# make predictions from a "KERE" object. Similar to other predict methods, this functions predicts fitted values and class labels from a fitted `KERE` object. ```r ## S3 method for class 'KERE' predict(object, kern, x, newx,...) ``` ## Arguments - `object`: fitted `KERE` model object. - `kern`: the built-in kernel classes in `KERE`. Objects can be created by calling the rbfdot, polydot, tanhdot, vanilladot, anovadot, besseldot, laplacedot, splinedot functions etc. (see example.) - `x`: the original design matrix for training `KERE`. - `newx`: matrix of new values for `x` at which predictions are to be made. NOTE: `newx` must be a matrix with each row as an observation. `predict` function does not accept a vector or other formats of `newx`. - ``...``: other parameters to `predict` function. ## Details The fitted $\alpha_0 + K * \alpha$ at newx is returned as a size `nrow(newx)*length(lambda)` matrix for various lambda values where the `KERE` model was fitted. ## Returns The fitted $\alpha_0 + K * \alpha$ is returned as a size `nrow(newx)*length(lambda)` matrix. The row represents the index for observations of newx. The column represents the index for the lambda sequence. ## 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 # create data N <- 100 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)) # run KERE m1 <- KERE(x=X, y=Y, kern=kern, lambda = lambda, omega = 0.5) # create newx for prediction N1 <- 5 X1 <- runif(N1) X2 <- 2*runif(N1) X3 <- 3*runif(N1) newx <- cbind(X1,X2,X3) # make prediction p1 <- predict.KERE(m1, kern, X, newx) p1 ```

predict.KERE function