> ## Documentation Index
> Fetch the complete documentation index at: https://nixtla-old-docs.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.
# 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”](https://proceedings.mlr.press/v162/zhou22g.html) Figure 1. FEDformer
Architecture.
## 1. Auxiliary functions
***
source
### AutoCorrelationLayer
> ```text theme={null}
> AutoCorrelationLayer (correlation, hidden_size, n_head, d_keys=None,
> d_values=None)
> ```
*Auto Correlation Layer*
***
source
### LayerNorm
> ```text theme={null}
> LayerNorm (channels)
> ```
*Special designed layernorm for the seasonal part*
***
source
### Decoder
> ```text theme={null}
> Decoder (layers, norm_layer=None, projection=None)
> ```
*FEDformer decoder*
***
source
### DecoderLayer
> ```text theme={null}
> 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*
***
source
### Encoder
> ```text theme={null}
> Encoder (attn_layers, conv_layers=None, norm_layer=None)
> ```
*FEDformer encoder*
***
source
### EncoderLayer
> ```text theme={null}
> EncoderLayer (attention, hidden_size, conv_hidden_size=None,
> MovingAvg=25, dropout=0.1, activation='relu')
> ```
*FEDformer encoder layer with the progressive decomposition
architecture*
***
source
### FourierCrossAttention
> ```text theme={null}
> 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*
***
source
### FourierBlock
> ```text theme={null}
> FourierBlock (in_channels, out_channels, seq_len, modes=0,
> mode_select_method='random')
> ```
*Fourier block*
***
source
### get\_frequency\_modes
> ```text theme={null}
> 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;*
## 2. Model
***
source
### FEDformer
> ```text theme={null}
> 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,
> 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,
> drop_last_loader:bool=False, alias:Optional[str]=None,
> 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.
`stat_exog_list`: str list, static exogenous columns.
`hist_exog_list`: str list, historic exogenous columns.
`futr_exog_list`: str list, future 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](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`valid_loss`: PyTorch module, instantiated validation loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`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. `step_size`: int=1, step size between each window of temporal
data. \
`scaler_type`: str=‘robust’, type of scaler for temporal inputs
normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).
`random_seed`: int=1, random\_seed for pytorch initializer and numpy
generators. `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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer). \*
***
### FEDformer.fit
> ```text theme={null}
> FEDformer.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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
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`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`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. \*
***
### FEDformer.predict
> ```text theme={null}
> FEDformer.predict (dataset, test_size=None, step_size=1,
> random_seed=None, quantiles=None,
> **data_module_kwargs)
> ```
\*Predict.
Neural network prediction with PL’s `Trainer` execution of
`predict_step`.
**Parameters:** `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).
`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. `quantiles`: list of floats,
optional (default=None), target quantiles to predict.
`**data_module_kwargs`: PL’s TimeSeriesDataModule args, see
[documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*
# Usage Example
```python theme={null}
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]].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()
```
