In SvenKlaassen/qboost: Quantile Boosting for High-Dimensions

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

knitr::opts_chunk$set(
 fig.width = 6,
 fig.asp = 0.8,
 out.width = "80%",
 fig.align = "center"
)

Installation

To install development version from GitHub, run the following commands:

# install.packages("devtools")
remotes::install_github("SvenKlaassen/qboost")

A simple Example

We generate data from a basic linear model $$ Y = \beta_0 + X^T\beta +\epsilon,$$ where $\beta_0=1$ and $\epsilon\sim t_2$. To account for a high-dimensional setting, we only generate $n = 200$ observations, whereas the covariates $X$ are generated from a standard multivariate gaussian distribution of dimension $p = 500$. The coefficient vector is set to $$ \beta_j = \begin{cases} 1,\quad j = 1,\dots s\ 0,\quad j = s+1,\dots,p\end{cases},$$ such that the first $s$ components are relevant.

library(MASS)
set.seed(42)
n <- 200; p <- 500; s <- 4
beta <- rep(c(1,0),c(s+1,p-s))

X = mvrnorm(n, rep(0, p), diag(p))
epsilon = rt(n, 2)
Y = cbind(1, X) %*% beta + epsilon

We can employ the crossvalidated version of the quantile boosting algorithm (here with $400$ steps). The autoplot method plots the crossvalidated loss against the check loss (and the smoothed version). Here, the loss is calculated on the training set.

library(qboost)
library(ggplot2)
model <- cv_qboost(X,Y, tau = 0.5, m_stop = 400,
                   h = 0.2, kernel = "Gaussian", stepsize = 0.1)
autoplot(model, new_Y = Y, newdata = X)

To predict new values one can use the predict method.

head(predict(model, newdata = X))

For the crossvalidated version the prediction is based on the Step with the smallest crossvalidated loss. This can be adjusted manually

head(predict(model, newdata = X, step = 0))

SvenKlaassen/qboost documentation built on Nov. 8, 2022, 12:13 p.m.