TSMixerx

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1. Auxiliary Functions

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1.1 Mixing layers

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

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MixingLayerWithStaticExogenous

 MixingLayerWithStaticExogenous (h, dropout, ff_dim, stat_input_size)

MixingLayerWithStaticExogenous

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MixingLayer

 MixingLayer (in_features, out_features, h, dropout, ff_dim)

MixingLayer

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FeatureMixing

 FeatureMixing (in_features, out_features, h, dropout, ff_dim)

FeatureMixing

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TemporalMixing

 TemporalMixing (num_features, h, dropout)

TemporalMixing

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1.2 Reversible InstanceNormalization

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

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2. Model

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TSMixerx

 TSMixerx (h, input_size, n_series, futr_exog_list=None,
           hist_exog_list=None, stat_exog_list=None, n_block=2, ff_dim=64,
           dropout=0.0, 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)

*TSMixerx

Time-Series Mixer exogenous (TSMixerx) is a MLP-based multivariate time-series forecasting model, with capability for additional exogenous inputs. TSMixerx 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=0.0, dropout rate between (0, 1) .
revin: bool=True, if True uses Reverse Instance Normalization on insample_y and applies it to the 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.”*

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TSMixerx.fit

 TSMixerx.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.
*

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TSMixerx.predict

 TSMixerx.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.*

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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 TSMixerx
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 = TSMixerx(h=12,
                input_size=24,
                n_series=2,
                stat_exog_list=['airline1'],
                futr_exog_list=['trend'],
                n_block=4,
                ff_dim=4,
                revin=True,
                scaler_type='standard',
                max_steps=500,
                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['TSMixerx'], 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['TSMixerx'], 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()