PatchTST

The PatchTST model is an efficient Transformer-based model for multivariate time series forecasting.

It is based on two key components: - segmentation of time series into windows (patches) which are served as input tokens to Transformer - channel-independence. where each channel contains a single univariate time series.

References
- Nie, Y., Nguyen, N. H., Sinthong, P., & Kalagnanam, J. (2022). “A Time Series is Worth 64 Words: Long-term Forecasting with Transformers”

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1. Backbone

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Auxiliary Functions

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get_activation_fn

 get_activation_fn (activation)

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Transpose

 Transpose (*dims, contiguous=False)

Transpose

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Positional Encoding

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positional_encoding

 positional_encoding (pe, learn_pe, q_len, hidden_size)

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Coord1dPosEncoding

 Coord1dPosEncoding (q_len, exponential=False, normalize=True)

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Coord2dPosEncoding

 Coord2dPosEncoding (q_len, hidden_size, exponential=False,
                     normalize=True, eps=0.001)

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PositionalEncoding

 PositionalEncoding (q_len, hidden_size, normalize=True)

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Encoder

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TSTEncoderLayer

 TSTEncoderLayer (q_len, hidden_size, n_heads, d_k=None, d_v=None,
                  linear_hidden_size=256, store_attn=False,
                  norm='BatchNorm', attn_dropout=0, dropout=0.0,
                  bias=True, activation='gelu', res_attention=False,
                  pre_norm=False)

TSTEncoderLayer

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TSTEncoder

 TSTEncoder (q_len, hidden_size, n_heads, d_k=None, d_v=None,
             linear_hidden_size=None, norm='BatchNorm', attn_dropout=0.0,
             dropout=0.0, activation='gelu', res_attention=False,
             n_layers=1, pre_norm=False, store_attn=False)

TSTEncoder

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TSTiEncoder

 TSTiEncoder (c_in, patch_num, patch_len, max_seq_len=1024, n_layers=3,
              hidden_size=128, n_heads=16, d_k=None, d_v=None,
              linear_hidden_size=256, norm='BatchNorm', attn_dropout=0.0,
              dropout=0.0, act='gelu', store_attn=False,
              key_padding_mask='auto', padding_var=None, attn_mask=None,
              res_attention=True, pre_norm=False, pe='zeros',
              learn_pe=True)

TSTiEncoder

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Flatten_Head

 Flatten_Head (individual, n_vars, nf, h, c_out, head_dropout=0)

Flatten_Head

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PatchTST_backbone

 PatchTST_backbone (c_in:int, c_out:int, input_size:int, h:int,
                    patch_len:int, stride:int,
                    max_seq_len:Optional[int]=1024, n_layers:int=3,
                    hidden_size=128, n_heads=16, d_k:Optional[int]=None,
                    d_v:Optional[int]=None, linear_hidden_size:int=256,
                    norm:str='BatchNorm', attn_dropout:float=0.0,
                    dropout:float=0.0, act:str='gelu',
                    key_padding_mask:str='auto',
                    padding_var:Optional[int]=None,
                    attn_mask:Optional[torch.Tensor]=None,
                    res_attention:bool=True, pre_norm:bool=False,
                    store_attn:bool=False, pe:str='zeros',
                    learn_pe:bool=True, fc_dropout:float=0.0,
                    head_dropout=0, padding_patch=None,
                    pretrain_head:bool=False, head_type='flatten',
                    individual=False, revin=True, affine=True,
                    subtract_last=False)

PatchTST_backbone

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2. Model

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PatchTST

 PatchTST (h, input_size, stat_exog_list=None, hist_exog_list=None,
           futr_exog_list=None, exclude_insample_y=False,
           encoder_layers:int=3, n_heads:int=16, hidden_size:int=128,
           linear_hidden_size:int=256, dropout:float=0.2,
           fc_dropout:float=0.2, head_dropout:float=0.0,
           attn_dropout:float=0.0, patch_len:int=16, stride:int=8,
           revin:bool=True, revin_affine:bool=False,
           revin_subtract_last:bool=True, activation:str='gelu',
           res_attention:bool=True, batch_normalization:bool=False,
           learn_pos_embed:bool=True, loss=MAE(), valid_loss=None,
           max_steps:int=5000, learning_rate:float=0.0001,
           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=1024,
           inference_windows_batch_size:int=1024,
           start_padding_enabled=False, 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)

*PatchTST

The PatchTST model is an efficient Transformer-based model for multivariate time series forecasting.

It is based on two key components: - segmentation of time series into windows (patches) which are served as input tokens to Transformer - channel-independence, where each channel contains a single univariate time series.

Parameters:
h: int, Forecast horizon.
input_size: int, autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].
stat_exog_list: str list, static exogenous columns.
hist_exog_list: str list, historic exogenous columns.
futr_exog_list: str list, future exogenous columns.
exclude_insample_y: bool=False, the model skips the autoregressive features y[t-input_size:t] if True.
encoder_layers: int, number of layers for encoder.
n_heads: int=16, number of multi-head’s attention.
hidden_size: int=128, units of embeddings and encoders.
linear_hidden_size: int=256, units of linear layer.
dropout: float=0.1, dropout rate for residual connection.
fc_dropout: float=0.1, dropout rate for linear layer.
head_dropout: float=0.1, dropout rate for Flatten head layer.
attn_dropout: float=0.1, dropout rate for attention layer.
patch_len: int=32, length of patch. Note: patch_len = min(patch_len, input_size + stride).
stride: int=16, stride of patch.
revin: bool=True, bool to use RevIn.
revin_affine: bool=False, bool to use affine in RevIn.
revin_substract_last: bool=False, bool to use substract last in RevIn.
activation: str=‘ReLU’, activation from [‘gelu’,‘relu’].
res_attention: bool=False, bool to use residual attention.
batch_normalization: bool=False, bool to use batch normalization.
learn_pos_embedding: bool=True, bool to learn positional embedding.
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=1024, number of windows to sample in each training batch, default uses all.
inference_windows_batch_size: int=1024, number of windows to sample in each inference batch.
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, 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:
-Nie, Y., Nguyen, N. H., Sinthong, P., & Kalagnanam, J. (2022). “A Time Series is Worth 64 Words: Long-term Forecasting with Transformers”*

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PatchTST.fit

 PatchTST.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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PatchTST.predict

 PatchTST.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.
random_seed: int=None, random_seed for pytorch initializer and numpy generators, overwrites model.__init__’s.
**data_module_kwargs: PL’s TimeSeriesDataModule args, see documentation.*

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Usage example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import PatchTST
from neuralforecast.losses.pytorch import DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic, augment_calendar_df

AirPassengersPanel, calendar_cols = augment_calendar_df(df=AirPassengersPanel, freq='M')

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

model = PatchTST(h=12,
                 input_size=104,
                 patch_len=24,
                 stride=24,
                 revin=False,
                 hidden_size=16,
                 n_heads=4,
                 scaler_type='robust',
                 loss=DistributionLoss(distribution='StudentT', level=[80, 90]),
                 #loss=MAE(),
                 learning_rate=1e-3,
                 max_steps=500,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

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

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])

if model.loss.is_distribution_output:
    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['PatchTST-median'], c='blue', label='median')
    plt.fill_between(x=plot_df['ds'][-12:], 
                    y1=plot_df['PatchTST-lo-90'][-12:].values, 
                    y2=plot_df['PatchTST-hi-90'][-12:].values,
                    alpha=0.4, label='level 90')
    plt.grid()
    plt.legend()
    plt.plot()
else:
    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['PatchTST'], c='blue', label='Forecast')
    plt.legend()
    plt.grid()