> ## Documentation Index
> Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt
> Use this file to discover all available pages before exploring further.
> DeepAR: Probabilistic autoregressive RNN for forecasting. Uses Monte Carlo sampling with distribution outputs for uncertainty quantification in time series.
# DeepAR
The DeepAR model produces probabilistic forecasts based on an
autoregressive recurrent neural network optimized on panel data using
cross-learning. DeepAR obtains its forecast distribution uses a Markov
Chain Monte Carlo sampler with the following conditional probability:
$\mathbb{P}(\mathbf{y}_{[t+1:t+H]}|\;\mathbf{y}_{[:t]},\; \mathbf{x}^{(f)}_{[:t+H]},\; \mathbf{x}^{(s)})$
where $\mathbf{x}^{(s)}$ are static exogenous inputs,
$\mathbf{x}^{(f)}_{[:t+H]}$ are future exogenous available at the time
of the prediction. The predictions are obtained by transforming the
hidden states $\mathbf{h}_{t}$ into predictive distribution parameters
$\theta_{t}$, and then generating samples $\mathbf{\hat{y}}_{[t+1:t+H]}$
through Monte Carlo sampling trajectories.
$$
\begin{align}
\mathbf{h}_{t} &= \textrm{RNN}([\mathbf{y}_{t},\mathbf{x}^{(f)}_{t+1},\mathbf{x}^{(s)}], \mathbf{h}_{t-1})\\
\mathbf{\theta}_{t}&=\textrm{Linear}(\mathbf{h}_{t}) \\
\hat{y}_{t+1}&=\textrm{sample}(\;\mathrm{P}(y_{t+1}\;|\;\mathbf{\theta}_{t})\;)
\end{align}
$$
**References**
* [David Salinas, Valentin Flunkert, Jan Gasthaus,
Tim Januschowski (2020). “DeepAR: Probabilistic forecasting with
autoregressive recurrent networks”. International Journal of
Forecasting.](https://www.sciencedirect.com/science/article/pii/S0169207019301888)
* [Alexander Alexandrov et. al (2020). “GluonTS: Probabilistic and Neural
Time Series Modeling in Python”. Journal of Machine Learning
Research.](https://www.jmlr.org/papers/v21/19-820.html)
> **Exogenous Variables, Losses, and Parameters Availability**
>
> Given the sampling procedure during inference, DeepAR only supports
> [`DistributionLoss`](./losses.pytorch.html#distributionloss)
> as training loss.
>
> Note that DeepAR generates a non-parametric forecast distribution
> using Monte Carlo. We use this sampling procedure also during
> validation to make it closer to the inference procedure. Therefore,
> only the
> [`MQLoss`](./losses.pytorch.html#mqloss)
> is available for validation.
>
> Aditionally, Monte Carlo implies that historic exogenous variables are
> not available for the model.
*Figure 1. DeepAR model, during training
the optimization signal comes from likelihood of observations, during
inference a recurrent multi-step strategy is used to generate predictive
distributions.*
## 1. DeepAR
### `DeepAR`
```python theme={null}
DeepAR(
h,
input_size=-1,
h_train=1,
lstm_n_layers=2,
lstm_hidden_size=128,
lstm_dropout=0.1,
decoder_hidden_layers=0,
decoder_hidden_size=0,
trajectory_samples=100,
stat_exog_list=None,
hist_exog_list=None,
futr_exog_list=None,
exclude_insample_y=False,
loss=DistributionLoss(
distribution="StudentT", level=[80, 90], return_params=False
),
valid_loss=MAE(),
max_steps=1000,
learning_rate=0.001,
num_lr_decays=3,
early_stop_patience_steps=-1,
val_monitor="ptl/val_loss",
val_check_steps=100,
batch_size=32,
valid_batch_size=None,
windows_batch_size=1024,
inference_windows_batch_size=-1,
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](#neuralforecast.common._base_model.BaseModel)
DeepAR
**Parameters:**
| Name | Type | Description | Default |
| -------------------------------------- | ------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------------------------------------------ |
| `h` | [int](#int) | Forecast horizon. | *required* |
| `input_size` | [int](#int) | maximum sequence length for truncated train backpropagation. Default -1 uses 3 \* horizon | -1 |
| `h_train` | [int](#int) | maximum sequence length for truncated train backpropagation. Default 1. | 1 |
| `lstm_n_layers` | [int](#int) | number of LSTM layers. | 2 |
| `lstm_hidden_size` | [int](#int) | LSTM hidden size. | 128 |
| `lstm_dropout` | [float](#float) | LSTM dropout. | 0.1 |
| `decoder_hidden_layers` | [int](#int) | number of decoder MLP hidden layers. Default: 0 for linear layer. | 0 |
| `decoder_hidden_size` | [int](#int) | decoder MLP hidden size. Default: 0 for linear layer. | 0 |
| `trajectory_samples` | [int](#int) | number of Monte Carlo trajectories during inference. | 100 |
| `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](#bool) | the model skips the autoregressive features y\[t-input\_size:t] if True. | False |
| `loss` | PyTorch module | instantiated train loss class from [losses collection](./losses.pytorch.html). | [DistributionLoss](#neuralforecast.losses.pytorch.DistributionLoss)(distribution='StudentT', level=\[80, 90], return\_params=False) |
| `valid_loss` | PyTorch module | instantiated valid loss class from [losses collection](./losses.pytorch.html). | [MAE](#neuralforecast.losses.pytorch.MAE)() |
| `max_steps` | [int](#int) | maximum number of training steps. | 1000 |
| `learning_rate` | [float](#float) | Learning rate between (0, 1). | 0.001 |
| `num_lr_decays` | [int](#int) | Number of learning rate decays, evenly distributed across max\_steps. | 3 |
| `early_stop_patience_steps` | [int](#int) | Number of validation iterations before early stopping. | -1 |
| `val_monitor` | [str](#str) | metric to monitor for early stopping. Valid options: "ptl/val\_loss", "valid\_loss", "train\_loss". Default: "ptl/val\_loss". | 'ptl/val\_loss' |
| `val_check_steps` | [int](#int) | Number of training steps between every validation loss check. | 100 |
| `batch_size` | [int](#int) | number of different series in each batch. | 32 |
| `valid_batch_size` | [int](#int) | number of different series in each validation and test batch, if None uses batch\_size. | None |
| `windows_batch_size` | [int](#int) | number of windows to sample in each training batch, default uses all. | 1024 |
| `inference_windows_batch_size` | [int](#int) | number of windows to sample in each inference batch, -1 uses all. | -1 |
| `start_padding_enabled` | [bool](#bool) | if True, the model will pad the time series with zeros at the beginning, by input size. | False |
| `training_data_availability_threshold` | [Union](#Union)\[[float](#float), [List](#List)\[[float](#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](#int) | step size between each window of temporal data. | 1 |
| `scaler_type` | [str](#str) | type of scaler for temporal inputs normalization see [temporal scalers](https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/common/_scalers.py). | 'identity' |
| `random_seed` | [int](#int) | random\_seed for pytorch initializer and numpy generators. | 1 |
| `drop_last_loader` | [bool](#bool) | if True `TimeSeriesDataLoader` drops last non-full batch. | False |
| `alias` | [str](#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](#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](#dict) | optional, list of parameters used by the user specified `lr_scheduler`. | None |
| `dataloader_kwargs` | [dict](#dict) | optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`. | None |
| `**trainer_kwargs` | [int](#int) | keyword trainer arguments inherited from [PyTorch Lighning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer). | {} |
References
* [David Salinas, Valentin Flunkert, Jan Gasthaus, Tim Januschowski (2020). "DeepAR: Probabilistic forecasting with autoregressive recurrent networks". International Journal of Forecasting.](https://www.sciencedirect.com/science/article/pii/S0169207019301888)
* [Alexander Alexandrov et. al (2020). "GluonTS: Probabilistic and Neural Time Series Modeling in Python". Journal of Machine Learning Research.](https://www.jmlr.org/papers/v21/19-820.html)
#### `DeepAR.fit`
```python theme={null}
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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).
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](#TimeSeriesDataset) | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `val_size` | [int](#int) | Validation size for temporal cross-validation. | 0 |
| `random_seed` | [int](#int) | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | None |
| `test_size` | [int](#int) | Test size for temporal cross-validation. | 0 |
**Returns:**
| Type | Description |
| ---- | ----------- |
| None | |
#### `DeepAR.predict`
```python theme={null}
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](#TimeSeriesDataset) | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `test_size` | [int](#int) | Test size for temporal cross-validation. | None |
| `step_size` | [int](#int) | Step size between each window. | 1 |
| `random_seed` | [int](#int) | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | None |
| `quantiles` | [list](#list) | Target quantiles to predict. | None |
| `h` | [int](#int) | Prediction horizon, if None, uses the model's fitted horizon. Defaults to None. | None |
| `explainer_config` | [dict](#dict) | configuration for explanations. | None |
| `**data_module_kwargs` | [dict](#dict) | PL's TimeSeriesDataModule args, see [documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule). | {} |
**Returns:**
| Type | Description |
| ---- | ----------- |
| None | |
### Usage Example
```python theme={null}
import pandas as pd
import matplotlib.pyplot as plt
from neuralforecast import NeuralForecast
from neuralforecast.models import DeepAR
from neuralforecast.losses.pytorch import DistributionLoss, MQLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
Y_train_df = AirPassengersPanel[AirPassengersPanel.ds=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test
nf = NeuralForecast(
models=[DeepAR(h=12,
input_size=24,
lstm_n_layers=1,
trajectory_samples=100,
loss=DistributionLoss(distribution='StudentT', level=[80, 90], return_params=True),
valid_loss=MQLoss(level=[80, 90]),
learning_rate=0.005,
stat_exog_list=['airline1'],
futr_exog_list=['trend'],
max_steps=100,
val_check_steps=10,
early_stop_patience_steps=-1,
scaler_type='standard',
enable_progress_bar=True,
),
],
freq='ME'
)
nf.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
Y_hat_df = nf.predict(futr_df=Y_test_df)
# Plot quantile predictions
Y_hat_df = Y_hat_df.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['DeepAR-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:],
y1=plot_df['DeepAR-lo-90'][-12:].values,
y2=plot_df['DeepAR-hi-90'][-12:].values,
alpha=0.4, label='level 90')
plt.legend()
plt.grid()
plt.plot()
```
## 2. Auxiliary functions