predict.lineqAGP: Prediction Method for the '"lineqAGP"' S3 Class

In lineqGPR: Gaussian Process Regression Models with Linear Inequality Constraints

Description

Prediction method for the "lineqAGP" S3 class.

Usage

## S3 method for class 'lineqAGP'
predict(object, xtest, ...)

Arguments

object	an object with class "lineqAGP".
xtest	a vector (or matrix) with the test input design.
...	further arguments passed to or from other methods.

Details

The posterior paramaters 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.

Lambda	a matrix corresponding to the linear set of inequality constraints.
lb	the lower bound vector of the inequalities constraints.
ub	the upper bound vector of the inequalities constraints.
Phi.test	a matrix corresponding to the hat basis functions evaluated at xtest. The basis functions are indexed by rows.
mu	the unconstrained GP mean predictor.
Sigma	the unconstrained GP prediction conditional covariance matrix.
xi.map	the GP maximum a posteriori (MAP) predictor given the inequality constraints.

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, simulate.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)

# predictions from the model
ntest <- 25
xtest  <- cbind(seq(0, 1, length = ntest), seq(0, 1, length = ntest))
ytest <- targetFun(xtest)
pred <- predict(model, xtest)
persp3D(x = unique(xtest[, 1]), y = unique(xtest[, 2]),
        z = outer(c(pred$Phi.test[[1]] %*% pred$xi.map[, 1]),
                  c(pred$Phi.test[[2]] %*% pred$xi.map[, 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.