gpHistVariance: gpHistVariance Function

In gpHist: Gaussian Process with Histogram Intersection Kernel

Description

This function is used to estimate (approximate) the variance of new sample from a trained GP.

Usage

gpHistVariance( GP,X,x_pred)

Arguments

GP	Gaussian Process object that has been trained with gpHist
X	Data that has been used to train the GP object
x_pred	New data whos variance has to be predicted

Details

Based on the number of estimaited eigenvalues/eigenvetors, the variance is approximated. When only 1 eigenvalue is used, the so called coarse approximation is used. If more eigenvectors are present, the so called fine approximation is used. For deatils look in to paper of refrenced under references

Value

Will return NAN on error or the estimated approximaited variances of the samples

Warning

A negative variance cen be retunred. For reasons and workarounds look into note section.

Note

A negative variance can be retunred. This can happen when one eigenvalue is not the highest, rather a lower one. Might also happen when eigenvalue and/or eigenvector is not estimated accurate enough. As workaround consider using less eigenvectors for the estimation of the Gaussian process. Or remove the lowest eigenvalue and vector from the object and call the variance function again. This of course will you provide a worse approximation, but give you a valid variance that you might be able to use instead.

Author(s)

Dennis Becker

References

The utilized approximations are described in the following paper:

Rodner, E., Freytag, A., Bodesheim, P., Froehlich, B., & Denzler, J. (2016). Large-Scale Gaussian Process Inference with Generalized Histogram Intersection Kernels for Visual Recognition Tasks. International Journal of Computer Vision, pp. 1-28. Springer US. doi:10.1007/s11263-016-0929-y

See Also

Package Overview: gpHist-Package

Function for estimation of the GP: gpHist

Function for prediction of the mean of new samples: gpHistPredict

Function for hyperparameter estimation: estimateHyperParameters

Examples

testFn = function(x){
  y = sin(2*pi*x*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)


x_pred = matrix(seq(0,1,0.01))

prediction = gpHistPredict(gp_hist,matrix( X), x_pred)

vars = gpHistVariance(gp_hist,matrix( X), x_pred)

plot(X,Y)
lines(x_pred, prediction,col='red')

lines(x_pred, prediction+sqrt(vars),lty=2,col='red')
lines(x_pred, prediction-sqrt(vars),lty=2,col='red')

legend('topleft',legend=c('Data', 'Approximation','Coarse std. dev'),
col=c('black','red','red') ,lty=c(NA,1,2),pch=c(1,NA,NA))

gpHist documentation built on Nov. 24, 2017, 5:03 p.m.