PatchTST

PatchTST: Efficient Transformer model for multivariate forecasting using patched time series and channel-independence for scalable long-term predictions.

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”

Figure 1. PatchTST.

1. PatchTST

PatchTST

PatchTST(
    h,
    input_size,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    exclude_insample_y=False,
    encoder_layers=3,
    n_heads=16,
    hidden_size=128,
    linear_hidden_size=256,
    dropout=0.2,
    fc_dropout=0.2,
    head_dropout=0.0,
    attn_dropout=0.0,
    patch_len=16,
    stride=8,
    revin=True,
    revin_affine=False,
    revin_subtract_last=True,
    activation="gelu",
    res_attention=True,
    batch_normalization=False,
    learn_pos_embed=True,
    loss=MAE(),
    valid_loss=None,
    max_steps=5000,
    learning_rate=0.0001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=1024,
    inference_windows_batch_size=1024,
    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

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:

Name	Type	Description	Default
h	int	forecast horizon.	required
input_size	int	autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].	required
stat_exog_list	str list	static exogenous columns.	None
hist_exog_list	str list	historic exogenous columns.	None
futr_exog_list	str list	future exogenous columns.	None
exclude_insample_y	bool	the model skips the autoregressive features y[t-input_size:t] if True.	False
encoder_layers	int	number of layers for encoder.	3
n_heads	int	number of multi-head’s attention.	16
hidden_size	int	units of embeddings and encoders.	128
linear_hidden_size	int	units of linear layer.	256
dropout	float	dropout rate for residual connection.	0.2
fc_dropout	float	dropout rate for linear layer.	0.2
head_dropout	float	dropout rate for Flatten head layer.	0.0
attn_dropout	float	dropout rate for attention layer.	0.0
patch_len	int	length of patch. Note: patch_len = min(patch_len, input_size + stride).	16
stride	int	stride of patch.	8
revin	bool	bool to use RevIn.	True
revin_affine	bool	bool to use affine in RevIn.	False
revin_subtract_last	bool	bool to use substract last in RevIn.	True
activation	str	activation from [‘gelu’,‘relu’].	‘gelu’
res_attention	bool	bool to use residual attention.	True
batch_normalization	bool	bool to use batch normalization.	False
learn_pos_embed	bool	bool to learn positional embedding.	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.	5000
learning_rate	float	learning rate between (0, 1).	0.0001
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, default uses all.	1024
inference_windows_batch_size	int	number of windows to sample in each inference batch.	1024
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.

PatchTST.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

PatchTST.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 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]),
                 learning_rate=1e-3,
                 max_steps=500,
                 val_check_steps=50,
                 early_stop_patience_steps=2)

nf = NeuralForecast(
    models=[model],
    freq='ME'
)
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()

2. Backbone

Auxiliary Functions

get_activation_fn

get_activation_fn(activation)

Transpose

Transpose(*dims, contiguous=False)

Bases: Module

Transpose

Positional Encoding

positional_encoding

positional_encoding(pe, learn_pe, q_len, hidden_size)

Coord1dPosEncoding

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

Coord2dPosEncoding

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

PositionalEncoding

PositionalEncoding(q_len, hidden_size, normalize=True)

Encoder

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,
)

Bases: Module

TSTEncoderLayer

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,
)

Bases: Module

TSTEncoder

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,
)

Bases: Module

TSTiEncoder

Flatten_Head

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

Bases: Module

Flatten_Head

PatchTST_backbone

PatchTST_backbone(
    c_in,
    c_out,
    input_size,
    h,
    patch_len,
    stride,
    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",
    key_padding_mask="auto",
    padding_var=None,
    attn_mask=None,
    res_attention=True,
    pre_norm=False,
    store_attn=False,
    pe="zeros",
    learn_pe=True,
    fc_dropout=0.0,
    head_dropout=0,
    padding_patch=None,
    pretrain_head=False,
    head_type="flatten",
    individual=False,
    revin=True,
    affine=True,
    subtract_last=False,
)

Bases: Module

PatchTST_backbone