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).

Figure 2. TSMixerX for multivariate time series forecasting.

1. TSMixerx

`TSMixerx`

TSMixerx(
    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=0.0,
    revin=True,
    loss=MAE(),
    valid_loss=None,
    max_steps=1000,
    learning_rate=0.001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=32,
    inference_windows_batch_size=32,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="identity",
    random_seed=1,
    drop_last_loader=False,
    alias=None,
    optimizer=None,
    optimizer_kwargs=None,
    lr_scheduler=None,
    lr_scheduler_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)

Bases: BaseModel 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:

Name	Type	Description	Default
`h`	`int`	forecast horizon.	required
`input_size`	`int`	considered autorregresive inputs (lags), y=[1,2,3,4] input_size=2 -> lags=[1,2].	required
`n_series`	`int`	number of time-series.	required
`futr_exog_list`	`str list`	future exogenous columns.	`None`
`hist_exog_list`	`str list`	historic exogenous columns.	`None`
`stat_exog_list`	`str list`	static exogenous columns.	`None`
`exclude_insample_y`	`bool`	if True excludes insample_y from the model.	`False`
`n_block`	`int`	number of mixing layers in the model.	`2`
`ff_dim`	`int`	number of units for the second feed-forward layer in the feature MLP.	`64`
`dropout`	`float`	dropout rate between (0, 1) .	`0.0`
`revin`	`bool`	if True uses Reverse Instance Normalization on `insample_y` and applies it to the outputs.	`True`
`loss`	`PyTorch module`	instantiated train loss class from losses collection.	`MAE()`
`valid_loss`	`PyTorch module`	instantiated valid loss class from losses collection.	`None`
`max_steps`	`int`	maximum number of training steps.	`1000`
`learning_rate`	`float`	Learning rate between (0, 1).	`0.001`
`num_lr_decays`	`int`	Number of learning rate decays, evenly distributed across max_steps.	`-1`
`early_stop_patience_steps`	`int`	Number of validation iterations before early stopping.	`-1`
`val_check_steps`	`int`	Number of training steps between every validation loss check.	`100`
`batch_size`	`int`	number of different series in each batch.	`32`
`valid_batch_size`	`int`	number of different series in each validation and test batch, if None uses batch_size.	`None`
`windows_batch_size`	`int`	number of windows to sample in each training batch.	`32`
`inference_windows_batch_size`	`int`	number of windows to sample in each inference batch, -1 uses all.	`32`
`start_padding_enabled`	`bool`	if True, the model will pad the time series with zeros at the beginning, by input size.	`False`
`training_data_availability_threshold`	`Union[float, List[float]]`	minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).	`0.0`
`step_size`	`int`	step size between each window of temporal data.	`1`
`scaler_type`	`str`	type of scaler for temporal inputs normalization see temporal scalers.	`‘identity’`
`random_seed`	`int`	random_seed for pytorch initializer and numpy generators.	`1`
`drop_last_loader`	`bool`	if True `TimeSeriesDataLoader` drops last non-full batch.	`False`
`alias`	`str`	optional, Custom name of the model.	`None`
`optimizer`	`Subclass of ‘torch.optim.Optimizer’`	optional, user specified optimizer instead of the default choice (Adam).	`None`
`optimizer_kwargs`	`dict`	optional, list of parameters used by the user specified `optimizer`.	`None`
`lr_scheduler`	`Subclass of ‘torch.optim.lr_scheduler.LRScheduler’`	optional, user specified lr_scheduler instead of the default choice (StepLR).	`None`
`lr_scheduler_kwargs`	`dict`	optional, list of parameters used by the user specified `lr_scheduler`.	`None`
`dataloader_kwargs`	`dict`	optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`.	`None`
`**trainer_kwargs`	`int`	keyword trainer arguments inherited from PyTorch Lighning’s trainer.

`TSMixerx.fit`

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:

Name	Type	Description	Default
`dataset`	`TimeSeriesDataset`	NeuralForecast’s `TimeSeriesDataset`, see documentation.	required
`val_size`	`int`	Validation size for temporal cross-validation.	`0`
`random_seed`	`int`	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	`None`
`test_size`	`int`	Test size for temporal cross-validation.	`0`

Returns:

Type	Description
None

`TSMixerx.predict`

predict(
    dataset,
    test_size=None,
    step_size=1,
    random_seed=None,
    quantiles=None,
    h=None,
    explainer_config=None,
    **data_module_kwargs
)

Predict. Neural network prediction with PL’s Trainer execution of predict_step. Parameters:

Name	Type	Description	Default
`dataset`	`TimeSeriesDataset`	NeuralForecast’s `TimeSeriesDataset`, see documentation.	required
`test_size`	`int`	Test size for temporal cross-validation.	`None`
`step_size`	`int`	Step size between each window.	`1`
`random_seed`	`int`	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	`None`
`quantiles`	`list`	Target quantiles to predict.	`None`
`h`	`int`	Prediction horizon, if None, uses the model’s fitted horizon. Defaults to None.	`None`
`explainer_config`	`dict`	configuration for explanations.	`None`
`**data_module_kwargs`	`dict`	PL’s TimeSeriesDataModule args, see documentation.

Returns:

Type	Description
None

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 GMM

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='robust',
                max_steps=500,
                early_stop_patience_steps=-1,
                val_check_steps=5,
                learning_rate=1e-3,
                loss = GMM(n_components=10, weighted=True),
                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=='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-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['TSMixerx-lo-90'][-12:].values,
                 y2=plot_df['TSMixerx-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['TSMixerx-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()

2. Auxiliary Functions

2.1 Mixing layers

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

`MixingLayerWithStaticExogenous`

MixingLayerWithStaticExogenous(h, dropout, ff_dim, stat_input_size)

Bases: Module MixingLayerWithStaticExogenous

`MixingLayer`

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

Bases: Module MixingLayer

`FeatureMixing`

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

Bases: Module FeatureMixing

`TemporalMixing`

TemporalMixing(num_features, h, dropout)

Bases: Module TemporalMixing

2.2 Reversible InstanceNormalization

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

Getting Started

Capabilities

Tutorials

Use cases

API Reference

1. TSMixerx

`TSMixerx`

`TSMixerx.fit`

`TSMixerx.predict`

Usage Examples

2. Auxiliary Functions

2.1 Mixing layers

`MixingLayerWithStaticExogenous`

`MixingLayer`

`FeatureMixing`

`TemporalMixing`

2.2 Reversible InstanceNormalization

Getting Started

Capabilities

Tutorials

Use cases

API Reference

​1. TSMixerx

​TSMixerx

​TSMixerx.fit

​TSMixerx.predict

​Usage Examples

​2. Auxiliary Functions

​2.1 Mixing layers

​MixingLayerWithStaticExogenous

​MixingLayer

​FeatureMixing

​TemporalMixing

​2.2 Reversible InstanceNormalization

1. TSMixerx

`TSMixerx`

`TSMixerx.fit`

`TSMixerx.predict`

Usage Examples

2. Auxiliary Functions

2.1 Mixing layers

`MixingLayerWithStaticExogenous`

`MixingLayer`

`FeatureMixing`

`TemporalMixing`

2.2 Reversible InstanceNormalization