C_var2 {activegp}

Alternative Variance of Update

Description

Defined as E[(C - E[C])^2], where A^2 = AA (not elementwise multiplication).

Usage

C_var2(C, xnew, grad = FALSE)

Arguments

C

A const_C object, the result of a call to C_GP.

xnew

The new design point

grad

If FALSE, calculate variance of update. If TRUE, returns the gradient.

Value

A real number giving the expected variance of C defined via matrix multiplication given the current design.

References

N. Wycoff, M. Binois, S. Wild (2019+), Sequential Learning of Active Subspaces, preprint.

Examples

################################################################################
### Norm of the variance of C criterion landscape
################################################################################
 
library(hetGP)
set.seed(42)
nvar <- 2
n <- 20

# theta gives the subspace direction
f <- function(x, theta = pi/6, nugget = 1e-6){
 if(is.null(dim(x))) x <- matrix(x, 1)
 xact <- cos(theta) * x[,1] - sin(theta) * x[,2]
 return(hetGP::f1d(xact) + rnorm(n = nrow(x), sd = rep(nugget, nrow(x))))
}

design <- matrix(signif(runif(nvar*n), 2), ncol = nvar)
response <- apply(design, 1, f)
model <- mleHomGP(design, response, lower = rep(1e-4, nvar),
                  upper = rep(0.5,nvar), known = list(g = 1e-4))
                  
C_hat <- C_GP(model)

ngrid <- 51
xgrid <- seq(0, 1,, ngrid)
Xgrid <- as.matrix(expand.grid(xgrid, xgrid))
filled.contour(matrix(f(Xgrid), ngrid))

cvar_crit <- function(C, xnew){
 return(sqrt(sum(C_var(C, xnew)^2)))
}

Cvar_grid <- apply(Xgrid, 1, cvar_crit, C = C_hat)
filled.contour(matrix(Cvar_grid, ngrid), color.palette = terrain.colors,
               plot.axes = {axis(1); axis(2); points(design, pch = 20)})