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Figure 1. Architecture of SOFTS. Figure 1. Architecture of SOFTS.

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1. TimeMixer

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TimeMixer

TimeMixer(
    h,
    input_size,
    n_series,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    d_model=32,
    d_ff=32,
    dropout=0.1,
    e_layers=4,
    top_k=5,
    decomp_method="moving_avg",
    moving_avg=25,
    channel_independence=0,
    down_sampling_layers=1,
    down_sampling_window=2,
    down_sampling_method="avg",
    use_norm=True,
    decoder_input_size_multiplier=0.5,
    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 TimeMixer Args: h (int): Forecast horizon. input_size (int): autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2]. n_series (int): number of time-series. stat_exog_list (list): static exogenous columns. hist_exog_list (list): historic exogenous columns. futr_exog_list (list): future exogenous columns. d_model (int): dimension of the model. d_ff (int): dimension of the fully-connected network. dropout (float): dropout rate. e_layers (int): number of encoder layers. top_k (int): number of selected frequencies. decomp_method (str): method of series decomposition [moving_avg, dft_decomp]. moving_avg (int): window size of moving average. channel_independence (int): 0: channel dependence, 1: channel independence. down_sampling_layers (int): number of downsampling layers. down_sampling_window (int): size of downsampling window. down_sampling_method (str): down sampling method [avg, max, conv]. use_norm (bool): whether to normalize or not. decoder_input_size_multiplier (float): 0.5. loss (PyTorch module): instantiated train loss class from losses collection. valid_loss (PyTorch module): instantiated valid loss class from losses collection. max_steps (int): maximum number of training steps. learning_rate (float): Learning rate between (0, 1). num_lr_decays (int): Number of learning rate decays, evenly distributed across max_steps. early_stop_patience_steps (int): Number of validation iterations before early stopping. val_check_steps (int): Number of training steps between every validation loss check. batch_size (int): number of different series in each batch. valid_batch_size (int): number of different series in each validation and test batch, if None uses batch_size. windows_batch_size (int): number of windows to sample in each training batch, default uses all. inference_windows_batch_size (int): number of windows to sample in each inference batch, -1 uses all. start_padding_enabled (bool): if True, the model will pad the time series with zeros at the beginning, by input size. 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). step_size (int): step size between each window of temporal data. scaler_type (str): type of scaler for temporal inputs normalization see temporal scalers. random_seed (int): random_seed for pytorch initializer and numpy generators. drop_last_loader (bool): 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 (keyword): trainer arguments inherited from PyTorch Lighning’s trainer.

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TimeMixer.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:
NameTypeDescriptionDefault
datasetTimeSeriesDatasetNeuralForecast’s TimeSeriesDataset, see documentation.required
val_sizeintValidation size for temporal cross-validation.0
random_seedintRandom seed for pytorch initializer and numpy generators, overwrites model.init’s.None
test_sizeintTest size for temporal cross-validation.0
Returns:
TypeDescription
None

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TimeMixer.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:
NameTypeDescriptionDefault
datasetTimeSeriesDatasetNeuralForecast’s TimeSeriesDataset, see documentation.required
test_sizeintTest size for temporal cross-validation.None
step_sizeintStep size between each window.1
random_seedintRandom seed for pytorch initializer and numpy generators, overwrites model.init’s.None
quantileslistTarget quantiles to predict.None
hintPrediction horizon, if None, uses the model’s fitted horizon. Defaults to None.None
explainer_configdictconfiguration for explanations.None
**data_module_kwargsdictPL’s TimeSeriesDataModule args, see documentation.
Returns:
TypeDescription
None

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Usage example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import TimeMixer
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 = TimeMixer(h=12,
                input_size=24,
                n_series=2,
                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='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['TimeMixer'], c='blue', label='median')
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['TimeMixer'], 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()

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2. Auxiliary Functions

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2.1 Embedding

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DataEmbedding_wo_pos

DataEmbedding_wo_pos(c_in, d_model, dropout=0.1, embed_type='fixed', freq='h')
Bases: Module DataEmbedding_wo_pos

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DFT_series_decomp

DFT_series_decomp(top_k)
Bases: Module Series decomposition block

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2.2 Mixing

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PastDecomposableMixing

PastDecomposableMixing(
    seq_len,
    pred_len,
    down_sampling_window,
    down_sampling_layers,
    d_model,
    dropout,
    channel_independence,
    decomp_method,
    d_ff,
    moving_avg,
    top_k,
)
Bases: Module PastDecomposableMixing

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MultiScaleTrendMixing

MultiScaleTrendMixing(seq_len, down_sampling_window, down_sampling_layers)
Bases: Module Top-down mixing trend pattern

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MultiScaleSeasonMixing

MultiScaleSeasonMixing(seq_len, down_sampling_window, down_sampling_layers)
Bases: Module Bottom-up mixing season pattern