warpFuns: Warpings for Ordinal Inputs

In kergp: Gaussian Process Laboratory

Description

Given warpings for ordinal inputs.

Usage

warpNorm
warpUnorm
warpPower
warpSpline1
warpSpline2

Format

The format is a list of 6:

$ fun : the warping function. The second argument is the vector of parameters. The function returns a numeric vector with an attribute "gradient" giving the derivative w.r.t. the parameters.

$ parNames : names of warping parameters (character vector).

$ parDefault: default values of warping parameters (numeric vector).

$ parLower : lower bounds of warping parameters (numeric vector).

$ parUpper : upper bounds of warping parameters (numeric vector).

$ hasGrad : a boolean equal to TRUE if gradient is supplied as an attribute of fun.

Details

See covOrd for the definition of a warping in this context. At this stage, two warpings corresponding to cumulative density functions (cdf) are implemented:

• Normal distribution, truncated to [0,1]:

  F(x) = [N(x) - N(0)] / [N(1) - N(0)]

  where N(x) = Phi([x - mu] / sigma) is the cdf of the normal distribution with mean mu and standard deviation sigma.

• Power distribution on [0, 1]: F(x) = x^pow.

Furthermore, a warping corresponding to unnormalized Normal cdf is implemented, as well as spline warpings of degree 1 and 2. Splines are defined by a sequence of k knots between 0 and 1. The first knot is 0, and the last is 1. A spline warping of degree 1 is a continuous piecewise linear function. It is parameterized by a positive vector of length k-1, representing the increments at knots. A spline warping of degree 2 is a non-decreasing quadratic spline. It is obtained by integrating a spline of degree 1. Its parameters form a positive vector of length k, representing the derivatives at knots. The implementation relies on the function scalingFun1d of DiceKriging package.

kergp documentation built on March 18, 2021, 5:06 p.m.