GPFDA (version 2.2)

gpfrpred: Prediction of the Gaussian Process using functional regression

Description

Predict the new points in Gaussian Process using the training results

Usage

gpfrpred(object,TestData,NewTime=NULL,lReg=NULL,fReg=NULL,gpReg=NULL,
        GP_predict=TRUE)

Arguments

object

The result from training with class`gpfda'. If missing, function stops running.

TestData

The test data. Must be matrix or fd object.

NewTime

New time for test data. If NULL, default setting will be applied.

lReg

The test scale data for functional regression with scale covariates.

fReg

The test functional data for functional regression with functional covariates.

gpReg

List of three items. The names of the items must be `response', `input', `time'. For type I prediction, `response' is the observed response for a new batch, `input' is the observed functional covariates for a new batch, `time' is the observation time for the previous two. If NULL, type II prediction will be carried out.

GP_predict

Logical. If true, GP prediction is carried out, otherwise functional prediction is carried out. Default to be True.

Value

ypred

matrix of predicted value with confidence interval. First column is the fitted value, second and third are the confidence interval.

ypred.mean

The mean value of the prediction.

ypred.sd

The standard deviation of the prediction.

time

time of test data

object

all items trained from gpfr if exists

Details

Two types of prediction are supplied. Type one is the new batch has a few observations, type two is the new batch has no observations.

References

Shi, J Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Springer, New York. Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

See Also

gpr

Examples

# NOT RUN {
library(GPFDA)

# code from: demo('gpfr') 

traindata <- vector('list',20)
for(i in 1:20) traindata[[i]]=i
n <- 50
traindata <- lapply(traindata,function(i) {
  x <- seq(-3,3,len=n)
  y <- sin(x^2)-x+0.2*rnorm(n,0,3)
  x1 <- 0.5*x^3+exp(x)+rnorm(n,0,3)
  x2 <- cos(x^3)+0.2*rnorm(n,0,3)
  mat <- cbind(x,x1,x2,y)
  colnames(mat) <- c('time','x1','x2','y')
  scale <- t(c(2*(mean(y)>0.25)-1,(var(y)>3.6)*2-1,(sd(y)-sd(x)>1.4)*2-1))
  i <- list(mat,scale)
})

n <- 800 #test input
x <- seq(-3,3,len=n)
y <- sin(x^2)-x+0.2*rnorm(n,0,3)
x1 <- 0.5*x^3+exp(x)+rnorm(n,0,3)
x2 <- cos(x^3)+0.2*rnorm(n,0,3)
mat <- cbind(x,x1,x2,y)
colnames(mat) <- c('time','x1','x2','y')
scale <- t(c(2*(mean(y)>0.25)-1,(var(y)>3.6)*2-1,(sd(y)-sd(x)>1.4)*2-1))
# testdata[[1]]=vector('list',3)
n <- 100 # test new points
xt <- seq(1,3,len=n)
yt <- sin(xt^2)-xt+0.2*rnorm(n,0,3)
xt1 <- 0.5*xt^3+exp(xt)+rnorm(n,0,3)
xt2 <- cos(xt^3)+0.2*rnorm(n,0,3)
mat_t <- cbind(xt,xt1,xt2)
colnames(mat_t) <- c('time','xt1','xt2')
td <- list(mat,scale,mat_t)



lx=do.call('rbind',lapply(traindata,function(i)i[[2]]))
fx1=do.call('rbind',lapply(traindata,function(i)i[[1]][,2]))
fx2=do.call('rbind',lapply(traindata,function(i)i[[1]][,3]))
fy1=do.call('rbind',lapply(traindata,function(i)i[[1]][,4]))
time_old=traindata[[1]][[1]][,1]

pfx=td[[1]][,c(2,3)]
pfy=td[[1]][,4]
ptime=td[[1]][,1]
time_new=td[[3]][,1]
tfx=td[[3]][,c(2,3)]
tx=td[[2]]

## comment out because running time is a bit long
# system.time(a1<-gpfr(response=(fy1),lReg=lx,fReg=NULL,gpReg=list(fx1,fx2),
# fyList=list(nbasis=23,lambda=0.1),fbetaList_l=list(list(lambda=100,
# nbasi=17)),hyper=NULL,Cov=c('pow.ex','linear'),fitting=TRUE,
# time=seq(-3,3,len=50),rPreIdx=TRUE,concurrent=TRUE))

# type I prediction
# system.time(b1<-gpfrpred(a1,TestData=(tfx),NewTime=time_new,lReg=tx,
# fReg=NULL,gpReg=list('response'=(pfy),'input'=(pfx),'time'=ptime)))

# type II prediction
# system.time(b2<-gpfrpred(a1,TestData=(tfx),NewTime=time_new,lReg=tx,
# fReg=NULL,gpReg=NULL))


# }