estimateHyperParameters: estimateHyperParameters Function

Description

This function can be used to estimate the hyperparameters of the GP Hist. THe function provides to set bounds on the parameters and the specification of a data transformation function. The data transformation function can be used to make use of the generalized HIK. Where this function provided the g() function that transforms the data.

Usage

estimateHyperParameters(X, Y, paramLower=0,paramUpper=1,datatransform=NULL,
nParams=0,it = 100,tol=0.001,k=1)

Arguments

Data used to estimate the GP

Y values of the data

paramLower

lower bound for each parameter

paramUpper

upper bound for each parameter

datatransform

Function that is used to transform the data. This function can make use of hyperparameters, but you have to preserve the orders of the values, because the orders object will be reused to save time

nParams

Number of hyperparameters to estimate. This will be number of parameters that are used in the datatransform function.

Maximal number of iterations in the downhillsimplex algorithm

tol

Tollerance till convergence of the downhillsimplex algorithm

Number of estimatied hyperparameters to approximate the log-likelihood. Note that number of eigenvectors scales quadratically in terms of runtime.

Value

Function will return a matrix of estimated hypervalues. First item will be the estimated sigma value. The other paramters will be the on you used in the datatransform function.

Details

This function is a wrapper for the downhillsimplex algoirthm and can be used to estimate hyperparameters of the GP HIST.

Examples

Run this code

# NOT RUN {
#We apply a shift to the function
testFn = function(x){
  y = sin(2*pi*x*2+0.2) 
}

#Get data
X = seq(0,1,0.1)
Y = testFn(X)

#Call gpHist function
#gp_hist = gpHist(matrix(X),matrix(Y),sigma=0.01)


#add a positive shift to the data
transform= function(X,p){
  X+p
}

##estimate hyperparameters
res = estimateHyperParameters(matrix(X),matrix(Y),paramLower = c(0.001,0.0001),
paramUpper = c(0.01,1),datatransform = transform,nParams = 1)

##data need to be trannsformed for the training
X_trans = matrix(transform(X,res[2] ) )
gp_hist = gpHist(X_trans,matrix(Y),sigma=res[1])

##new data to be predicted has also be to transformed
x_pred = matrix(seq(0,1,0.01))
x_pred_trans = transform(x_pred,res[2])

prediction = gpHistPredict(gp_hist,X_trans, x_pred_trans)

plot(X,Y)
## note that we need to use the data before transformation for real x values
lines(x_pred, prediction,col='red')


legend('topleft',legend=c('Data', 'Approximation'), col=c('black','red'),
lty=c(NA,1),pch=c(1,NA))

# }