MLP

One of the simplest neural architectures are Multi Layer Perceptrons (MLP) composed of stacked Fully Connected Neural Networks trained with backpropagation. Each node in the architecture is capable of modeling non-linear relationships granted by their activation functions. Novel activations like Rectified Linear Units (ReLU) have greatly improved the ability to fit deeper networks overcoming gradient vanishing problems that were associated with Sigmoid and TanH activations. For the forecasting task the last layer is changed to follow a auto-regression problem.

References
-Rosenblatt, F. (1958). “The perceptron: A probabilistic model for information storage and organization in the brain.”
-Fukushima, K. (1975). “Cognitron: A self-organizing multilayered neural network.”
-Vinod Nair, Geoffrey E. Hinton (2010). “Rectified Linear Units Improve Restricted Boltzmann Machines”

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MLP

 MLP (h, input_size, stat_exog_list=None, hist_exog_list=None,
      futr_exog_list=None, exclude_insample_y=False, num_layers=2,
      hidden_size=1024, loss=MAE(), valid_loss=None, max_steps:int=1000,
      learning_rate:float=0.001, 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=-1,
      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)

*MLP

Simple Multi Layer Perceptron architecture (MLP). This deep neural network has constant units through its layers, each with ReLU non-linearities, it is trained using ADAM stochastic gradient descent. The network accepts static, historic and future exogenous data, flattens the inputs and learns fully connected relationships against the target variable.

Parameters:
h: int, forecast horizon.
input_size: int, considered autorregresive inputs (lags), y=[1,2,3,4] input_size=2 -> lags=[1,2].
stat_exog_list: str list, static exogenous columns.
hist_exog_list: str list, historic exogenous columns.
futr_exog_list: str list, future exogenous columns.
exclude_insample_y: bool=False, the model skips the autoregressive features y[t-input_size:t] if True.
num_layers: int, number of layers for the MLP.
hidden_size: int, number of units for each layer of the MLP.
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=-1, number of windows to sample in each inference batch, -1 uses all.
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=‘identity’, 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.
*

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MLP.fit

 MLP.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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MLP.predict

 MLP.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.*

Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import MLP
from neuralforecast.losses.pytorch import DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic

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 = MLP(h=12, input_size=24,
            loss=DistributionLoss(distribution='Normal', level=[80, 90]),
            scaler_type='robust',
            learning_rate=1e-3,
            max_steps=200,
            val_check_steps=10,
            early_stop_patience_steps=2)

fcst = NeuralForecast(
    models=[model],
    freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = fcst.predict(futr_df=Y_test_df)

# Plot predictions
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])

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['MLP-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['MLP-lo-90'][-12:].values, 
                 y2=plot_df['MLP-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.grid()
plt.legend()
plt.plot()