Extremal Random Forests

The package erf implements the extremal random forests (ERF), an algorithm to predict extreme conditional quantiles in large dimensions. For more details see Gnecco, Terefe, and Engelke (2023, https://arxiv.org/abs/2201.12865).

Installation

install.packages("erf")

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("nicolagnecco/erf")

Example

This basic example shows how to fit and predict conditional quantiles with erf.

library(erf)
library(ggplot2)
library(dplyr)

# Function to model scale
scale_step <- function(X) {
  ## numeric_vecotr -> numeric_vector
  ## produce scale function: scale(X) = step function

  sigma_x <- 1 + 1 * (X > 0)

  return(sigma_x)
}

# Generate data
set.seed(42)

n <- 2000
p <- 10
X <- matrix(runif(n * p, min = -1, max = 1), n, p)
Y <- scale_step(X[, 1]) * rnorm(n)

# Fit ERF
fit_erf <- erf(X, Y, intermediate_quantile = 0.8)

# Predict ERF
quantiles <- c(0.9, 0.99)
pred_erf <- predict(fit_erf, newdata = X, quantiles = quantiles)

true_quantiles <- matrix(rep(qnorm(quantiles), n), 
                         ncol = length(quantiles),
                         byrow = TRUE) * scale_step(X[, 1])

# Plot results
my_palette <- list(
  "red" = "#D55E00",
  "blue" = "#0072B2"
)

ggplot() +
  geom_point(aes(x = X[, 1], y = Y), alpha = .5, col = "grey") +
  geom_point(aes(x = X[, 1], y = pred_erf[, 2]), alpha = .5, 
             col = my_palette$blue) +
  geom_line(aes(x = X[, 1], y = true_quantiles[, 2]), col = my_palette$red, 
            linetype = "dashed", size = 1) +
  theme_bw()
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
#> ℹ Please use `linewidth` instead.

References

Gnecco, Nicola, Edossa Merga Terefe, and Sebastian Engelke. 2023. “Extremal Random Forests.” https://arxiv.org/abs/2201.12865.