> ## 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.
> 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. This version is multivariate, indicating that it will predict all time series of the forecasting problem jointly.
**References** -[Rosenblatt, F. (1958). "The perceptron: A probabilistic model for information storage and organization in the brain."](https://psycnet.apa.org/record/1959-09865-001) -[Fukushima, K. (1975). "Cognitron: A self-organizing multilayered neural network."](https://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCAL7750396723) -[Vinod Nair, Geoffrey E. Hinton (2010). "Rectified Linear Units Improve Restricted Boltzmann Machines"](https://www.cs.toronto.edu/~fritz/absps/reluICML.pdf)
# MLPMultivariate
Figure 1. Three layer MLP with
autorregresive inputs.
***
source
### MLPMultivariate
> ```text theme={null}
> MLPMultivariate (h, input_size, n_series, 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=32, inference_windows_batch_size=32,
> 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)
> ```
\*MLPMultivariate
Simple Multi Layer Perceptron architecture (MLP) for multivariate
forecasting. 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 variables.
**Parameters:** `h`: int, forecast horizon. `input_size`: int,
considered autorregresive inputs (lags), y=\[1,2,3,4] input\_size=2 ->
lags=\[1,2]. `n_series`: int, number of time-series.
`stat_exog_list`: str list, static exogenous columns.
`hist_exog_list`: str list, historic exogenous columns.
`futr_exog_list`: str list, future exogenous columns. `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](https://nixtla.github.io/neuralforecast/losses.pytorch.html).
`valid_loss`: PyTorch module=`loss`, instantiated valid 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=32, number of windows to
sample in each training batch, default uses all.
`inference_windows_batch_size`: int=32, 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](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). \*
***
### MLPMultivariate.fit
> ```text theme={null}
> MLPMultivariate.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. \*
***
### MLPMultivariate.predict
> ```text theme={null}
> MLPMultivariate.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 MLPMultivariate
from neuralforecast.losses.pytorch import MAE
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test
model = MLPMultivariate(h=12,
input_size=24,
n_series=2,
stat_exog_list=['airline1'],
futr_exog_list=['trend'],
loss = MAE(),
scaler_type='robust',
learning_rate=1e-3,
stat_exog_list=['airline1'],
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['MLPMultivariate'], c='blue', label='median')
plt.grid()
plt.legend()
plt.plot()
```
