Getting Started with fastkqr

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