simulate.lineqAGP: Simulation Method for the '"lineqAGP"' S3 Class

In lineqGPR: Gaussian Process Regression Models with Linear Inequality Constraints

Description

Simulation method for the "lineqAGP" S3 class.

Usage

## S3 method for class 'lineqAGP'
simulate(object, nsim = 1, seed = NULL, xtest, ...)

Arguments

object	an object with class "lineqAGP".
nsim	the number of simulations.
seed	see simulate.
xtest	a vector (or matrix) with the test input design.
...	further arguments passed to or from other methods.

Details

The posterior sample-path of the finite-dimensional GP with linear inequality constraints are computed. Here, ξ is a centred Gaussian vector with covariance Γ, s.t. Φ ξ = y (interpolation constraints) and lb ≤ Λ ξ ≤ ub (inequality constraints).

Value

A "lineqAGP" object with the following elements.

x	a vector (or matrix) with the training input design.
y	the training output vector at x.
xtest	a vector (or matrix) with the test input design.
Phi.test	a matrix corresponding to the hat basis functions evaluated at xtest. The basis functions are indexed by rows.
xi.sim	the posterior sample-path of the finite-dimensional Gaussian vector.
ysim	the posterior sample-path of the observed GP. Note: ysim = Phi.test %*% xi.sim.

Author(s)

A. F. Lopez-Lopera.

References

Lopez-Lopera, A. F., Bachoc, F., Durrande, N., and Roustant, O. (2017), "Finite-dimensional Gaussian approximation with linear inequality constraints". ArXiv e-prints [link]

See Also

create.lineqAGP, augment.lineqAGP, predict.lineqAGP

Examples

library(plot3D)
# creating the model
d <- 2
fun1 <- function(x) return(4*(x-0.5)^2)
fun2 <- function(x) return(2*x)
targetFun <- function(x) return(fun1(x[, 1]) + fun2(x[, 2])) 
xgrid <- expand.grid(seq(0, 1, 0.01), seq(0, 1, 0.01))
ygrid <- targetFun(xgrid)
xdesign <- rbind(c(0.5, 0), c(0.5, 0.5), c(0.5, 1), c(0, 0.5), c(1, 0.5))
ydesign <- targetFun(xdesign)
model <- create(class = "lineqAGP", x = xdesign, y = ydesign,
                constrType = c("convexity", "monotonicity"))

# updating and expanding the model
model$localParam$m <- rep(10, d)
model$kernParam[[1]]$type <- "matern52"
model$kernParam[[2]]$type <- "matern52"
model$kernParam[[1]]$par <- c(1, 0.2)
model$kernParam[[2]]$par <- c(1, 0.3)
model$nugget <- 1e-9
model$varnoise <- 1e-5
model <- augment(model)

# sampling from the model
ntest <- 25
xtest  <- cbind(seq(0, 1, length = ntest), seq(0, 1, length = ntest))
ytest <- targetFun(xtest)
sim.model <- simulate(model, nsim = 1e3, seed = 1, xtest = xtest)
persp3D(x = unique(xtest[, 1]), y = unique(xtest[, 2]),
        z = outer(rowMeans(sim.model$ysim[[1]]),
                  rowMeans(sim.model$ysim[[2]]), "+"),
        xlab = "x1", ylab = "x2", zlab = "mode(x1,x2)", zlim = c(0, 3),
        phi = 20, theta = -30, alpha = 1, colkey = FALSE)
points3D(x = xdesign[,1], y = xdesign[,2], z = ydesign, col = "black", pch = 19, add = TRUE)

lineqGPR documentation built on Jan. 11, 2020, 9:23 a.m.