​
1. Auxiliary Functions

​
1.1 Mixing layers

A mixing layer consists of a sequential time- and feature Multi Layer Perceptron (MLP).

​
1.2 Reversible InstanceNormalization

An Instance Normalization Layer that is reversible, based on this reference implementation.

​
2. Model

source

​
TSMixer

 TSMixer (h, input_size, n_series, futr_exog_list=None,
          hist_exog_list=None, stat_exog_list=None, n_block=2, ff_dim=64,
          dropout=0.9, revin=True, 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, 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, lr_scheduler=None,
          lr_scheduler_kwargs=None, **trainer_kwargs)

*TSMixer

Time-Series Mixer (TSMixer) is a MLP-based multivariate time-series forecasting model. TSMixer jointly learns temporal and cross-sectional representations of the time-series by repeatedly combining time- and feature information using stacked mixing layers. A mixing layer consists of a sequential time- and feature Multi Layer Perceptron (MLP).

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.
futr_exog_list: str list, future exogenous columns.
hist_exog_list: str list, historic exogenous columns.
stat_exog_list: str list, static exogenous columns.
n_block: int=2, number of mixing layers in the model.
ff_dim: int=64, number of units for the second feed-forward layer in the feature MLP.
dropout: float=0.9, dropout rate between (0, 1) .
revin: bool=True, if True uses Reverse Instance Normalization to process inputs and outputs.
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.
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.
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.
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.

**trainer_kwargs: int, keyword trainer arguments inherited from PyTorch Lighning’s trainer.

References:
- Chen, Si-An, Chun-Liang Li, Nate Yoder, Sercan O. Arik, and Tomas Pfister (2023). “TSMixer: An All-MLP Architecture for Time Series Forecasting.”*

​
TSMixer.fit

 TSMixer.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.
test_size: int, test size for temporal cross-validation.
*

​
TSMixer.predict

 TSMixer.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.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

​
3. Usage Examples

Train model and forecast future values with predict method.

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

from neuralforecast import NeuralForecast
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MAE

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

model = TSMixer(h=12,
                input_size=24,
                n_series=2, 
                n_block=4,
                ff_dim=4,
                dropout=0,
                revin=True,
                scaler_type='standard',
                max_steps=200,
                early_stop_patience_steps=-1,
                val_check_steps=5,
                learning_rate=1e-3,
                loss=MAE(),
                valid_loss=MAE(),
                batch_size=32
                )

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

# Plot predictions
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
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['TSMixer'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

Using cross_validation to forecast multiple historic values.

fcst = NeuralForecast(models=[model], freq='M')
forecasts = fcst.cross_validation(df=AirPassengersPanel, static_df=AirPassengersStatic, n_windows=2, step_size=12)

# Plot predictions
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
Y_hat_df = forecasts.loc['Airline1']
Y_df = AirPassengersPanel[AirPassengersPanel['unique_id']=='Airline1']

plt.plot(Y_df['ds'], Y_df['y'], c='black', label='True')
plt.plot(Y_hat_df['ds'], Y_hat_df['TSMixer'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()