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)

*Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes::

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call :meth:to, etc.

.. note:: As per the example above, an __init__() call to the parent class must be made before assignment on the child.

:ivar training: Boolean represents whether this module is in training or evaluation mode. :vartype training: bool*

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ProbAttention

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

*Base class for all neural network modules.

Your models should also subclass this class.

Modules can also contain other Modules, allowing to nest them in a tree structure. You can assign the submodules as regular attributes::

import torch.nn as nn
import torch.nn.functional as F

class Model(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(1, 20, 5)
        self.conv2 = nn.Conv2d(20, 20, 5)

    def forward(self, x):
        x = F.relu(self.conv1(x))
        return F.relu(self.conv2(x))

Submodules assigned in this way will be registered, and will have their parameters converted too when you call :meth:to, etc.

.. note:: As per the example above, an __init__() call to the parent class must be made before assignment on the child.

:ivar training: Boolean represents whether this module is in training or evaluation mode. :vartype training: bool*

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ProbMask

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

Initialize self. See help(type(self)) for accurate signature.

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2. Informer

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Informer

 Informer (h:int, input_size:int, stat_exog_list=None,
           hist_exog_list=None, futr_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,
           num_workers_loader:int=0, drop_last_loader:bool=False,
           optimizer=None, optimizer_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. 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.
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.
n_head: int=4, controls number of multi-head’s attention.
dropout: float (0, 1), dropout throughout Informer architecture.
factor: int=3, Probsparse attention factor.
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.
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.
**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,
                   **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.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

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Usage Example

import numpy as np
import pandas as pd
import pytorch_lightning as pl
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import MLP
from neuralforecast.losses.pytorch import MQLoss, DistributionLoss
from neuralforecast.tsdataset import TimeSeriesDataset
from neuralforecast.utils import AirPassengers, 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=DistributionLoss(distribution='StudentT', level=[80, 90]),
                 loss=MAE(),
                 futr_exog_list=calendar_cols,
                 scaler_type='robust',
                 learning_rate=1e-3,
                 max_steps=5,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='M'
)
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()
Vanilla TransformerAutoformer