modelLinear: Distance based Linear Model

Description

A simple linear model based on arbitrary distances. Comparable to a k nearest neighbor model, but potentially able to extrapolate into regions of improvement. Used as a simple baseline by Zaefferer et al.(2014).

Usage

modelLinear(x, y, distanceFunction, control = list())

Value

a fit (list, modelLinear), with the options and found parameters for the model which has to be passed to the predictor function:

x: samples in input space (see parameters)
y: observations for each sample (see parameters)
distanceFunction: distance function (see parameters)

Arguments

x: list of samples in input space
y: matrix, vector of observations for each sample
distanceFunction: a suitable distance function of type f(x1,x2), returning a scalar distance value, preferably between 0 and 1. Maximum distances larger 1 are no problem, but may yield scaling bias when different measures are compared. Should be non-negative and symmetric.
control: currently unused, defaults to list()

References

Zaefferer, Martin; Stork, Joerg; Friese, Martina; Fischbach, Andreas; Naujoks, Boris; Bartz-Beielstein, Thomas. (2014). Efficient global optimization for combinatorial problems. In Proceedings of the 2014 conference on Genetic and evolutionary computation (GECCO '14). ACM, New York, NY, USA, 871-878. DOI=10.1145/2576768.2598282

Examples

Run this code

#set random number generator seed
set.seed(1)
#simple test landscape
fn <- landscapeGeneratorUNI(1:5,distancePermutationHamming)
#generate data for training and test
x <- unique(replicate(40,sample(5),FALSE))
xtest <- x[-(1:15)]
x <- x[1:15]
#determin true objective function values
y <- fn(x)
ytest <- fn(xtest)
#build model
fit <- modelLinear(x,y,distancePermutationHamming)
#predicted obj. function values
ypred <- predict(fit,xtest)$y
#plot
plot(ytest,ypred,xlab="true value",ylab="predicted value",
    pch=20,xlim=c(0.3,1),ylim=c(min(ypred)-0.1,max(ypred)+0.1))
abline(0,1,lty=2)