covOrd {kergp}

Warping-Based Covariance for an Ordinal Input

Description

Creator function for the class covOrd-class

Usage

covOrd(ordered, 
       k1Fun1 = k1Fun1Matern5_2, 
       warpFun = c("norm", "unorm", "power", "spline1", "spline2"), 
       cov = c("corr", "homo"), 
       hasGrad = TRUE, inputs = "u", 
       par = NULL, parLower = NULL, parUpper = NULL, 
       warpKnots = NULL, nWarpKnots = NULL,
       label = "Ordinal kernel", 
       intAsChar = TRUE, 
       ...)

Arguments

ordered

An object coerced to ordered representing an ordinal input. Only the levels and their order will be used.

k1Fun1

A function representing a 1-dimensional stationary kernel function, with no or fixed parameters.

warpFun

Character corresponding to an increasing warping function. See warpFun.

cov

Character indicating whether a correlation or homoscedastic kernel is used.

hasGrad

Object of class "logical". If TRUE, both k1Fun1 and warpFun must return the gradient as an attribute of the result.

inputs

Character: name of the ordinal input.

par, parLower, parUpper

Numeric vectors containing covariance parameter values/bounds in the following order: warping, range and variance if required (cov == "homo").

warpKnots

Numeric vector containing the knots used when a spline warping is chosen. The knots must be in [0, 1], and 0 and 1 are automatically added if not provided. The number of knots cannot be greater than the number of levels.

nWarpKnots

Number of knots when a spline warping is used. Ignored if warpKnots is given. nWarpKnots cannot be greater than the number of levels.

label

Character giving a brief description of the kernel.

intAsChar

Logical. If TRUE (default), an integer-valued input will be coerced into a character. Otherwise, it will be coerced into a factor.

...

Not used at this stage.

Details

Covariance kernel for qualitative ordered inputs obtained by warping.

Let u be an ordered factor with levels u_1, \dots, u_L. Let k_1 be a 1-dimensional stationary kernel (with no or fixed parameters), F a warping function i.e. an increasing function on the interval [0,1] and \theta a scale parameter. Then k is defined by:

k(u_i, u_j) = k_1([F(z_i) - F(z_{j})]/\theta)

where z_1, \dots, z_L form a regular sequence from 0 to 1 (included). At this stage, the possible choices are:

• A distribution function (cdf) truncated to [0,1], among the Power and Normal cdfs.

• For the Normal distribution, an unnormalized version, corresponding to the restriction of the cdf on [0,1], is also implemented (warp = "unorm").

• An increasing spline of degree 1 (piecewise linear function) or 2. In this case, F is unnormalized. For degree 2, the implementation depends on scaling functions from DiceKriging package, which must be loaded here.

Notice that for unnormalized F, we set \theta to 1, in order to avoid overparameterization.

Value

An object of class covOrd-class, inheriting from covQual-class.

See Also

covOrd-class, warpFun

Examples

u <- ordered(1:6, labels = letters[1:6])

myCov <- covOrd(ordered = u, cov = "homo", intAsChar = FALSE)
myCov
coef(myCov) <- c(mean = 0.5, sd = 1, theta = 3, sigma2 = 2)
myCov

checkX(myCov, X = data.frame(u = c(1L, 3L)))
covMat(myCov, X = data.frame(u = c(1L, 3L)))

myCov2 <- covOrd(ordered = u, k1Fun1 = k1Fun1Cos, warpFun = "power")
coef(myCov2) <- c(pow = 1, theta = 1) 
myCov2

plot(myCov2, type = "cor", method = "ellipse")
plot(myCov2, type = "warp", col = "blue", lwd = 2)

myCov3 <- covOrd(ordered = u, k1Fun1 = k1Fun1Cos, warpFun = "spline1")
coef(myCov3) <- c(rep(0.5, 2), 2, rep(0.5, 2))
myCov3

plot(myCov3, type = "cor", method = "ellipse")
plot(myCov3, type = "warp", col = "blue", lwd = 2)


str(warpPower)  # details on the list describing the Power cdf
str(warpNorm)   # details on the list describing the Normal cdf