ARCHISSUR (version 0.0.1)

predict_update_gpc_parallel: Quick update of conditional variances when one or many new points are added to the DoE.

Description

The functions uses Gaussian Process Classification (GPC) update formulas to quickly compute conditional variances at points newdata, when r new points newX are added.

Usage

predict_update_gpc_parallel(Sigma.r, newdata.oldsd, kn)

Value

a list with:

sd

updated conditional standard deviation at points newdata.

lambda

new GPC weight of x_(n+1),...,x_(n+r) for the prediction at points newdata.

Arguments

Sigma.r

an r*r conditional covariance matrix at r points newX(x_(n+1),...,x_(n+r)). It represents the covariance matrix cov obtained through the predict function at newX.

newdata.oldsd

conditional standard deviations vector at the points newdata, (before adding x_(n+1),...,x_(n+r)).

kn

conditional covariances between the points newdata and the r points newX.

Author

Morgane MENZ, Delphine SINOQUET, Miguel MUNOZ-ZUNIGA. Contributors: Naoual SERRAJI.

References

Menz, M., Munoz-Zuniga, M., Sinoquet, D. Estimation of simulation failure set with active learning based on Gaussian Process classifiers and random set theory (2023). https://hal.science/hal-03848238.

Chevalier, C., Ginsbourger, D. (2014). Corrected Kriging update formulae for batch-sequential data assimilation, in Pardo-Iguzquiza, E., et al. (Eds.) Mathematics of Planet Earth, pp 119-122

Examples

#-------------------------------------------------------------------
#------------------- predict_update_gpc_parallel -------------------
#-------------------------------------------------------------------

## 20-points DoE, and the corresponding response
d <- 2
nb_PX <- 20
x <- matrix(c(0.205293785978832, 0.0159983370750337,
              0.684774733109666, 0.125251417595962,
              0.787208786290006, 0.700475706055049,
              0.480507717105934, 0.359730889653793,
              0.543665267336735, 0.565974761807069,
              0.303412043992361, 0.471502352650857,
              0.839505250127309, 0.504914690245002,
              0.573294917143728, 0.784444726564573,
              0.291681289223421, 0.255053812451938,
              0.87233450888786, 0.947168337730927,
              0.648262257638515, 0.973264712407035,
              0.421877310273815, 0.0686662506387988,
              0.190976166753807, 0.810964668176754,
              0.918527262507395, 0.161973686467513,
              0.0188128700859558, 0.43522031347403,
              0.99902788789426, 0.655561821513544,
              0.741113863862512, 0.321050086076934,
              0.112003007565305, 0.616551317575545,
              0.383511473487687, 0.886611679106771,
              0.0749211435982952, 0.205805968972305),
            byrow = TRUE, ncol = d)
require(DiceKriging)
fx <- apply(x, 1, branin)
f <- ifelse(fx < 14, -1, 1)
Xf <- as.matrix(x)

require(future)
plan(multisession)

## gpcm object
require(GPCsign)
model <- gpcm(f, Xf, coef.m = -1.25, coef.cov = c(1.17,0.89))

##
n.grid <- 20
x.grid <- seq(0,1,length=n.grid)
newdata <- expand.grid(x.grid,x.grid)
newdata <- as.matrix(newdata)
pred1 <- predict(object=model,newdata=newdata)
precalc.data <- list()
precalc.data$c.K <- crossprod(pred1$c, model@invK)
newdata.oldsd <- sqrt(pred1$Zsimu_var)

# new points added
new.x <- matrix(c(0.1,0.2),ncol=2)

# predicion at new points
pred2 <- predict(object=model,newdata=new.x)
Sigma.r <- pred2$cov

newdata <- scale(x = newdata, center = [e-mail], scale = [e-mail])
new.x <- scale(x = new.x, center = [e-mail], scale = [e-mail])
kn <- computeQuickgpccov(object = model,
                         integration.points = newdata,
                         X.new = new.x,
                         precalc.data = precalc.data,
                         c.newdata = pred2$c)

updated.predictions <- predict_update_gpc_parallel(Sigma.r = Sigma.r,
                                                   newdata.oldsd = newdata.oldsd,
                                                   kn = kn)
plan(sequential)