gpr1sample: Perform one-sample GP regression

Description

Computes the optimal GP model by optimizing the marginal likelihood

Usage

gpr1sample(x, y, x.targets, noise = NULL, nsnoise = TRUE, nskernel = TRUE, expectedmll = FALSE, params = NULL, defaultparams = NULL, lbounds = NULL, ubounds = NULL, optim.restarts = 3, derivatives = FALSE)

Arguments

input points

output values (same length as x)

x.targets

target points

noise

observational noise (variance), either NULL, a constant scalar or a vector

nsnoise

estimate non-stationary noise from replicates, if possible (default)

nskernel

use non-stationary kernel

expectedmll

use an alternative expected mll optimization criteria

params

gaussian kernel parameters: (sigma.f, sigma.n, l, lmin, c)

defaultparams

initial parameters for optimization (5-length vector)

lbounds

lower bounds for parameters (5-length vector)

ubounds

upper bounds for parameters (5-length vector)

optim.restarts

restarts in the gradient ascent (default=3)

derivatives

compute also GP derivatives

Value

targets: data frame of predictions with points as rows and columns..
_$x: points
_$pmean: posterior mean of the gp
_$pstd: posterior standard deviation of the gp
_$noisestd: noises (variance)
_$mll: the MLL log likelihood ratio
_$emll: the EMLL log likelihood ratio
_$pc: the posterior concentration log likelihood ratio
_$npc: the noisy posterior concentration log likelihood ratio
cov: learned covariance matrix
mll: marginal log likelihood value
emll: expected marginal log likelihood value
kernel: the kernel matrix used
ekernel: the EMLL kernel matrix
params: the learned parameter vector:
_$sigma.f: kernel variance
_$sigma.n: kernel noise
_$l: maximum lengthscale
_$lmin: minimum lengthscale
_$c: curvature
x: the input points
y: the output values

Details

Parameter optimization performed through L-BFGS using analytical gradients with restarts. The input points x and output values y need to be matching length vectors. If replicates are provided, they are used to estimate dynamic observational noise.

The resulting GP model is encapsulated in the return object. The estimated posterior is in targets$pmean and targets$pstd for target points x.targets. Use plot.gp to visualize the GP.

Examples

Run this code

# load example data
data(toydata)

## Not run: can take sevaral minutes
#  # perform gpr
#  res = gpr1sample(toydata$ctrl$x, toydata$ctrl$y, seq(0,22,0.1))
#  print(res)## End(Not run)

# pre-computed toydata model
data(toygps)
print(toygps$ctrlmodel)