lineqGPR (version 0.1.1)

predict.lineqGP: Prediction Method for the "lineqGP" S3 Class

Description

Prediction method for the "lineqGP" S3 class.

Usage

# S3 method for lineqGP
predict(object, xtest, ...)

Arguments

object

an object with class "lineqGP".

xtest

a vector (or matrix) with the test input design.

...

further arguments passed to or from other methods.

Value

A "lineqGP" 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.

Details

The posterior paramaters of the finite-dimensional GP with linear inequality constraints are computed. Here, \(\boldsymbol{\xi}\) is a centred Gaussian vector with covariance \(\boldsymbol{\Gamma}\), s.t. \(\boldsymbol{\Phi} \boldsymbol{\xi} = \boldsymbol{y}\) (interpolation constraints) and \(\boldsymbol{l} \leq \boldsymbol{\Lambda} \boldsymbol{\xi} \leq \boldsymbol{u}\) (inequality constraints).

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.lineqGP, augment.lineqGP, simulate.lineqGP

Examples

# NOT RUN {
# creating the model
sigfun <- function(x) return(1/(1+exp(-7*(x-0.5))))
x <- seq(0, 1, length = 5)
y <- sigfun(x)
model <- create(class = "lineqGP", x, y, constrType = "monotonicity")

# updating and expanding the model
model$localParam$m <- 30
model$kernParam$par <- c(1, 0.2)
model <- augment(model)

# predictions from the model
xtest <- seq(0, 1, length = 100)
ytest <- sigfun(xtest)
pred <- predict(model, xtest)
plot(xtest, ytest, type = "l", lty = 2, main = "Kriging predictions")
lines(xtest, pred$Phi.test %*% pred$mu, type = "l", col = "blue")
lines(xtest, pred$Phi.test %*% pred$xi.map, type = "l", col = "red")
legend("right", c("ytest", "mean", "mode"), lty = c(2,1,1),
       col = c("black", "blue", "red"))

# }