# Cross-validation for KERE Does k-fold cross-validation for `KERE`, produces a plot, and returns a value for `lambda`. ```r ## S3 method for class 'KERE' cv(x, y, kern, lambda = NULL, nfolds = 5, foldid, omega = 0.5, ...) ``` ## Arguments - `x`: matrix of predictors, of dimension $N*p$; each row is an observation vector. - `y`: response variable. - `kern`: the built-in kernel classes in `KERE`. The `kern` parameter can be set to any function, of class kernel, which computes the inner product in feature space between two vector arguments. `KERE` provides the most popular kernel functions which can be initialized by using the following functions: * `rbfdot` Radial Basis kernel function, * `polydot` Polynomial kernel function, * `vanilladot` Linear kernel function, * `tanhdot` Hyperbolic tangent kernel function, * `laplacedot` Laplacian kernel function, * `besseldot` Bessel kernel function, * `anovadot` ANOVA RBF kernel function, * `splinedot` the Spline kernel. Objects can be created by calling the rbfdot, polydot, tanhdot, vanilladot, anovadot, besseldot, laplacedot, splinedot functions etc. (see example.) - `lambda`: a user supplied `lambda` sequence. It is better to supply a decreasing sequence of `lambda` values, if not, the program will sort user-defined `lambda` sequence in decreasing order automatically. - `nfolds`: number of folds - default is 5. Although `nfolds` can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is `nfolds=3`. - `foldid`: an optional vector of values between 1 and `nfold` identifying what fold each observation is in. If supplied, `nfold` can be missing. - `omega`: the parameter $omega$ in the expectile regression model. The value must be in (0,1). Default is 0.5. - ``...``: other arguments that can be passed to `KERE`. ## Details The function runs `KERE` `nfolds`+1 times; the first to get the `lambda` sequence, and then the remainder to compute the fit with each of the folds omitted. The average error and standard deviation over the folds are computed. ## Returns an object of class `cv.KERE` is returned, which is a list with the ingredients of the cross-validation fit. - **lambda**: the values of `lambda` used in the fits. - **cvm**: the mean cross-validated error - a vector of length `length(lambda)`. - **cvsd**: estimate of standard error of `cvm`. - **cvupper**: upper curve = `cvm+cvsd`. - **cvlo**: lower curve = `cvm-cvsd`. - **name**: a character string "Expectile Loss" - **lambda.min**: the optimal value of `lambda` that gives minimum cross validation error `cvm`. - **cvm.min**: the minimum cross validation error `cvm`. ## Author(s) Yi Yang, Teng Zhang and Hui Zou Maintainer: Yi Yang ## References Y. Yang, T. Zhang, and H. Zou. "Flexible Expectile Regression in Reproducing Kernel Hilbert Space." ArXiv e-prints: stat.ME/1508.05987, August 2015. ## Examples ```r N <- 200 X1 <- runif(N) X2 <- 2*runif(N) X3 <- 3*runif(N) SNR <- 10 # signal-to-noise ratio Y <- X1**1.5 + 2 * (X2**.5) + X1*X3 sigma <- sqrt(var(Y)/SNR) Y <- Y + X2*rnorm(N,0,sigma) X <- cbind(X1,X2,X3) # set gaussian kernel kern <- rbfdot(sigma=0.1) # define lambda sequence lambda <- exp(seq(log(0.5),log(0.01),len=10)) cv.KERE(x=X, y=Y, kern, lambda = lambda, nfolds = 5, omega = 0.5) ```

cv.KERE function