A user-friendly framework for forecasting and extrapolating extreme measures of conditional risk using flexible neural network architectures. It allows for capturing complex multivariate dependencies, including dependencies between observations, such as sequential dependence (time-series). The implementation is based on the article “Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk” by Olivier C. Pasche and Sebastian Engelke (ArXiv:2208.07590).
Installation
To install the development version of EQRN, simply run from R:
# install.packages("devtools")
devtools::install_github("opasche/EQRN")When the package is first loaded after installation (e.g. with library(EQRN) or EQRN::fct()), the necessary backend software from the torch dependency is automatically installed. (Alternatively, EQRN::install_backend() can be called to perform the backend installation manually.) For more information about the torch backend and troubleshooting, visit the torch installation guide.
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, 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 example below shows in three simple steps how 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.
Step 1. Construct intermediate quantiles
This can be achieved with any suitable quantile regression method. We here use generalised random forests from the grf package, as they are very easy to use and already quite flexible. One could for example use a quantile regression neural network instead.
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))$predictionsStep 2. Fit the tail model
Fit the EQRN network on the training set, with the intermediate quantiles as a varying threshold. Here:
- the argument
shape_fixed=TRUEremoves covariate dependence from the shape output, - the argument
net_structure=c(5,5)sets two hidden layers of 5 neurons each as an architecture, - the network is trained for 100 epochs (with a seed for reproducibility).
Step 3. Predict conditional quantiles and risk metrics for new test observations
# Desired probability levels at which to predict the conditional quantiles.
levels_predict <- c(0.999, 0.9999)
# Predict intermediate test quantiles using the intermediate model.
intermediateq_test <- predict(fit_grf, newdata=X_test, quantiles=c(interm_lvl))$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)
# 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)
#> X1 X2 pred_Y_Q_80 pred_Y_Q_99.9 pred_Y_Q_99.99 Pr_Y_exceed_10
#> 1 0.5876351 0.83797214 2.741546 15.87502 33.91469 0.004054095
#> 2 0.9493471 0.74616973 2.123687 15.33688 33.48605 0.003427602
#> 3 0.7456916 0.24237508 2.698117 15.73987 33.65356 0.003939998
#> 4 0.2319869 0.70261432 3.041587 15.96008 33.70446 0.004288765
#> 5 0.7706744 0.19874048 4.725495 18.06010 36.37603 0.008155741
#> 6 0.7746018 0.03440777 5.414535 18.79252 37.16805 0.010750530
#> 7 0.7776956 0.33728896 3.136478 16.29012 34.35749 0.004594990
#> 8 0.2586140 0.49574342 3.457248 16.39834 34.17376 0.004917901
#> 9 0.7935616 0.60815766 2.557475 15.71578 33.78956 0.003852441
#> 10 0.1613134 0.52083200 2.045515 14.71575 32.11914 0.003049184Package created by Olivier C. PASCHE
Research Center for Statistics, University of Geneva (CH), 2022.
Supported by the Swiss National Science Foundation.