Extremal Random Forests

The package erf implements the extremal random forests (ERF), an algorithm to predict extreme conditional quantiles in large dimensions.

Installation

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()