README.Rmd

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# EQRN: Extreme Quantile Regression Neural Networks for Conditionnal Risk Prediction

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EQRN is a framework for forecasting and extrapolating measures of conditional risk (e.g. of extreme or unprecedented events), 
including quantiles and exceedance probabilities, using extreme value statistics and flexible neural network architectures. 
It allows for capturing complex multivariate dependencies, including dependencies between observations, such as sequential (time) dependence.
This implementation is based on the methodology introduced in [Pasche and Engelke (2024)](#references-and-links) 
[[doi](https://doi.org/10.1214/24-AOAS1907), [pdf](https://raw.githubusercontent.com/opasche/EQRN_Results/main/article/24-AOAS1907.pdf), [suppl.](https://raw.githubusercontent.com/opasche/EQRN_Results/main/article/aoas1907suppa.pdf)]. 

## Installation

To install EQRN from CRAN, simply run from R:

``` r
install.packages("EQRN")
```

Or, to install the development version of EQRN, run:

``` r
# install.packages("devtools")
devtools::install_github("opasche/EQRN")
```

When the package is first loaded interactively after installation (e.g. with `library(EQRN)` or with any `EQRN::fct()`), 
you'll be prompted to allow the automatic installation of the necessary backend software (LibTorch and LibLantern) for the [`torch`](https://torch.mlverse.org/) dependency. 
Alternatively, `EQRN::install_backend()` can be called to perform the backend installation manually (necessary for non-interactive environments). 
For more information about the torch backends and troubleshooting, visit the [torch installation guide](https://torch.mlverse.org/docs/articles/installation).


## Motivation

Risk assessment for extreme events requires accurate estimation of high quantiles that go beyond the range of historical observations. When the risk depends on the values of observed predictors, regression techniques are used to interpolate in the predictor space. In this package we propose the EQRN model that combines tools from neural networks and extreme value theory into a method capable of extrapolation in the presence of complex predictor dependence. Neural networks can naturally incorporate additional structure in the data. The recurrent version of EQRN is able to capture complex sequential dependence in time series. 

In [the corresponding article](https://doi.org/10.1214/24-AOAS1907), EQRN is applied to forecasting of flood risk in the Swiss Aare catchment. It exploits information from multiple covariates in space and time to provide one-day-ahead predictions of return levels and exceedances probabilities. This output complements the static return level from a traditional extreme value analysis and the predictions are able to adapt to distributional shifts as experienced in a changing climate. Our model can help authorities to manage flooding more effectively and to minimize their disastrous impacts through early warning systems.


## Basic usage example for exchangeable data


The minimal example below illustrates, in three simple steps, how to use the package functions to fit the EQRN model and predict extreme conditional quantiles and other metrics on new test data. In this example, a toy i.i.d. dataset is used.



### 0. Generate a toy dataset

```{r data}
scale_fct <- function(x1,x2){ 3 + cos(x1 + x2 + 0.5) }

set.seed(1)
X_train <- matrix(stats::runif(5120), ncol=2)
y_train <- scale_fct(X_train[,1], X_train[,2]) * stats::rt(2560, 4)

X_test <- matrix(stats::runif(2560), ncol=2)
```


### Step 1. Construct intermediate quantiles

This can be achieved with any suitable quantile regression method. We here use generalised random forests from the [`grf`](https://grf-labs.github.io/grf/) package, as they are very easy to use and already quite flexible. One could for example use a quantile regression neural network instead.

```{r intermediate}
library(grf)

# Choose an intermediate probability level.
interm_lvl <- 0.8

# Fit a GRF for quantile regression with 500 trees (the more the better) on the training set (with a seed for reproducibility).
fit_grf <- grf::quantile_forest(X_train, y_train, num.trees=1000, seed=21)

# Construct out-of-bag intermediate quantiles on the training set.
intermediateq_train <- predict(fit_grf, newdata=NULL, quantiles=c(interm_lvl))$predictions
```


### Step 2. Fit the tail model


Fit the EQRN network on the training set, with the intermediate quantiles as a varying threshold. Here:

- the argument `shape_fixed=TRUE` removes covariate dependence from the shape output,
- the argument `net_structure=c(5,5)` sets two hidden layers of 5 neurons each as an architecture,
- the network is trained for 100 epochs (with a seed for reproducibility).

```{r tail}
library(EQRN)

fit_eqrn <- EQRN_fit(X_train, y_train, intermediateq_train, interm_lvl,
                     shape_fixed=TRUE, net_structure=c(5,5), n_epochs=100, seed=42)
```

The arguments values are here arbitrarily chosen for illustration. 
As for any machine learning approach, hyperparameters should be tuned using set-aside validation data to obtain an accurate fit. 
Stopping criteria are also available for the number of fitting epochs. 
Refer to the [documentation](https://opasche.github.io/EQRN/reference/index.html#fitting-eqrn-tail-neural-networks) for a detailed description of the arguments, and to the [article's repository](https://github.com/opasche/EQRN_Results) for more advanced examples. 


### Step 3. Predict conditional quantiles and risk metrics for new test observations

```{r predictions}
# Desired probability levels at which to predict the conditional quantiles.
levels_predict <- c(0.999, 0.9999)

# Predict intermediate test quantiles using the intermediate model.
intermediateq_test <- predict(fit_grf, newdata=X_test, quantiles=c(interm_lvl))$predictions

# Predict the desired conditional extreme quantiles on the test set.
qpred_eqrn <- EQRN_predict(fit_eqrn, X_test, levels_predict, intermediateq_test)

# Forecast the probability that Y_test would exceed a certain large value.
large_value <- 10
ppred_eqrn <- EQRN_excess_probability(large_value, fit_eqrn, X_test, intermediateq_test)
```


```{r results}
# Print some predictions:
hn <- 10
results <- data.frame(X1=X_test[1:hn,1], X2=X_test[1:hn,2], pred_Y_Q_80=intermediateq_test[1:hn],
                      pred_Y_Q_99.9=qpred_eqrn[1:hn,1], pred_Y_Q_99.99=qpred_eqrn[1:hn,2], Pr_Y_exceed_10=ppred_eqrn[1:hn])

print(results)
```


## References and links

> Pasche, O. C. and Engelke, S. (2024). "Neural networks for extreme quantile regression with an application to forecasting of flood risk". <i>Annals of Applied Statistics</i> 18(4), 2818–2839. https://doi.org/10.1214/24-AOAS1907 

**Published article:** [DOI:10.1214/24-AOAS1907](https://doi.org/10.1214/24-AOAS1907) ([PDF](https://raw.githubusercontent.com/opasche/EQRN_Results/main/article/24-AOAS1907.pdf), [Supplement](https://raw.githubusercontent.com/opasche/EQRN_Results/main/article/aoas1907suppa.pdf)).  
**Article's usage examples:** <https://github.com/opasche/EQRN_Results>

Preprint (2022): [ArXiv:2208.07590](https://arxiv.org/abs/2208.07590) ([PDF](https://arxiv.org/pdf/2208.07590)).  


____

Package created by Olivier C. PASCHE  
Research Center for Statistics, University of Geneva (CH), 2022.  
Supported by the Swiss National Science Foundation.