PatchTST - Nixtla

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

​1. PatchTST

​PatchTST

​PatchTST.fit

​PatchTST.predict

​Usage example

​2. Backbone

​Auxiliary Functions

​get_activation_fn

​Transpose

​Positional Encoding

​positional_encoding

​Coord1dPosEncoding

​Coord2dPosEncoding

​PositionalEncoding

​Encoder

​TSTEncoderLayer

​TSTEncoder

​TSTiEncoder

​Flatten_Head

​PatchTST_backbone