Gaussian Process Regression

Wajid Jawaid 2018-04-13

gpr

Gaussian Process Regression allows simple use of gaussian processes to fit optimum lines without choosing a specific function.

Example

This is an example taken from Carl Rassmussen's book on Gaussian processes. We can first sample from the prior.

library(gpr)

d <- .1
x <- seq(-5,5,d)
K <- covMat(x, x, function(xx,xy) cf(xx,xy, l = 2))
L <- cholesky(K)

plot(NULL, xlim=c(-5,5), ylim=c(-2.5,2.5), xlab = "time", ylab = "counts")
rect(-6, -2, 6, 2, col="#44444411", lty=0)
for (i in 1:4) {
    y <- sampleFromL(L)
    points(x,y, pch=16, xlim=c(-5,5), ylim=c(-2,2), cex=.2, col = i, type = "l")
}

Now we can add data points (-4,-2); (-3,0); (-1,1); (0,2) and (2,-1). Now we can find the posterior distribution.

x <- c(-4,-3,-1,0,2)
y <- c(-2,0,1,2,-1)

pst <- predictGP(x, y, xs = seq(-5,5,.1), cvFunc = cf, sigman = 0.1, l = 1)
plot(pst, p.pch = 3, p.cex = 2, xlab = "x", ylab = "y")

Now we can sample from the new posterior.

plot(pst, p.pch = 3, p.cex = 2, xlab = "x", ylab = "y")
L <- cholesky(pst$cv)

for (i in 1:5) {
    yo <- sampleFromL(L, mu = pst$mean)
    points(pst$x,yo, pch=16, xlim=c(-5,5), ylim=c(-2,2), cex=.2, col = i, type = "l")
}