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The fastkqr package fits kernel quantile regression, non-crossing kernel quantile regression, and regularized linear quantile regression. Kernel methods currently support rbfdot and laplacedot. For parametric linear quantile regression, use qr().

The examples below use a small synthetic data set so that the vignette can run quickly during package checks.

library(fastkqr)
#> 
#> Attaching package: 'fastkqr'
#> The following object is masked from 'package:base':
#> 
#>     qr

set.seed(1)
x <- matrix(rnorm(80), 40, 2)
y <- sin(x[, 1]) + 0.5 * x[, 2] + rnorm(40, sd = 0.2)
lambda <- 10^seq(0, -2, length.out = 3)

Kernel Quantile Regression

kqr() estimates a kernel quantile regression model over a sequence of penalty values. The default kernel is rbfdot.

fit <- kqr(x, y, lambda = lambda, tau = 0.5)
coef_fit <- coef(fit)
pred_fit <- predict(fit, x, x[1:5, , drop = FALSE])
dim(coef_fit)
#> [1] 41  3
dim(pred_fit)
#> [1] 5 3

cv.kqr() performs cross-validation over the same lambda path.

foldid <- rep(1:3, length.out = nrow(x))
cv_fit <- cv.kqr(x, y, lambda = lambda, tau = 0.5, foldid = foldid)
cv_fit$lambda.min
#> [1] 0.01

Non-Crossing Kernel Quantile Regression

nckqr() estimates non-crossing kernel quantile regression across multiple quantile levels. The example below keeps the grid small.

tau <- c(0.25, 0.5, 0.75)
lambda1 <- 1
lambda2 <- lambda

fit_nc <- nckqr(
  x, y,
  lambda1 = lambda1,
  lambda2 = lambda2,
  tau = tau
)

coef_nc <- coef(fit_nc, s1 = lambda1, s2 = lambda2[1])
pred_nc <- predict(fit_nc, x, x[1:5, , drop = FALSE],
  s1 = lambda1, s2 = lambda2[1])
dim(coef_nc)
#> [1] 41  3  1
dim(pred_nc)
#> [1] 5 3 1

cv.nckqr() selects lambda2 for a fixed lambda1.

cv_fit_nc <- cv.nckqr(
  x, y,
  lambda1 = lambda1,
  lambda2 = lambda2,
  tau = tau,
  foldid = foldid
)
cv_fit_nc$lambda.min
#> [1] 0.01

Regularized Linear Quantile Regression

qr() fits a parametric linear quantile regression model. This function masks base::qr(); use base::qr() when base QR decomposition is needed.

fit_lqr <- qr(x, y, lambda = lambda, tau = 0.5)
coef_lqr <- coef(fit_lqr)
pred_lqr <- predict(fit_lqr, x[1:5, , drop = FALSE])
dim(coef_lqr)
#> [1] 3 3
dim(pred_lqr)
#> [1] 5 3

cv.qr() performs cross-validation for the linear model.

cv_fit_lqr <- cv.qr(x, y, lambda = lambda, tau = 0.5, foldid = foldid)
cv_fit_lqr$lambda.min
#> [1] 0.01

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.