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The Informer model tackles the vanilla Transformer computational complexity challenges for long-horizon forecasting. The architecture has three distinctive features: - A ProbSparse self-attention mechanism with an O time and memory complexity Llog(L). - A self-attention distilling process that prioritizes attention and efficiently handles long input sequences. - An MLP multi-step decoder that predicts long time-series sequences in a single forward operation rather than step-by-step. The Informer model utilizes a three-component approach to define its embedding: - It employs encoded autoregressive features obtained from a convolution network. - It uses window-relative positional embeddings derived from harmonic functions. - Absolute positional embeddings obtained from calendar features are utilized. References
- Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, Wancai Zhang. “Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting”

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1. Auxiliary Functions

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ConvLayer

 ConvLayer (c_in)
ConvLayer
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ProbAttention

 ProbAttention (mask_flag=True, factor=5, scale=None,
                attention_dropout=0.1, output_attention=False)
ProbAttention
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ProbMask

 ProbMask (B, H, L, index, scores, device='cpu')
ProbMask

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2. Informer

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Informer

 Informer (h:int, input_size:int, futr_exog_list=None,
           hist_exog_list=None, stat_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, distil:bool=True,
           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)
*Informer 
The Informer model tackles the vanilla Transformer computational complexity challenges for long-horizon forecasting. 
The architecture has three distinctive features:
1) A ProbSparse self-attention mechanism with an O time and memory complexity Llog(L).
2) A self-attention distilling process that prioritizes attention and efficiently handles long input sequences.
3) An MLP multi-step decoder that predicts long time-series sequences in a single forward operation rather than step-by-step.
The Informer model utilizes a three-component approach to define its embedding: 1) It employs encoded autoregressive features obtained from a convolution network. 2) It uses window-relative positional embeddings derived from harmonic functions. 3) Absolute positional embeddings obtained from calendar features are utilized. Parameters:
h: int, forecast horizon.
input_size: int, maximum sequence length for truncated train backpropagation.
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.
dropout: float (0, 1), dropout throughout Informer architecture.
factor: int=3, Probsparse attention factor.
n_head: int=4, 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.
distil: bool = True, wether the Informer decoder uses bottlenecks.
loss: PyTorch module, instantiated train loss class from losses collection.
valid_loss: PyTorch module=loss, instantiated valid 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.
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.
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.
 
*References*<br/>
- [Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, Wancai Zhang. "Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting"](https://arxiv.org/abs/2012.07436)<br/>*

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Informer.fit

 Informer.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.
*

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Informer.predict

 Informer.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, 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.
quantiles: list of floats, optional (default=None), target quantiles to predict.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

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Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import Informer
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 = Informer(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=200,
                 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['Informer-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['Informer-lo-90'][-12:].values, 
                    y2=plot_df['Informer-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['Informer'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()