Gaussian Process Fitting

Fits a Gaussian process model to data. Gaussian processes are commonly used in computer experiments to fit an interpolating model. The model is stored as an 'R6' object and can be easily updated with new data. There are options to run in parallel (not for Windows), and 'Rcpp' has been used to speed up calculations. Other R packages that perform similar calculations include 'laGP', 'DiceKriging', 'GPfit', and 'mlegp'.

GauPro

Overview

This package allows you to fit a Gaussian process to a dataset. A Gaussian process is a commonly used model in computer simulation. It assumes that the distribution of any set of points is multivariate normal with a constant mean and a correlation function.

The newest release allows you to use different kernel and trend functions, instead of just a squared exponential covariance.

You should probably use a different package for your modeling, such as laGP, mlegp, or GPfit if you are using R, or GPy if you are using Python.

Installation

You can install like any other package

install.packages('GauPro')

The most up-to-date version can be downloaded from my Github account. devtools::install_github("CollinErickson/GauPro")

Examples in 1-Dimension

Fit a sine curve with noise.

n <- 12
x <- matrix(seq(0,1,length.out = n), ncol=1)
y <- sin(2*pi*x) + rnorm(n,0,1e-1)
gp <- GauPro::GauPro(X=x, Z=y)
curve(gp$pred(x));points(x,y)
curve(gp$pred(x)+2*gp$pred(x,T)$se,col=2,add=T);curve(gp$pred(x)-2*gp$pred(x,T)$se,col=2,add=T)

This is the likelihood as a function of the log of theta. It is not convex and is difficult to optimize in general.

curve(sapply(x, gp$deviance_theta_log),-10,10, n = 300) # deviance profile

Fit a sawtooth function with no noise.

n <- 12
x <- matrix(seq(0,1,length.out = n), ncol=1)
y <- (2*x) %%1
gp <- GauPro::GauPro(X=x, Z=y)
curve(gp$pred(x));points(x,y)
curve(gp$pred(x)+2*gp$pred(x,T)$se,col=2,add=T);curve(gp$pred(x)-2*gp$pred(x,T)$se,col=2,add=T)

curve(sapply(x, gp$deviance_theta_log),-10,10, n = 300) # deviance profile