buildBO: Bayesian Optimization Model Interface

Description

Bayesian Optimization Model Interface

Usage

buildBO(x, y, control = list())

Arguments

matrix of input parameters. Rows for each point, columns for each parameter.

one column matrix of observations to be modeled.

control

list of control parameters:

thetaLower: lower boundary for theta, default is 1e-4
thetaUpper: upper boundary for theta, default is 1e2
algTheta: algorithm used to find theta, default is L-BFGS-B
budgetAlgTheta: budget for the above mentioned algorithm, default is 200. The value will be multiplied with the length of the model parameter vector to be optimized.
optimizeP: boolean that specifies whether the exponents (p) should be optimized. Else they will be set to two. Default is FALSE
useLambda: whether or not to use the regularization constant lambda (nugget effect). Default is TRUE
lambdaLower: lower boundary for log10lambda, default is -6
lambdaUpper: upper boundary for log10lambda, default is 0
startTheta: optional start value for theta optimization, default is NULL
reinterpolate: whether (TRUE,default) or not (FALSE) reinterpolation should be performed
target: target values of the prediction, a vector of strings. Each string specifies a value to be predicted, e.g., "y" for mean, "s" for standard deviation, "ei" for expected improvement. See also predict.kriging

Value

an object of class "spotBOModel", with a predict method and a print method. Basically a list, with the options and found parameters for the model which has to be passed to the predictor function:

x: sample locations
y: observations at sample locations (see parameters)
min: min y val
thetaLower: lower boundary for theta (see parameters)
thetaUpper: upper boundary for theta (see parameters)
algTheta: algorithm to find theta (see parameters)
budgetAlgTheta: budget for the above mentioned algorithm (see parameters)
lambdaLower: lower boundary for log10lambda, default is -6
lambdaUpper: upper boundary for log10lambda, default is 0
dmodeltheta: vector of activity parameters
dmodellambda: regularization constant (nugget)
mu: mean mu
ssq: sigma square
Psi: matrix large Psi
Psinv: inverse of Psi
nevals: number of Likelihood evaluations during MLE

References

Forrester, Alexander I.J.; Sobester, Andras; Keane, Andy J. (2008). Engineering Design via Surrogate Modelling - A Practical Guide. John Wiley & Sons.

Gramacy, R. B. Surrogates. CRC press, 2020.

Jones, D. R., Schonlau, M., and Welch, W. J. Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13, 4 (1998), 455<U+2013>492.

Examples

Run this code

# NOT RUN {
## Reproduction of Gramacy's classic EI illustration with data from Jones et al.
## Generates Fig. 7.6 from the Gramacy book "Surrogates".
x <- c(1, 2, 3, 4, 12)
y <- c(0, -1.75, -2, -0.5, 5)
## Build BO Model
m1 <- buildBO(x = matrix(x, ncol = 1), 
 y = matrix(y, ncol=1),
 control = list(target="ei"))
xx <- seq(0, 13, length=1000)
yy <- predict(object = m1, newdata = xx)
m <- which.min(y)
fmin <- y[m]
mue <- matrix(yy$y, ncol = 1)
s2 <- matrix(yy$s, ncol = 1)
ei <- matrix(yy$ei, ncol = 1)
## Plotting the Results (similar to Fig. 7.6 in Gramacy's Surrogate book)
par(mfrow=c(1,2))
plot(x, y, pch=19, xlim=c(0,13), ylim=c(-4,9), main="predictive surface")
lines(xx, mue)
lines(xx, mue + 2*sqrt(s2), col=2, lty=2)
lines(xx, mue - 2*sqrt(s2), col=2, lty=2)
abline(h=fmin, col=3, lty=3)
legend("topleft", c("mean", "95% PI", "fmin"), lty=1:3,   col=1:3, bty="n")
plot(xx, ei, type="l", col="blue", main="EI", xlab="x", ylim=c(0,max(ei)))
      
# }