Package 'GPCsign' reference manual

Title:	Gaussian Process Classification as Described in Bachoc et al. (2020)
Description:	Parameter estimation and prediction of Gaussian Process Classifier models as described in Bachoc et al. (2020) <doi:10.1007/S10898-020-00920-0>. Important functions : gpcm(), predict.gpcm(), update.gpcm().
Authors:	Morgane Menz [aut, cre], Céline Helbert [aut], Victor Picheny [aut], François Bachoc [aut], Naoual Serraji [ctb]
Maintainer:	Morgane Menz <[email protected]>
License:	GPL-3
Version:	0.1.0
Built:	2024-11-23 05:34:08 UTC
Source:	https://github.com/cran/GPCsign

Fit and/or create a Gaussian Process Classification (GPC) model

Description

gpcm is used to fit GPC models. When parameters are known, the function creates a model using given parameters. Otherwise, they are estimated by Maximum Likelihood. In both cases, the result is a gpcm object.

Usage

gpcm(f, Xf, covtype = "matern5_2", noise.var = 1e-6,
     coef.cov = NULL, coef.m = NULL, multistart = 1,
     seed = NULL, lower = NULL, upper = NULL, nsimu = 100,
     normalize = TRUE, X.mean = NULL, X.std = NULL)
gpcm(f, Xf, covtype = "matern5_2", noise.var = 1e-6,
     coef.cov = NULL, coef.m = NULL, multistart = 1,
     seed = NULL, lower = NULL, upper = NULL, nsimu = 100,
     normalize = TRUE, X.mean = NULL, X.std = NULL)

Arguments

`f`	a vector containing the binary observations (+/-1) corresponding to the class labels.
`Xf`	a matrix representing the design of experiments.
`covtype`	a character string specifying the covariance structure for the latent GP. Default is `matern_5_2`.
`noise.var`	variance value standing for the homogeneous nugget effect. Default is 1e-6.
`coef.cov`	an optional vector containing the values for covariance parameters for the latent GP. (See below).
`coef.m`	an optional scalar corresponding to the mean value of the latent GP. If both `coef.cov` and `coef.m` are provided, no covariance parameter estimation is performed. If at least one of them is missing, both are estimated.
`multistart`	an optional integer indicating the number of initial points from which running the `BFGS` for covariance parameter optimization. The multiple optimizations will be performed in parallel provided that a parallel backend is registered (see package future)
`seed`	to fix the seed, default is `NULL`.
`lower`	(see below).
`upper`	`lower`, `upper`: bounds for the covariance parameters (scalars or vectors), if `NULL` they are set to 0.2 and 3, respectively.
`nsimu`	the number of samples of the latent process at observation points `Xf` to generate. Must be a non-null integer.
`normalize`	a logical parameter indicating whether to normalize the input matrix `Xf`. If `TRUE`, the matrix will be normalized using `X.mean` and `X.std` values if given; otherwise, the mean and standard deviation are computed and used for normalization.
`X.mean`	(see below).
`X.std`	optional vectors containing mean and standard deviation values for each column of the input matrix. If they are not provided, they are computed from the input matrix `Xf`.

Details

The generation of the matrix of samples of the latent process Z_obs is done using Gibbs sampling. See rtmvnorm function in tmvtnorm package.

Value

An object of class gpcm. See gpcm-class.

Author(s)

Morgane MENZ, Céline HELBERT, Victor PICHENY, François BACHOC. Contributors: Naoual SERRAJI.

References

Bachoc, F., Helbert, C. & Picheny, V. Gaussian process optimization with failures: classification and convergence proof. J Glob Optim 78, 483–506 (2020). doi:10.1007/s10898-020-00920-0.

Kotecha, J. H., Djuric, P. M. (1999). Gibbs Sampling Approach For Generation of Truncated Multivariate Gaussian Random Variables. IEEE Computer Society, 1757–1760.

Wilhelm, S. tmvtnorm: Truncated Multivariate Normal and Student t Distribution. R package version 1.6. https://CRAN.R-project.org/package=tmvtnorm.

Roustant, O., Ginsbourger, D. & Deville, Y. Contributors: Chevalier, C. , Richet, Y. DiceKriging: Kriging Methods for Computer Experiments. R package version 1.6.0. https://CRAN.R-project.org/package=DiceKriging.

Byrd, R. H., Lu, P., Nocedal, J. and Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16, 1190–1208. doi:10.1137/0916069.

Examples

# ----------------------------------
# A 1D example - sinusoidal function
# ----------------------------------
sinusoidal_function <- function(x) {
  sin(4 * pi * x)
}

# Design of Experiments Xf and the corresponding signs f
Xf <- as.matrix(c(0.07, 0.19, 0.42, 0.56, 0.81, 0.90))
f <- rep(1, length(Xf))
f[(sinusoidal_function(Xf) < 0)] <- -1

# GPC model
GPCmodel <- gpcm(f, Xf, multistart = 3)

# Graphics of predictions
x <- as.matrix(seq(0, 1, length.out = 101))
result <- predict(object = GPCmodel, newdata = x)
probabilities <- result$prob
index <- match(Xf, x)
plot(x, probabilities, pch = "-")
points(Xf[f == 1], probabilities[index[f == 1]], pch = 20, col = "blue")
points(Xf[f == -1], probabilities[index[f == -1]], pch = 20, col = "red")
abline(h = 0.5, lty = 2)
legend("topright",title = "DoE Xf",title.cex = 0.7, legend = c("+", "-"), 
     col = c("blue", "red"), pch = 20)


# ----------------------------------
# A 2D example - Branin-Hoo function
# ----------------------------------

# 30-points DoE, and the corresponding response
d <- 2
nb_PX <- 30
require(DiceDesign)
X <- lhsDesign(nb_PX, d, seed = 123)$design
Xopt <- maximinSA_LHS(X, T0 = 10, c = 0.99, it = 10000)
x <- Xopt$design
require(DiceKriging)
fx <- apply(x, 1, branin)
f <- ifelse(fx < 14, -1, 1)
Xf <- as.matrix(x)

# Fit and create a GPC model without parallelisation
t0 <- proc.time()
GPCmodel <- gpcm(f, Xf, multistart = 3, seed = 123)
t1 = proc.time() - t0
cat(" time elapsed : ",t1[3])
print(GPCmodel)

# Graphics - Predict probabilities
ngrid <- 50
x.grid <- seq(0, 1., length.out = ngrid)
grid <- as.matrix(expand.grid(x.grid, x.grid))
probabilities <- predict(GPCmodel, newdata = grid, light.return = TRUE)
filled.contour(x.grid, x.grid, matrix(probabilities, ngrid, ngrid),
               color.palette = function(n) hcl.colors(n, "RdYlBu", rev = FALSE),
               main = "probabilities map",
               plot.axes = {
                 axis(1)
                 axis(2)
                 points(Xf[f == 1, 1], Xf[f == 1, 2], col = "blue", pch = 21, bg = "blue")
                 points(Xf[f == -1, 1], Xf[f == -1, 2], col = "red", pch = 21, bg = "red")
               }
)

# Fit and create a GPC model with parallelisation
## Use multisession futures
require(future)
plan(multisession)
t0 = proc.time()
GPCmodel2 <-  gpcm(f,Xf, multistart = 3, seed = 123 )
t1 = proc.time() - t0
cat(" time elapsed : ",t1[3])
print(GPCmodel2)
## Explicitly close multisession workers by switching plan
plan(sequential)

# ----------------------------------
# A 1D example - sinusoidal function
# ----------------------------------
sinusoidal_function <- function(x) {
  sin(4 * pi * x)
}

# Design of Experiments Xf and the corresponding signs f
Xf <- as.matrix(c(0.07, 0.19, 0.42, 0.56, 0.81, 0.90))
f <- rep(1, length(Xf))
f[(sinusoidal_function(Xf) < 0)] <- -1

# GPC model
GPCmodel <- gpcm(f, Xf, multistart = 3)

# Graphics of predictions
x <- as.matrix(seq(0, 1, length.out = 101))
result <- predict(object = GPCmodel, newdata = x)
probabilities <- result$prob
index <- match(Xf, x)
plot(x, probabilities, pch = "-")
points(Xf[f == 1], probabilities[index[f == 1]], pch = 20, col = "blue")
points(Xf[f == -1], probabilities[index[f == -1]], pch = 20, col = "red")
abline(h = 0.5, lty = 2)
legend("topright",title = "DoE Xf",title.cex = 0.7, legend = c("+", "-"), 
     col = c("blue", "red"), pch = 20)


# ----------------------------------
# A 2D example - Branin-Hoo function
# ----------------------------------

# 30-points DoE, and the corresponding response
d <- 2
nb_PX <- 30
require(DiceDesign)
X <- lhsDesign(nb_PX, d, seed = 123)$design
Xopt <- maximinSA_LHS(X, T0 = 10, c = 0.99, it = 10000)
x <- Xopt$design
require(DiceKriging)
fx <- apply(x, 1, branin)
f <- ifelse(fx < 14, -1, 1)
Xf <- as.matrix(x)

# Fit and create a GPC model without parallelisation
t0 <- proc.time()
GPCmodel <- gpcm(f, Xf, multistart = 3, seed = 123)
t1 = proc.time() - t0
cat(" time elapsed : ",t1[3])
print(GPCmodel)

# Graphics - Predict probabilities
ngrid <- 50
x.grid <- seq(0, 1., length.out = ngrid)
grid <- as.matrix(expand.grid(x.grid, x.grid))
probabilities <- predict(GPCmodel, newdata = grid, light.return = TRUE)
filled.contour(x.grid, x.grid, matrix(probabilities, ngrid, ngrid),
               color.palette = function(n) hcl.colors(n, "RdYlBu", rev = FALSE),
               main = "probabilities map",
               plot.axes = {
                 axis(1)
                 axis(2)
                 points(Xf[f == 1, 1], Xf[f == 1, 2], col = "blue", pch = 21, bg = "blue")
                 points(Xf[f == -1, 1], Xf[f == -1, 2], col = "red", pch = 21, bg = "red")
               }
)

# Fit and create a GPC model with parallelisation
## Use multisession futures
require(future)
plan(multisession)
t0 = proc.time()
GPCmodel2 <-  gpcm(f,Xf, multistart = 3, seed = 123 )
t1 = proc.time() - t0
cat(" time elapsed : ",t1[3])
print(GPCmodel2)
## Explicitly close multisession workers by switching plan
plan(sequential)

Gaussian Process Classification (GPC) models class

Description

S4 class for GPC models.

Slots

d: Object of class "integer". The spatial dimension.
n: Object of class "integer". The number of observations.
X: Object of class "matrix". The design of experiments.
y: Object of class "matrix". The vector of binary observations at design points (+/-1) corresponding to the class labels.
X.std: Object of class "numeric". The vector of standard deviation values of design points.
X.mean: Object of class "numeric". The vector of mean values of design points.
call: Object of class "language". User call reminder.
coef.m: Object of class "numeric". Mean coefficient of latent GP.
coef.cov: Object of class "numeric". Covariance coefficients of latent GP.
covariance: Object of class "covKernel". A DiceKriging object specifying the covariance structure.
noise.flag: Object of class "logical". Are the observations noisy?
noise.var: Object of class "numeric". Nugget effect.
param.estim: Object of class "logical". TRUE if at least one parameter is estimated, FALSE otherwise.
lower: Object of class "numeric". Lower bounds for covariance parameters estimation.
upper: Object of class "numeric". Upper bounds for covariance parameters estimation.
logLik: Object of class "numeric". Value of the log-Likelihood at its optimum.
Z_obs: Object of class "matrix". A nobs * nsimu matrix of samples of the latent process at design points.
l: Object of class "numeric". Lower truncation points. Parameter to generate new Z_obs.
u: Object of class "numeric". Upper truncation points. Parameter to generate new Z_obs.
K: Object of class "matrix". Covariance matrix of design points. Parameter to generate new Z_obs
invK: Object of class "matrix". The inverse of the matrix K whose Cholesky decomposition was given.

Objects from the Class

To create a gpcm object, use gpcm. See also this function for more details.

Author(s)

Morgane MENZ, Céline HELBERT, Victor PICHENY, François BACHOC. Contributors: Naoual SERRAJI.

Compute logLikelihood

Description

Computes and returns the log-likelihood value, the covariance matrix of latent process and covariance structure of a Gaussian Process Classification (GPC) model.

Usage

logLikFunc(par, f, Xf, covtype = "matern5_2", noise.var = 1e-6,
     seed = NULL, return.all = FALSE)
logLikFunc(par, f, Xf, covtype = "matern5_2", noise.var = 1e-6,
     seed = NULL, return.all = FALSE)

Arguments

`par`	vector contains the `coef.m` and the log of `coef.cov`.
`f`	vector of binary observations (+/-1) corresponding to the class labels.
`Xf`	a matrix representing the design of experiments.
`covtype`	a character string specifying the covariance structure for the latent GP. Default is `matern_5_2`.
`noise.var`	nugget effect. Default is 1e-6.
`seed`	to fix the seed, default is `NULL`.
`return.all`	an optional boolean. If `FALSE`, only the log-likelihood is returned; if `TRUE`, `K` and `cov.fun` are also returned. Default is `FALSE`.

Value

`logLik`	the log-likelihood.
`K`	the covariance matrix of latent process.
`cov.fun`	a DiceKriging object specifying the covariance structure.

Author(s)

Morgane MENZ, Céline HELBERT, Victor PICHENY, François BACHOC. Contributors: Naoual SERRAJI.

References

Bachoc, F., Helbert, C. & Picheny, V. Gaussian process optimization with failures: classification and convergence proof. J Glob Optim 78, 483–506 (2020). doi:10.1007/s10898-020-00920-0

Botev, Z., Belzile, L. TruncatedNormal: Truncated Multivariate Normal and Student Distributions. R package version 2.2.2 https://cran.r-project.org/package=TruncatedNormal

Botev, Z. I. (2017), The normal law under linear restrictions:simulation and estimation via minimax tilting, Journal of the Royal Statistical Society, Series B, 79 (1), pp. 1-24.

Examples

# ------------
# A 1D example
# ------------

# Design of Experiments Xf and the corresponding signs f
Xf <- as.matrix(c(0.08, 0.27, 0.42, 0.65, 0.78, 0.84))
f <- c(1, -1, -1, 1, -1, -1)

# loglikelihood and covariance matrix at Xf 
par <- c(coef.cov = 0.1, coef.m = 0)
result <- logLikFunc(par = par, f = f, Xf = Xf, return.all = TRUE)
K <- result$K
logLik <- result$logLik
print(logLik)

# ------------
# A 1D example
# ------------

# Design of Experiments Xf and the corresponding signs f
Xf <- as.matrix(c(0.08, 0.27, 0.42, 0.65, 0.78, 0.84))
f <- c(1, -1, -1, 1, -1, -1)

# loglikelihood and covariance matrix at Xf 
par <- c(coef.cov = 0.1, coef.m = 0)
result <- logLikFunc(par = par, f = f, Xf = Xf, return.all = TRUE)
K <- result$K
logLik <- result$logLik
print(logLik)

Predict class probability at newdata for a Gaussian Process Classification (GPC) model

Description

Predicted probability of class 1. Optionally, conditional covariance based on a gpcm model and 95% quantiles of the probability of class 1 are returned.

Usage

## S3 method for class 'gpcm'
predict(object, newdata, nsimu = NULL, 
light.return = FALSE, checkNames=FALSE, seed = NULL, ...)
## S3 method for class 'gpcm'
predict(object, newdata, nsimu = NULL, 
light.return = FALSE, checkNames=FALSE, seed = NULL, ...)

Arguments

`object`	an object of class `gpcm`.
`newdata`	a vector, matrix of points to be predicted.
`nsimu`	an optional integer indicating whether to resample latent GP at observation points and how many samples are required. If `NULL`, current samples are used. Default is `NULL`.
`light.return`	an optional boolean. If `TRUE`, only `prob` is returned. Default is `FALSE`.
`checkNames`	an optional boolean. If `TRUE`, a consistency test is performed between the names of newdata and the names of the experimental design (contained in `object@Xf`). Default is `FALSE`.
`seed`	to fix the seed (used if `nsimu` is not `NULL`). Default is `NULL`.
`...`	no other argument for this method

Value

`prob`	the (averaged) probability of class 1 at `newdata`.
`lower95`, `upper95`	95% confidence bounds for the probability at `newdata`.
`probs`	a matrix of sample predicted probabilities.
`Zsimu_var`, `Zsimu_mean`	conditional variance vector and mean matrix of the latent GP at `newdata`.
`cov`	conditional covariance matrix at `newdata`.
`c`	an auxiliary matrix, containing all the covariances between `newdata` and design points `Xf`.
`lambda`	an auxiliary vector, product of the inverse covariance matrix `invK` returned by `object` and the unconditional covariance matrix `c` between `newdata` and design points `Xf`.
`kz`	an auxiliary matrix, corresponding to the unconditional covariance matrix at `newdata`.

Author(s)

Morgane MENZ, Céline HELBERT, Victor PICHENY, François BACHOC. Contributors: Naoual SERRAJI.

References

Bachoc, F., Helbert, C. & Picheny, V. Gaussian process optimization with failures: classification and convergence proof. J Glob Optim 78, 483–506 (2020). doi:10.1007/s10898-020-00920-0.

Examples

# ----------------------------------
# A 2D example - Branin-Hoo function
# ----------------------------------

# 30-points DoE, and the corresponding response
d <- 2
nb_PX <- 30
require(DiceDesign)
X <- lhsDesign(nb_PX, d, seed = 123)$design
Xopt <- maximinSA_LHS(X, T0 = 10, c = 0.99, it = 1000)
x <- Xopt$design
require(DiceKriging)
fx <- apply(x, 1, branin)
s <- ifelse(fx < 14, -1, 1)
f <- s
Xf <- as.matrix(x)

# Bulding GPC model
GPCmodel <- gpcm(f = f, Xf = Xf, coef.m = -0.1, coef.cov=c(0.8,0.5))

# Graphics - Predict probabilities
ngrid <- 50
x.grid <- seq(0, 1., length.out = ngrid)
grid <- as.matrix(expand.grid(x.grid, x.grid))
probabilities <- predict(object = GPCmodel, newdata = grid)$prob
filled.contour(x.grid, x.grid, matrix(probabilities, ngrid, ngrid),
               color.palette = function(n) hcl.colors(n, "RdYlBu", rev = FALSE),
               main = "probabilities map",
               plot.axes = {
                 axis(1)
                 axis(2)
                 points(Xf[f == 1, 1], Xf[f == 1, 2], col = "blue", pch = 21, bg = "blue")
                 points(Xf[f == -1, 1], Xf[f == -1, 2], col = "red", pch = 21, bg = "red")
               }
)
# ----------------------------------
# A 2D example - Branin-Hoo function
# ----------------------------------

# 30-points DoE, and the corresponding response
d <- 2
nb_PX <- 30
require(DiceDesign)
X <- lhsDesign(nb_PX, d, seed = 123)$design
Xopt <- maximinSA_LHS(X, T0 = 10, c = 0.99, it = 1000)
x <- Xopt$design
require(DiceKriging)
fx <- apply(x, 1, branin)
s <- ifelse(fx < 14, -1, 1)
f <- s
Xf <- as.matrix(x)

# Bulding GPC model
GPCmodel <- gpcm(f = f, Xf = Xf, coef.m = -0.1, coef.cov=c(0.8,0.5))

# Graphics - Predict probabilities
ngrid <- 50
x.grid <- seq(0, 1., length.out = ngrid)
grid <- as.matrix(expand.grid(x.grid, x.grid))
probabilities <- predict(object = GPCmodel, newdata = grid)$prob
filled.contour(x.grid, x.grid, matrix(probabilities, ngrid, ngrid),
               color.palette = function(n) hcl.colors(n, "RdYlBu", rev = FALSE),
               main = "probabilities map",
               plot.axes = {
                 axis(1)
                 axis(2)
                 points(Xf[f == 1, 1], Xf[f == 1, 2], col = "blue", pch = 21, bg = "blue")
                 points(Xf[f == -1, 1], Xf[f == -1, 2], col = "red", pch = 21, bg = "red")
               }
)

Print values of a Gaussian Process Classification (GPC) model

Description

Show method for gpcm object. Printing the main features of a GPC model.

Usage

show.gpcm(object)
show.gpcm(object)

Arguments

object

an object of class gpcm. See gpcm.

Value

returns an invisible 'NULL'

Author(s)

Morgane MENZ, Céline HELBERT, Victor PICHENY, François BACHOC. Contributors: Naoual SERRAJI.

Examples

## 20-points DoE, and the corresponding response
d <- 2
nb_PX <- 20
require(DiceDesign)
x <- lhsDesign(nb_PX, d, seed = 123)$design
require(DiceKriging)
fx <- apply(x, 1, branin)
f <- ifelse(fx < 14, -1, 1)
Xf <- as.matrix(x)

## GPC model 
model <- gpcm(f, Xf, coef.m=0, coef.cov=c(0.5,0.5))

## print the result 
show(model)
## 20-points DoE, and the corresponding response
d <- 2
nb_PX <- 20
require(DiceDesign)
x <- lhsDesign(nb_PX, d, seed = 123)$design
require(DiceKriging)
fx <- apply(x, 1, branin)
f <- ifelse(fx < 14, -1, 1)
Xf <- as.matrix(x)

## GPC model 
model <- gpcm(f, Xf, coef.m=0, coef.cov=c(0.5,0.5))

## print the result 
show(model)

Update of a Gaussian Process Classification (GPC) model

Description

Update a gpcm object when one or many new observations are added.

Usage

## S3 method for class 'gpcm'
update(object, newf, newXf, newX.alreadyExist,
 newnoise.var, covandmean.reestim=TRUE, multistart = 1, seed = NULL,
  lower = NULL, upper = NULL, nsimu = 100, normalize = TRUE, ...)
## S3 method for class 'gpcm'
update(object, newf, newXf, newX.alreadyExist,
 newnoise.var, covandmean.reestim=TRUE, multistart = 1, seed = NULL,
  lower = NULL, upper = NULL, nsimu = 100, normalize = TRUE, ...)

Arguments

`object`	an object of `gpcm` class.
`newf`	a vector corresponding to the new binary observations (+/-1) at `newXf` locations. These locations can be new locations or existing ones.
`newXf`	a matrix with `object@d` columns representing the locations to be updated. These locations can be new locations or existing ones.
`newX.alreadyExist`	Boolean: indicate whether the locations `newXf` are all news or not. Default: `TRUE`, corresponding to existing locations in newX.
`newnoise.var`	optional scalar, nugget effect at new observations.
`covandmean.reestim`	should the mean and covariance parameters be re-estimated? Default is `TRUE`.
`multistart`	an optional integer indicating the number of initial points from which running the `BFGS` for covariance parameter optimization. Default is 1.
`seed`	to fix the seed, default is `NULL`.
`lower`	(see below).
`upper`	`lower`, `upper`: bounds for the covariance parameters (scalars or vectors), if `NULL` they are set to 0.2 and 3, respectively.
`nsimu`	an integer indicating the number of samples of the latent GP at observation points `Xf` to generate. Must be a non-null integer. Default is 100.
`normalize`	a logical parameter indicating whether to normalize the input matrix `Xf`. If `TRUE`, the matrix will be normalized using `X.mean` and `X.std` values if given; otherwise, the mean and standard deviation are calculated and used for normalization.
`...`	no other argument for this method

Value

Updated gpcm object.

Author(s)

Morgane MENZ, Céline HELBERT, Victor PICHENY, François BACHOC. Contributors: Naoual SERRAJI.

References

Bachoc, F., Helbert, C. & Picheny, V. Gaussian process optimization with failures: classification and convergence proof. J Glob Optim 78, 483–506 (2020). doi:10.1007/s10898-020-00920-0.

Kotecha, J. H., Djuric, P. M. (1999). Gibbs Sampling Approach For Generation of Truncated Multivariate Gaussian Random Variables. IEEE Computer Society, 1757–1760.

Wilhelm, S. tmvtnorm: Truncated Multivariate Normal and Student t Distribution. R package version 1.6. https://CRAN.R-project.org/package=tmvtnorm.

Byrd, R. H., Lu, P., Nocedal, J. and Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing, 16, 1190–1208. doi:10.1137/0916069.

Examples

# ----------------------------------
# A 1D example - sinusoidal function
# ----------------------------------

# Test function
sinusoidal_function <- function(x) {
  sin(4 * pi * x)}

# Desing of Experiment Xf and the corresponding sign f
Xf <- as.matrix(c(0.07, 0.19, 0.42, 0.56, 0.81, 0.90))
f <- rep(1,length(Xf)); f[(sinusoidal_function(Xf)<0)]<- -1

# Builidng a GPC model
GPCmodel1 <- gpcm(f = f, Xf = Xf, coef.m=0, coef.cov=0.26)
print(GPCmodel1)

# New points added to the gpcm object.
newXf <- as.matrix(c(0.1,0.5,0.7, 0.95))
newf <- rep(1,length(newXf)); newf[(sinusoidal_function(newXf)<0)]<- -1

# Updating GPC model
NewGPCmodel <- update(object = GPCmodel1, newf = newf, newXf = newXf)
print(NewGPCmodel)
# ----------------------------------
# A 1D example - sinusoidal function
# ----------------------------------

# Test function
sinusoidal_function <- function(x) {
  sin(4 * pi * x)}

# Desing of Experiment Xf and the corresponding sign f
Xf <- as.matrix(c(0.07, 0.19, 0.42, 0.56, 0.81, 0.90))
f <- rep(1,length(Xf)); f[(sinusoidal_function(Xf)<0)]<- -1

# Builidng a GPC model
GPCmodel1 <- gpcm(f = f, Xf = Xf, coef.m=0, coef.cov=0.26)
print(GPCmodel1)

# New points added to the gpcm object.
newXf <- as.matrix(c(0.1,0.5,0.7, 0.95))
newf <- rep(1,length(newXf)); newf[(sinusoidal_function(newXf)<0)]<- -1

# Updating GPC model
NewGPCmodel <- update(object = GPCmodel1, newf = newf, newXf = newXf)
print(NewGPCmodel)

Package 'GPCsign'

Help Index

Fit and/or create a Gaussian Process Classification (GPC) model

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Gaussian Process Classification (GPC) models class

Description

Slots

Objects from the Class

Author(s)

See Also

Compute logLikelihood

Description

Usage

Arguments

Value

Author(s)

References

Examples

Predict class probability at newdata for a Gaussian Process Classification (GPC) model

Description

Usage

Arguments

Value

Author(s)

References

Examples

Print values of a Gaussian Process Classification (GPC) model

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Update of a Gaussian Process Classification (GPC) model

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples