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). Note: this model cannot handle exogenous inputs. If you want to use additional exogenous inputs, use TSMixerx.

1. Auxiliary Functions

1.1 Mixing layers

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

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MixingLayer

 MixingLayer (n_series, input_size, dropout, ff_dim)

MixingLayer

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FeatureMixing

 FeatureMixing (n_series, input_size, dropout, ff_dim)

FeatureMixing

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TemporalMixing

 TemporalMixing (n_series, input_size, dropout)

TemporalMixing

2. Model

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TSMixer

 TSMixer (h, input_size, n_series, futr_exog_list=None,
          hist_exog_list=None, stat_exog_list=None,
          exclude_insample_y=False, 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, 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)

*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.
exclude_insample_y: bool=False, if True excludes the target variable from the input features.
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.
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.
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:
- Chen, Si-An, Chun-Liang Li, Nate Yoder, Sercan O. Arik, and Tomas Pfister (2023). “TSMixer: An All-MLP Architecture for Time Series Forecasting.”*

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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.
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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TSMixer.predict

 TSMixer.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.*

# Unit tests for models
logging.getLogger("pytorch_lightning").setLevel(logging.ERROR)
logging.getLogger("lightning_fabric").setLevel(logging.ERROR)
with warnings.catch_warnings():
    warnings.simplefilter("ignore")
    check_model(TSMixer, ["airpassengers"])

3. Usage Examples

Train model and forecast future values with predict method.

import pandas as pd
import matplotlib.pyplot as plt

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

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=500,
                early_stop_patience_steps=-1,
                val_check_steps=5,
                learning_rate=1e-3,
                loss=MQLoss(),
                batch_size=32
                )

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
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=='Airline2'].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-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['TSMixer-lo-90'][-12:].values,
                 y2=plot_df['TSMixer-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
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-median'], 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()