gpr1sample: Perform one-sample GP regression

In nsgp: Non-Stationary Gaussian Process 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

x	input points
y	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

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.

Value

A gp-object (list) containing following elements

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

See Also

gpr2sample plot.gp

Examples

# 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)

Example output

Gaussian process model for 221 timepoints: (0, 0.1, 0.2, ..., 21.9, 22)

           MLL EMLL Avg.posterior.std Avg.noise.std
GP model -5.83 55.2             0.155         0.198

Parameters:
 sigma.f = 0.61 
 sigma.n = 1.00 
       l = 9.73 
    lmin = 0.62 
       c = 0.02 
Gaussian process model for 221 timepoints: (0, 0.1, 0.2, ..., 21.9, 22)

           MLL EMLL Avg.posterior.std Avg.noise.std
GP model -5.83 55.2             0.155         0.198

Parameters:
 sigma.f = 0.61 
 sigma.n = 1.00 
       l = 9.73 
    lmin = 0.62 
       c = 0.02 

nsgp documentation built on May 2, 2019, 9:19 a.m.