KRLS (version 0.3-1)

predict.krls: Predict method for Kernel-based Regularized Least Squares (KRLS) Model Fits

Description

Predicted values and standard errors based on krls model object.

Usage

## S3 method for class 'krls':
predict(object, newdata, se.fit = FALSE , \dots)

Arguments

object

Fitted krls model, i.e. an object of class krls

newdata

An n by k data frame or matrix with variables values at which to predict the outcome. Variable columns in newdata have to match the corresponding covariates used in the krls model object.

se.fit

logical flag if standard errors should be computed for pointwise predictions.

...

additional arguments affecting the predictions produced.

Value

• fit
  n by 1 vector of fitted values for n test points.
• se.fit
  n by 1 vector of standard errors for the fitted values for n test points (NULL unless se.fit=TRUE is specified).
• vcov.fit
  n by n variance-covariance matrix for the fitted values for n test points (NULL unless se.fit=TRUE is specified).
• newdata
  n by k data matrix for test points
• newdataK
  n by m data matrix for pairwise Gauss Kernel distances between test points and m training points from krls model fit.

Details

Function produces predicted values, obtained by evaluating the fitted krls function with the newdata (ie. the test points). The prediction at a new test point x_i is based on f(x_i)= sum_j=1^n c_j K_{x_j}(x_i) where K is the kernel matrix and thus K_{x_j} is a vector whose j-th entry is K(x_j,x_i) (e.g. the distance between the test point x_i and the training point x_j). The training points are passed to the function with the krls object.

See Also

krls

Examples

## 2D example:
# predictor data
X <- matrix(seq(-3,3,.1))
# true function
Ytrue <- sin(X)
# add noise 
Y     <- sin(X) + rnorm(length(X),sd=.3)
# approximate function using KRLS
out <- krls(y=Y,X=X,derivative=TRUE)
# get fitted values and ses
fit <- predict.krls(out,newdata=X,se.fit=TRUE)
# results
par(mfrow=c(2,1))
plot(y=Ytrue,x=X,type="l",col="red",ylim=c(-1.2,1.2),lwd=2,main="f(x)")
points(y=fit$fit,X,col="blue",pch=19)
arrows(y1=fit$fit+1.96*fit$se.fit,
       y0=fit$fit-1.96*fit$se.fit,
       x1=X,x0=X,col="blue",length=0)
legend("bottomright",legend=c("true f(x)=sin(x)","KRLS fitted f(x)"),
       lty=c(1,NA),pch=c(NA,19),lwd=c(2,NA),col=c("red","blue"),cex=.8)

plot(y=cos(X),x=X,type="l",col="red",ylim=c(-1.2,1.2),lwd=2,main="df(x)/dx")
points(y=out$derivatives,X,col="blue",pch=19)

legend("bottomright",legend=c("true df(x)/dx=cos(x)","KRLS fitted df(x)/dx"),
       lty=c(1,NA),pch=c(NA,19),lwd=c(2,NA),col=c("red","blue"),,cex=.8)

## 3D example
# plot true function
par(mfrow=c(1,2))
f<-function(x1,x2){ sin(x1)*cos(x2)}
x1 <- x2 <-seq(0,2*pi,.2)
z   <-outer(x1,x2,f)
persp(x1, x2, z,theta=30,main="true f(x1,x2)=sin(x1)cos(x2)")
# approximate function with KRLS
# data and outcomes
X <- cbind(sample(x1,200,replace=TRUE),sample(x2,200,replace=TRUE))
y   <- f(X[,1],X[,2])+ runif(nrow(X))
# fit surface
krlsout <- krls(X=X,y=y)
# plot fitted surface
ff  <- function(x1i,x2i,krlsout){predict(object=krlsout,newdata=cbind(x1i,x2i))$fit}
z   <- outer(x1,x2,ff,krlsout=krlsout)
persp(x1, x2, z,theta=30,main="KRLS fitted f(x1,x2)")