GPFDA (version 1.1)

gpfr: Gaussian Process in functional data.

Description

Use functional regression to be the mean structure and Gaussian Process to be the covariance structure.

Usage

gpfr(TrainData,CovType = c("linear", "pow.ex"), hyper=NULL,NewHyper=NULL, gamma = 1,
  nbasis = NULL, norder = 6, lambda1 = 1e-07, lambda2 = 1e-05, pen.order = 2, 
  new.sample = NULL,accuracy=c('high','normal','low'),trace.iter=5,fitting=F)

Arguments

TrainData

The train data. Must from "wrap" or with certain data.table format.

CovType

Kernel function or covariance function type(s).

hyper

Hyper parameter initial value. Default to be NULL.

NewHyper

Vector of the names of the new hyper parameters from customized kernel function.

gamma

Power parameter used in powered exponential.

nbasis

Number of basis to use in the functional regression. Default to be the integer of dimension of train data over 5.

norder

Order of basis function in functional regression. Default to be 4.

lambda1

Smoothing parameter for curve fitting. Default to be 1e-07

lambda2

Smoothing parameter for functional regression. Default to be 1e-05

pen.order

Order of penalty term. Default to be 2.

new.sample

The dimension of the new sampled matrix (if applicable). Default to be the maximum dimension in the data.

accuracy

Optimization accuracy. Default to be high.

trace.iter

Print the processing of iterations of optimization.

fitting

Is fitting required or not. Default to be F.

Value

• A list of
• hyper
  estimated hyper-parameters
• I
  A vector of estimated standard deviation of hyper-parameters
• betaestlist
  estimated functional coefficient
• iuu
  scale part of the data
• CovFun
  Covariance function

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

library(GPFDA)

traindata=vector('list',20)
for(i in 1:20) traindata[[i]]=i
n=500
traindata=lapply(traindata,function(i) {
  x=seq(-3,3,len=n)
  y=sin(x^2)-x+0.2*rnorm(n,runif(1,-3,3),runif(1,0.5,3))
  x1=0.5*x^3+exp(x)+rnorm(n,runif(1,-3,3),runif(1,0.5,5))
  x2=cos(x^3)+0.2*rnorm(n,runif(1,-3,3),runif(1,0.5,5))
  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=300 #test input
x=seq(-3,3,len=n)
y=sin(x^2)-x+0.2*rnorm(n,runif(1,-3,3),runif(1,0.5,3))
x1=0.5*x^3+exp(x)+rnorm(n,runif(1,-3,3),runif(1,0.5,5))
x2=cos(x^3)+0.2*rnorm(n,runif(1,-3,3),runif(1,0.5,5))
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,runif(1,-3,3),runif(1,0.5,3))
xt1=0.5*xt^3+exp(xt)+rnorm(n,runif(1,-3,3),runif(1,0.5,5))
xt2=cos(xt^3)+0.2*rnorm(n,runif(1,-3,3),runif(1,0.5,5))
mat_t=cbind(xt,xt1,xt2,yt)
colnames(mat_t)=c('time','xt1','xt2','y')
td=list(mat,scale,mat_t)


trdata=wrap(functional=lapply(traindata,function(i)i[[1]]),
     do.call('rbind',lapply(traindata,function(i)i[[2]])),
     list='traindata',time='time',response='y')
tedata=wrap(functional=td[[1]],scale=td[[2]],testdata=td[[3]],
     list='testdata',time='time',response='y')

# system.time(result<-gpfr(trdata,tedata))