qrsvm: Fits a quantile regression SVM based on the Pinball Loss

In ChingChuan-Chen/qrsvm: SVM Quantile Regression with the Pinball Loss

Description

Fits a quantile regression SVM based on the Pinball Loss

Usage

qrsvm(x, y, kernel = "rbfdot", cost = 1, tau = 0.95, sigma = 5,
  degree = 2, scale = 1, offset = 1, order = 1)

Arguments

x	An n X m matrix containing the predictors (n = number of observatiosn, m = number of predictors).
y	The Response onto which the qrsvm shall be fitted.
kernel	A string giving the type of kernels from kernelMatrix. Default value is "rbfdot" for Radial Basis Function Kernel. All Kernels except stringdot supported.
cost	The cost parameter see svm and kernelMatrix.
tau	The quantile that shall be estimated. 0<=tau<=1.
sigma, degree, scale, offset, order	A possible tuning parameter for specific Kernelfunctions, see rbfdot, polydot, vanilladot, tanhdot, laplacedot, besseldot or anovadot.

Details

There is no preimplemented scaling of the input variables which should be considered beforehand. Also optimization is based on "quadprog:solve.QP" function which can be considerably slow compared to other SVM implementations.

Value

An object of class "qrsvm".

References

"Nonparametric Quantile Regression" by I.Takeuchi, Q.V. Le, T. Sears, A.J. Smola (2004)

Examples

# data generation
n <- 200
x <- as.matrix(seq(-1.5, 1.5, length.out = n))
y <- rnorm(n) * (0.3 + abs(sin(x)))

# fit models
mod005 <- qrsvm(x, y, tau = 0.05)
mod050 <- qrsvm(x, y, tau = 0.5)
mod095 <- qrsvm(x, y, tau = 0.95)

# methods
print(mod050)
summary(mod050)
fittedDf <- data.frame(x, fitted05 = fitted(mod005), fitted50 = fitted(mod050),
                       fitted95 = fitted(mod095))
predict(mod050, c(-1, 0, 1))

# graph
library(ggplot2)
ggplot(data.frame(x, y), aes(x, y)) + geom_point() +
  geom_line(aes(x, fitted05, colour = "P05"), fittedDf) +
  geom_line(aes(x, fitted50, colour = "P50"), fittedDf) +
  geom_line(aes(x, fitted95, colour = "P95"), fittedDf) +
  labs(colour = expression(tau))

ChingChuan-Chen/qrsvm documentation built on May 17, 2019, 12:48 p.m.