`AutoCorrelationLayer`

`LayerNorm`

`Decoder`

`DecoderLayer`

`Encoder`

`EncoderLayer`

`FourierCrossAttention`

`FourierBlock`

`FourierBlock.compl_mul1d`

`FourierBlock.forward`

`FourierBlock.index`

`FourierBlock.scale`

`FourierBlock.weights1`

`get_frequency_modes`