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Type:

Package

Title:

Gaussian Process Fitting

Version:

0.2.17

Maintainer:

Collin Erickson <collinberickson@gmail.com>

Description:

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, and 'Rcpp' has been used to speed up calculations. For more info about Gaussian process software, see Erickson et al. (2018) <doi:10.1016/j.ejor.2017.10.002>.

License:

GPL-3

LinkingTo:

Rcpp, RcppArmadillo

Imports:

ggplot2, Rcpp, R6, lbfgs

RoxygenNote:

7.3.2

Depends:

mixopt (> 0.1.0), numDeriv, rmarkdown, tidyr

Suggests:

ContourFunctions, dplyr, ggrepel, gridExtra, knitr, lhs,MASS, microbenchmark, rlang, splitfngr, testthat, testthatmulti

VignetteBuilder:

knitr

URL:

https://github.com/CollinErickson/GauPro

BugReports:

https://github.com/CollinErickson/GauPro/issues

Encoding:

UTF-8

NeedsCompilation:

yes

Packaged:

2025-11-21 00:30:16 UTC; colli

Author:

Collin Erickson [aut, cre]

Repository:

CRAN

Date/Publication:

2025-11-21 20:20:27 UTC

Kernel product

Description

Kernel product

Usage

## S3 method for class 'GauPro_kernel'k1 * k2

Arguments

k1

First kernel

k2

Second kernel

Value

Kernel which is product of two kernels

Examples

k1 <- Exponential$new(beta=1)k2 <- Matern32$new(beta=0)k <- k1 * k2k$k(matrix(c(2,1), ncol=1))

Kernel sum

Description

Kernel sum

Usage

## S3 method for class 'GauPro_kernel'k1 + k2

Arguments

k1

First kernel

k2

Second kernel

Value

Kernel which is sum of two kernels

Examples

k1 <- Exponential$new(beta=1)k2 <- Matern32$new(beta=0)k <- k1 + k2k$k(matrix(c(2,1), ncol=1))

Cubic Kernel R6 class

Description

Cubic Kernel R6 class

Usage

k_Cubic(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_Cubic

Methods

Public methods

Inherited methods

Method`k()`

Calculate covariance between two points

Usage

Cubic$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Cubic$kone(x, y, beta, theta, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Cubic$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Cubic$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`print()`

Print this object

Usage

Cubic$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Cubic$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Cubic$new(beta=runif(6)-.5)plot(k1)n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Cubic$new(1),                              parallel=FALSE, restarts=0)gp$predict(.454)

Exponential Kernel R6 class

Description

Exponential Kernel R6 class

Usage

k_Exponential(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_Exponential

Methods

Public methods

Inherited methods

Method`k()`

Calculate covariance between two points

Usage

Exponential$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Exponential$kone(x, y, beta, theta, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Exponential$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Exponential$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`print()`

Print this object

Usage

Exponential$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Exponential$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Exponential$new(beta=0)

Factor Kernel R6 class

Description

Initialize kernel object

Usage

k_FactorKernel(  s2 = 1,  D,  nlevels,  xindex,  p_lower = 0,  p_upper = 0.9,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  p,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2

Initial variance

D

Number of input dimensions of data

nlevels

Number of levels for the factor

xindex

Index of the factor (which column of X)

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

p

Vector of correlations

useC

Should C code used? Not implemented for FactorKernel yet.

offdiagequal

What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Format

R6Class object.

Details

For a factor that has been converted to its indices.Each factor will need a separate kernel.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_FactorKernel

Public fields

p: Parameter for correlation
p_est: Should p be estimated?
p_lower: Lower bound of p
p_upper: Upper bound of p
p_length: length of p
s2: variance
s2_est: Is s2 estimated?
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2
xindex: Index of the factor (which column of X)
nlevels: Number of levels for the factor
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

FactorKernel$new(  s2 = 1,  D,  nlevels,  xindex,  p_lower = 0,  p_upper = 0.9,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  p,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2: Initial variance
D: Number of input dimensions of data
nlevels: Number of levels for the factor
xindex: Index of the factor (which column of X)
p_lower: Lower bound for p
p_upper: Upper bound for p
p_est: Should p be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
p: Vector of correlations
useC: Should C code used? Not implemented for FactorKernel yet.
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`k()`

Calculate covariance between two points

Usage

FactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
p: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

FactorKernel$kone(x, y, p, s2, isdiag = TRUE, offdiagequal = self$offdiagequal)

Arguments

x: vector
y: vector
p: correlation parameters on regular scale
s2: Variance parameter
isdiag: Is this on the diagonal of the covariance?
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

FactorKernel$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

FactorKernel$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

FactorKernel$dC_dx(XX, X, ...)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
...: Additional args, not used

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

FactorKernel$param_optim_start(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

FactorKernel$param_optim_start0(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

FactorKernel$param_optim_lower(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

FactorKernel$param_optim_upper(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

FactorKernel$set_params_from_optim(  optim_out,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`s2_from_params()`

Get s2 from params vector

Usage

FactorKernel$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

FactorKernel$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

FactorKernel$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

kk <- FactorKernel$new(D=1, nlevels=5, xindex=1)kk$p <- (1:10)/100kmat <- outer(1:5, 1:5, Vectorize(kk$k))kmatkk$plot()# 2D, Gaussian on 1D, index on 2nd dimif (requireNamespace("dplyr", quietly=TRUE)) {library(dplyr)n <- 20X <- cbind(matrix(runif(n,2,6), ncol=1),           matrix(sample(1:2, size=n, replace=TRUE), ncol=1))X <- rbind(X, c(3.3,3))n <- nrow(X)Z <- X[,1] - (X[,2]-1.8)^2 + rnorm(n,0,.1)tibble(X=X, Z) %>% arrange(X,Z)k2a <- IgnoreIndsKernel$new(k=Gaussian$new(D=1), ignoreinds = 2)k2b <- FactorKernel$new(D=2, nlevels=3, xind=2)k2 <- k2a * k2bk2b$p_upper <- .65*k2b$p_uppergp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,                              nug.min=1e-2, restarts=0)gp$kernel$k1$kernel$betagp$kernel$k2$pgp$kernel$k(x = gp$X)tibble(X=X, Z=Z, pred=gp$predict(X)) %>% arrange(X, Z)tibble(X=X[,2], Z) %>% group_by(X) %>% summarize(n=n(), mean(Z))curve(gp$pred(cbind(matrix(x,ncol=1),1)),2,6, ylim=c(min(Z), max(Z)))points(X[X[,2]==1,1], Z[X[,2]==1])curve(gp$pred(cbind(matrix(x,ncol=1),2)), add=TRUE, col=2)points(X[X[,2]==2,1], Z[X[,2]==2], col=2)curve(gp$pred(cbind(matrix(x,ncol=1),3)), add=TRUE, col=3)points(X[X[,2]==3,1], Z[X[,2]==3], col=3)legend(legend=1:3, fill=1:3, x="topleft")# See which points affect (5.5, 3 themost)data.frame(X, cov=gp$kernel$k(X, c(5.5,3))) %>% arrange(-cov)plot(k2b)}

GauPro_selector

Description

GauPro_selector

Usage

GauPro(..., type = "Gauss")

Arguments

...

Pass on

type

Type of Gaussian process, or the kind of correlation function.

Value

A GauPro object

Examples

n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)#y <- sin(2*pi*x) + rnorm(n,0,1e-1)y <- (2*x) %%1gp <- GauPro(X=x, Z=y, parallel=FALSE)

Corr Gauss GP using inherited optim

Description

Corr Gauss GP using inherited optim

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_base ->GauPro_Gauss

Public fields

corr: Name of correlation
theta: Correlation parameters
theta_length: Length of theta
theta_map: Map for theta
theta_short: Short vector for theta
separable: Are the dimensions separable?

Methods

Public methods

Inherited methods

Method`new()`

Create GauPro object

Usage

GauPro_Gauss$new(  X,  Z,  verbose = 0,  separable = T,  useC = F,  useGrad = T,  parallel = FALSE,  nug = 1e-06,  nug.min = 1e-08,  nug.est = T,  param.est = T,  theta = NULL,  theta_short = NULL,  theta_map = NULL,  ...)

Arguments

X: Matrix whose rows are the input points
Z: Output points corresponding to X
verbose: Amount of stuff to print. 0 is little, 2 is a lot.
separable: Are dimensions separable?
useC: Should C code be used when possible? Should be faster.
useGrad: Should the gradient be used?
parallel: Should code be run in parallel? Make optimizationfaster but uses more computer resources.
nug: Value for the nugget. The starting value if estimating it.
nug.min: Minimum allowable value for the nugget.
nug.est: Should the nugget be estimated?
param.est: Should the kernel parameters be estimated?
theta: Correlation parameters
theta_short: Correlation parameters, not recommended
theta_map: Correlation parameters, not recommended
...: Not used

Method`corr_func()`

Correlation function

Usage

GauPro_Gauss$corr_func(x, x2 = NULL, theta = self$theta)

Arguments

x: First point
x2: Second point
theta: Correlation parameter

Method`deviance_theta()`

Calculate deviance

Usage

GauPro_Gauss$deviance_theta(theta)

Arguments

theta: Correlation parameter

Method`deviance_theta_log()`

Calculate deviance

Usage

GauPro_Gauss$deviance_theta_log(beta)

Arguments

beta: Correlation parameter on log scale

Method`deviance()`

Calculate deviance

Usage

GauPro_Gauss$deviance(theta = self$theta, nug = self$nug)

Arguments

theta: Correlation parameter
nug: Nugget

Method`deviance_grad()`

Calculate deviance gradient

Usage

GauPro_Gauss$deviance_grad(  theta = NULL,  nug = self$nug,  joint = NULL,  overwhat = if (self$nug.est) "joint" else "theta")

Arguments

theta: Correlation parameter
nug: Nugget
joint: Calculate over theta and nug at same time?
overwhat: Calculate over theta and nug at same time?

Method`deviance_fngr()`

Calculate deviance and gradient at same time

Usage

GauPro_Gauss$deviance_fngr(  theta = NULL,  nug = NULL,  overwhat = if (self$nug.est) "joint" else "theta")

Arguments

theta: Correlation parameter
nug: Nugget
overwhat: Calculate over theta and nug at same time?
joint: Calculate over theta and nug at same time?

Method`deviance_log()`

Calculate deviance gradient

Usage

GauPro_Gauss$deviance_log(beta = NULL, nug = self$nug, joint = NULL)

Arguments

beta: Correlation parameter on log scale
nug: Nugget
joint: Calculate over theta and nug at same time?

Method`deviance_log2()`

Calculate deviance on log scale

Usage

GauPro_Gauss$deviance_log2(beta = NULL, lognug = NULL, joint = NULL)

Arguments

beta: Correlation parameter on log scale
lognug: Log of nugget
joint: Calculate over theta and nug at same time?

Method`deviance_log_grad()`

Calculate deviance gradient on log scale

Usage

GauPro_Gauss$deviance_log_grad(  beta = NULL,  nug = self$nug,  joint = NULL,  overwhat = if (self$nug.est) "joint" else "theta")

Arguments

beta: Correlation parameter
nug: Nugget
joint: Calculate over theta and nug at same time?
overwhat: Calculate over theta and nug at same time?

Method`deviance_log2_grad()`

Calculate deviance gradient on log scale

Usage

GauPro_Gauss$deviance_log2_grad(  beta = NULL,  lognug = NULL,  joint = NULL,  overwhat = if (self$nug.est) "joint" else "theta")

Arguments

beta: Correlation parameter
lognug: Log of nugget
joint: Calculate over theta and nug at same time?
overwhat: Calculate over theta and nug at same time?

Method`deviance_log2_fngr()`

Calculate deviance and gradient on log scale

Usage

GauPro_Gauss$deviance_log2_fngr(  beta = NULL,  lognug = NULL,  joint = NULL,  overwhat = if (self$nug.est) "joint" else "theta")

Arguments

beta: Correlation parameter
lognug: Log of nugget
joint: Calculate over theta and nug at same time?
overwhat: Calculate over theta and nug at same time?

Method`get_optim_functions()`

Get optimization functions

Usage

GauPro_Gauss$get_optim_functions(param_update, nug.update)

Arguments

param_update: Should the parameters be updated?
nug.update: Should the nugget be updated?

Method`param_optim_lower()`

Lower bound of params

Usage

GauPro_Gauss$param_optim_lower()

Method`param_optim_upper()`

Upper bound of params

Usage

GauPro_Gauss$param_optim_upper()

Method`param_optim_start()`

Start value of params for optim

Usage

GauPro_Gauss$param_optim_start()

Method`param_optim_start0()`

Start value of params for optim

Usage

GauPro_Gauss$param_optim_start0()

Method`param_optim_jitter()`

Jitter value of params for optim

Usage

GauPro_Gauss$param_optim_jitter(param_value)

Arguments

param_value: param value to add jitter to

Method`update_params()`

Update value of params after optim

Usage

GauPro_Gauss$update_params(restarts, param_update, nug.update)

Arguments

restarts: Number of restarts
param_update: Are the params being updated?
nug.update: Is the nugget being updated?

Method`grad()`

Calculate the gradient

Usage

GauPro_Gauss$grad(XX)

Arguments

XX: Points to calculate grad at

Method`grad_dist()`

Calculate the gradient distribution

Usage

GauPro_Gauss$grad_dist(XX)

Arguments

XX: Points to calculate grad at

Method`hessian()`

Calculate the hessian

Usage

GauPro_Gauss$hessian(XX, useC = self$useC)

Arguments

XX: Points to calculate grad at
useC: Should C code be used to speed up?

Method`print()`

Print this object

Usage

GauPro_Gauss$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_Gauss$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_Gauss$new(X=x, Z=y, parallel=FALSE)

Corr Gauss GP using inherited optim

Description

Corr Gauss GP using inherited optim

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_base ->GauPro::GauPro_Gauss ->GauPro_Gauss_LOO

Public fields

use_LOO: Should the leave-one-out correction be used?
tmod: Second GP model fit to the t-values of leave-one-out predictions

Methods

Public methods

Inherited methods

Method`update()`

Update the model, can be data and parameters

Usage

GauPro_Gauss_LOO$update(  Xnew = NULL,  Znew = NULL,  Xall = NULL,  Zall = NULL,  restarts = 5,  param_update = self$param.est,  nug.update = self$nug.est,  no_update = FALSE)

Arguments

Xnew: New X matrix
Znew: New Z values
Xall: Matrix with all X values
Zall: All Z values
restarts: Number of optimization restarts
param_update: Should the parameters be updated?
nug.update: Should the nugget be updated?
no_update: Should none of the parameters/nugget be updated?

Method`pred_one_matrix()`

Predict mean and se for given matrix

Usage

GauPro_Gauss_LOO$pred_one_matrix(XX, se.fit = F, covmat = F)

Arguments

XX: Points to predict at
se.fit: Should the se be returned?
covmat: Should the covariance matrix be returned?

Method`print()`

Print this object

Usage

GauPro_Gauss_LOO$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_Gauss_LOO$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_Gauss_LOO$new(X=x, Z=y, parallel=FALSE)

Class providing object with methods for fitting a GP model

Description

Class providing object with methods for fitting a GP model

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Methods

new(X, Z, corr="Gauss", verbose=0, separable=T, useC=F,useGrad=T, parallel=T, nug.est=T, ...): This method is used to create object of this class withX andZ as the data.
update(Xnew=NULL, Znew=NULL, Xall=NULL, Zall=NULL,restarts = 5,param_update = T, nug.update = self$nug.est): This method updates the model, adding new data if given, then running optimization again.

Public fields

X: Design matrix
Z: Responses
N: Number of data points
D: Dimension of data
nug.min: Minimum value of nugget
nug: Value of the nugget, is estimated unless told otherwise
verbose: 0 means nothing printed, 1 prints some, 2 prints most.
useGrad: Should grad be used?
useC: Should C code be used?
parallel: Should the code be run in parallel?
parallel_cores: How many cores are there? It will self detect,do not set yourself.
nug.est: Should the nugget be estimated?
param.est: Should the parameters be estimated?
mu_hat: Mean estimate
s2_hat: Variance estimate
K: Covariance matrix
Kchol: Cholesky factorization of K
Kinv: Inverse of K

Methods

Public methods

Method`corr_func()`

Correlation function

Usage

GauPro_base$corr_func(...)

Arguments

...: Does nothing

Method`new()`

Create GauPro object

Usage

GauPro_base$new(  X,  Z,  verbose = 0,  useC = F,  useGrad = T,  parallel = FALSE,  nug = 1e-06,  nug.min = 1e-08,  nug.est = T,  param.est = TRUE,  ...)

Arguments

X: Matrix whose rows are the input points
Z: Output points corresponding to X
verbose: Amount of stuff to print. 0 is little, 2 is a lot.
useC: Should C code be used when possible? Should be faster.
useGrad: Should the gradient be used?
parallel: Should code be run in parallel? Make optimizationfaster but uses more computer resources.
nug: Value for the nugget. The starting value if estimating it.
nug.min: Minimum allowable value for the nugget.
nug.est: Should the nugget be estimated?
param.est: Should the kernel parameters be estimated?
...: Not used

Method`initialize_GauPr()`

Not used

Usage

GauPro_base$initialize_GauPr()

Method`fit()`

Fit the model, never use this function

Usage

GauPro_base$fit(X, Z)

Arguments

X: Not used
Z: Not used

Method`update_K_and_estimates()`

Update Covariance matrix and estimated parameters

Usage

GauPro_base$update_K_and_estimates()

Method`predict()`

Predict mean and se for given matrix

Usage

GauPro_base$predict(XX, se.fit = F, covmat = F, split_speed = T)

Arguments

XX: Points to predict at
se.fit: Should the se be returned?
covmat: Should the covariance matrix be returned?
split_speed: Should the predictions be split up for speed

Method`pred()`

Predict mean and se for given matrix

Usage

GauPro_base$pred(XX, se.fit = F, covmat = F, split_speed = T)

Arguments

XX: Points to predict at
se.fit: Should the se be returned?
covmat: Should the covariance matrix be returned?
split_speed: Should the predictions be split up for speed

Method`pred_one_matrix()`

Predict mean and se for given matrix

Usage

GauPro_base$pred_one_matrix(XX, se.fit = F, covmat = F)

Arguments

XX: Points to predict at
se.fit: Should the se be returned?
covmat: Should the covariance matrix be returned?

Method`pred_mean()`

Predict mean

Usage

GauPro_base$pred_mean(XX, kx.xx)

Arguments

XX: Points to predict at
kx.xx: Covariance matrix between X and XX

Method`pred_meanC()`

Predict mean using C code

Usage

GauPro_base$pred_meanC(XX, kx.xx)

Arguments

XX: Points to predict at
kx.xx: Covariance matrix between X and XX

Method`pred_var()`

Predict variance

Usage

GauPro_base$pred_var(XX, kxx, kx.xx, covmat = F)

Arguments

XX: Points to predict at
kxx: Covariance matrix of XX with itself
kx.xx: Covariance matrix between X and XX
covmat: Not used

Method`pred_LOO()`

Predict at X using leave-one-out. Can use for diagnostics.

Usage

GauPro_base$pred_LOO(se.fit = FALSE)

Arguments

se.fit: Should the standard error and t values be returned?

Method`plot()`

Plot the object

Usage

GauPro_base$plot(...)

Arguments

...: Parameters passed to cool1Dplot(), plot2D(), or plotmarginal()

Method`cool1Dplot()`

Make cool 1D plot

Usage

GauPro_base$cool1Dplot(  n2 = 20,  nn = 201,  col2 = "gray",  xlab = "x",  ylab = "y",  xmin = NULL,  xmax = NULL,  ymin = NULL,  ymax = NULL)

Arguments

n2: Number of things to plot
nn: Number of things to plot
col2: color
xlab: x label
ylab: y label
xmin: xmin
xmax: xmax
ymin: ymin
ymax: ymax

Method`plot1D()`

Make 1D plot

Usage

GauPro_base$plot1D(  n2 = 20,  nn = 201,  col2 = 2,  xlab = "x",  ylab = "y",  xmin = NULL,  xmax = NULL,  ymin = NULL,  ymax = NULL)

Arguments

n2: Number of things to plot
nn: Number of things to plot
col2: Color of the prediction interval
xlab: x label
ylab: y label
xmin: xmin
xmax: xmax
ymin: ymin
ymax: ymax

Method`plot2D()`

Make 2D plot

Usage

GauPro_base$plot2D()

Method`loglikelihood()`

Calculate the log likelihood, don't use this

Usage

GauPro_base$loglikelihood(mu = self$mu_hat, s2 = self$s2_hat)

Arguments

mu: Mean vector
s2: s2 param

Method`optim()`

Optimize parameters

Usage

GauPro_base$optim(  restarts = 5,  param_update = T,  nug.update = self$nug.est,  parallel = self$parallel,  parallel_cores = self$parallel_cores)

Arguments

restarts: Number of restarts to do
param_update: Should parameters be updated?
nug.update: Should nugget be updated?
parallel: Should restarts be done in parallel?
parallel_cores: If running parallel, how many cores should be used?

Method`optimRestart()`

Run a single optimization restart.

Usage

GauPro_base$optimRestart(  start.par,  start.par0,  param_update,  nug.update,  optim.func,  optim.grad,  optim.fngr,  lower,  upper,  jit = T)

Arguments

start.par: Starting parameters
start.par0: Starting parameters
param_update: Should parameters be updated?
nug.update: Should nugget be updated?
optim.func: Function to optimize.
optim.grad: Gradient of function to optimize.
optim.fngr: Function that returns the function valueand its gradient.
lower: Lower bounds for optimization
upper: Upper bounds for optimization
jit: Is jitter being used?

Method`update()`

Update the model, can be data and parameters

Usage

GauPro_base$update(  Xnew = NULL,  Znew = NULL,  Xall = NULL,  Zall = NULL,  restarts = 5,  param_update = self$param.est,  nug.update = self$nug.est,  no_update = FALSE)

Arguments

Xnew: New X matrix
Znew: New Z values
Xall: Matrix with all X values
Zall: All Z values
restarts: Number of optimization restarts
param_update: Should the parameters be updated?
nug.update: Should the nugget be updated?
no_update: Should none of the parameters/nugget be updated?

Method`update_data()`

Update the data

Usage

GauPro_base$update_data(Xnew = NULL, Znew = NULL, Xall = NULL, Zall = NULL)

Arguments

Xnew: New X matrix
Znew: New Z values
Xall: Matrix with all X values
Zall: All Z values

Method`update_corrparams()`

Update the correlation parameters

Usage

GauPro_base$update_corrparams(...)

Arguments

...: Args passed to update

Method`update_nugget()`

Update the nugget

Usage

GauPro_base$update_nugget(...)

Arguments

...: Args passed to update

Method`deviance_searchnug()`

Optimize deviance for nugget

Usage

GauPro_base$deviance_searchnug()

Method`nugget_update()`

Update the nugget

Usage

GauPro_base$nugget_update()

Method`grad_norm()`

Calculate the norm of the gradient at XX

Usage

GauPro_base$grad_norm(XX)

Arguments

XX: Points to calculate at

Method`sample()`

Sample at XX

Usage

GauPro_base$sample(XX, n = 1)

Arguments

XX: Input points to sample at
n: Number of samples

Method`print()`

Print object

Usage

GauPro_base$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_base$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

#n <- 12#x <- matrix(seq(0,1,length.out = n), ncol=1)#y <- sin(2*pi*x) + rnorm(n,0,1e-1)#gp <- GauPro(X=x, Z=y, parallel=FALSE)

Kernel R6 class

Description

Kernel R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Public fields

D: Number of input dimensions of data
useC: Should C code be used when possible? Can be much faster.

Methods

Public methods

Method`plot()`

Plot kernel decay.

Usage

GauPro_kernel$plot(X = NULL)

Arguments

X: Matrix of points the kernel is used with. Some will be usedto demonstrate how the covariance changes.

Method`print()`

Print this object

Usage

GauPro_kernel$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_kernel$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

#k <- GauPro_kernel$new()

Beta Kernel R6 class

Description

Beta Kernel R6 class

Format

R6Class object.

Details

This is the base structure for a kernel that uses beta = log10(theta)for the lengthscale parameter.It standardizes the params because they all use the same underlyingstructure.Kernels that inherit this only need to implement kone and dC_dparams.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_beta

Public fields

beta: Parameter for correlation. Log of theta.
beta_est: Should beta be estimated?
beta_lower: Lower bound of beta
beta_upper: Upper bound of beta
beta_length: length of beta
s2: variance
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster.
isotropic: If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Methods

Public methods

Inherited methods

Method`new()`

Initialize kernel object

Usage

GauPro_kernel_beta$new(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta: Initial beta value
s2: Initial variance
D: Number of input dimensions of data
beta_lower: Lower bound for beta
beta_upper: Upper bound for beta
beta_est: Should beta be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster.
isotropic: If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Method`k()`

Calculate covariance between two points

Usage

GauPro_kernel_beta$k(  x,  y = NULL,  beta = self$beta,  s2 = self$s2,  params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters. Log of theta.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Calculate covariance between two points

Usage

GauPro_kernel_beta$kone(x, y, beta, theta, s2)

Arguments

x: vector.
y: vector.
beta: Correlation parameters. Log of theta.
theta: Correlation parameters.
s2: Variance parameter.

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

GauPro_kernel_beta$param_optim_start(  jitter = F,  y,  beta_est = self$beta_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
beta_est: Is beta being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

GauPro_kernel_beta$param_optim_start0(  jitter = F,  y,  beta_est = self$beta_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
beta_est: Is beta being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Upper bounds of parameters for optimization

Usage

GauPro_kernel_beta$param_optim_lower(  beta_est = self$beta_est,  s2_est = self$s2_est)

Arguments

beta_est: Is beta being estimated?
s2_est: Is s2 being estimated?
p_est: Is p being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

GauPro_kernel_beta$param_optim_upper(  beta_est = self$beta_est,  s2_est = self$s2_est)

Arguments

beta_est: Is beta being estimated?
s2_est: Is s2 being estimated?
p_est: Is p being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

GauPro_kernel_beta$set_params_from_optim(  optim_out,  beta_est = self$beta_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
beta_est: Is beta being estimated?
s2_est: Is s2 being estimated?

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

GauPro_kernel_beta$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`s2_from_params()`

Get s2 from params vector

Usage

GauPro_kernel_beta$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_kernel_beta$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

#k1 <- Matern52$new(beta=0)

Gaussian process model with kernel

Description

Class providing object with methods for fitting a GP model.Allows for different kernel and trend functions to be used.The object is an R6 object with many methods that can be called.

'gpkm()' is equivalent to 'GauPro_kernel_model$new()', but is easier to typeand gives parameter autocomplete suggestions.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Methods

new(X, Z, corr="Gauss", verbose=0, separable=T, useC=F, useGrad=T, parallel=T, nug.est=T, ...): This method is used to create object of thisclass withX andZ as the data.
update(Xnew=NULL, Znew=NULL, Xall=NULL, Zall=NULL,restarts = 0,param_update = T, nug.update = self$nug.est): This method updates themodel, adding new data if given, then running optimization again.

Public fields

X: Design matrix
Z: Responses
N: Number of data points
D: Dimension of data
nug.min: Minimum value of nugget
nug.max: Maximum value of the nugget.
nug.est: Should the nugget be estimated?
nug: Value of the nugget, is estimated unless told otherwise
param.est: Should the kernel parameters be estimated?
verbose: 0 means nothing printed, 1 prints some, 2 prints most.
useGrad: Should grad be used?
useC: Should C code be used?
parallel: Should the code be run in parallel?
parallel_cores: How many cores are there? By default it detects.
kernel: The kernel to determine the correlations.
trend: The trend.
mu_hatX: Predicted trend value for each point in X.
s2_hat: Variance parameter estimate
K: Covariance matrix
Kchol: Cholesky factorization of K
Kinv: Inverse of K
Kinv_Z_minus_mu_hatX: K inverse times Z minus the predictedtrend at X.
restarts: Number of optimization restarts to do when updating.
normalize: Should the inputs be normalized?
normalize_mean: If using normalize, the mean of each column.
normalize_sd: If using normalize, the standarddeviation of each column.
optimizer: What algorithm should be used to optimize theparameters.
track_optim: Should it track the parameters evaluatedwhile optimizing?
track_optim_inputs: If track_optim is TRUE,this will keep a list of parameters evaluated.View them with plot_track_optim.
track_optim_dev: If track_optim is TRUE,this will keep a vector of the deviance values calculatedwhile optimizing parameters.View them with plot_track_optim.
formula: Formula
convert_formula_data: List for storing data to convert datausing the formula

Methods

Public methods

Method`new()`

Create kernel_model object

Usage

GauPro_kernel_model$new(  X,  Z,  kernel,  trend,  verbose = 0,  useC = TRUE,  useGrad = TRUE,  parallel = FALSE,  parallel_cores = "detect",  nug = 1e-06,  nug.min = 1e-08,  nug.max = 100,  nug.est = TRUE,  param.est = TRUE,  restarts = 0,  normalize = FALSE,  optimizer = "L-BFGS-B",  track_optim = FALSE,  formula,  data,  ...)

Arguments

X: Matrix whose rows are the input points
Z: Output points corresponding to X
kernel: The kernel to use. E.g., Gaussian$new().
trend: Trend to use. E.g., trend_constant$new().
verbose: Amount of stuff to print. 0 is little, 2 is a lot.
useC: Should C code be used when possible? Should be faster.
useGrad: Should the gradient be used?
parallel: Should code be run in parallel? Make optimizationfaster but uses more computer resources.
parallel_cores: When using parallel, how many cores shouldbe used?
nug: Value for the nugget. The starting value if estimating it.
nug.min: Minimum allowable value for the nugget.
nug.max: Maximum allowable value for the nugget.
nug.est: Should the nugget be estimated?
param.est: Should the kernel parameters be estimated?
restarts: How many optimization restarts should be used whenestimating parameters?
normalize: Should the data be normalized?
optimizer: What algorithm should be used to optimize theparameters.
track_optim: Should it track the parameters evaluatedwhile optimizing?
formula: Formula for the data if giving in a data frame.
data: Data frame of data. Use in conjunction with formula.
...: Not used

Method`fit()`

Fit model

Usage

GauPro_kernel_model$fit(X, Z)

Arguments

X: Inputs
Z: Outputs

Method`update_K_and_estimates()`

Update covariance matrix and estimates

Usage

GauPro_kernel_model$update_K_and_estimates()

Method`predict()`

Predict for a matrix of points

Usage

GauPro_kernel_model$predict(  XX,  se.fit = F,  covmat = F,  split_speed = F,  mean_dist = FALSE,  return_df = TRUE)

Arguments

XX: points to predict at
se.fit: Should standard error be returned?
covmat: Should covariance matrix be returned?
split_speed: Should the matrix be split for faster predictions?
mean_dist: Should the error be for the distribution of the mean?
return_df: When returning se.fit, should it be returned ina data frame? Otherwise it will be a list, which is faster.

Method`pred()`

Predict for a matrix of points

Usage

GauPro_kernel_model$pred(  XX,  se.fit = F,  covmat = F,  split_speed = F,  mean_dist = FALSE,  return_df = TRUE)

Arguments

XX: points to predict at
se.fit: Should standard error be returned?
covmat: Should covariance matrix be returned?
split_speed: Should the matrix be split for faster predictions?
mean_dist: Should the error be for the distribution of the mean?
return_df: When returning se.fit, should it be returned ina data frame? Otherwise it will be a list, which is faster.

Method`pred_one_matrix()`

Predict for a matrix of points

Usage

GauPro_kernel_model$pred_one_matrix(  XX,  se.fit = F,  covmat = F,  return_df = FALSE,  mean_dist = FALSE)

Arguments

XX: points to predict at
se.fit: Should standard error be returned?
covmat: Should covariance matrix be returned?
return_df: When returning se.fit, should it be returned ina data frame? Otherwise it will be a list, which is faster.
mean_dist: Should the error be for the distribution of the mean?

Method`pred_mean()`

Predict mean

Usage

GauPro_kernel_model$pred_mean(XX, kx.xx)

Arguments

XX: points to predict at
kx.xx: Covariance of X with XX

Method`pred_meanC()`

Predict mean using C

Usage

GauPro_kernel_model$pred_meanC(XX, kx.xx)

Arguments

XX: points to predict at
kx.xx: Covariance of X with XX

Method`pred_var()`

Predict variance

Usage

GauPro_kernel_model$pred_var(XX, kxx, kx.xx, covmat = F)

Arguments

XX: points to predict at
kxx: Covariance of XX with itself
kx.xx: Covariance of X with XX
covmat: Should the covariance matrix be returned?

Method`pred_LOO()`

leave one out predictions

Usage

GauPro_kernel_model$pred_LOO(se.fit = FALSE)

Arguments

se.fit: Should standard errors be included?

Method`pred_var_after_adding_points()`

Predict variance after adding points

Usage

GauPro_kernel_model$pred_var_after_adding_points(add_points, pred_points)

Arguments

add_points: Points to add
pred_points: Points to predict at

Method`pred_var_after_adding_points_sep()`

Predict variance reductions after adding each point separately

Usage

GauPro_kernel_model$pred_var_after_adding_points_sep(add_points, pred_points)

Arguments

add_points: Points to add
pred_points: Points to predict at

Method`pred_var_reduction()`

Predict variance reduction for a single point

Usage

GauPro_kernel_model$pred_var_reduction(add_point, pred_points)

Arguments

add_point: Point to add
pred_points: Points to predict at

Method`pred_var_reductions()`

Predict variance reductions

Usage

GauPro_kernel_model$pred_var_reductions(add_points, pred_points)

Arguments

add_points: Points to add
pred_points: Points to predict at

Method`plot()`

Plot the object

Usage

GauPro_kernel_model$plot(...)

Arguments

...: Parameters passed to cool1Dplot(), plot2D(), or plotmarginal()

Method`cool1Dplot()`

Make cool 1D plot

Usage

GauPro_kernel_model$cool1Dplot(  n2 = 20,  nn = 201,  col2 = "green",  xlab = "x",  ylab = "y",  xmin = NULL,  xmax = NULL,  ymin = NULL,  ymax = NULL,  gg = TRUE)

Arguments

n2: Number of things to plot
nn: Number of things to plot
col2: color
xlab: x label
ylab: y label
xmin: xmin
xmax: xmax
ymin: ymin
ymax: ymax
gg: Should ggplot2 be used to make plot?

Method`plot1D()`

Make 1D plot

Usage

GauPro_kernel_model$plot1D(  n2 = 20,  nn = 201,  col2 = 2,  col3 = 3,  xlab = "x",  ylab = "y",  xmin = NULL,  xmax = NULL,  ymin = NULL,  ymax = NULL,  gg = TRUE)

Arguments

n2: Number of things to plot
nn: Number of things to plot
col2: Color of the prediction interval
col3: Color of the interval for the mean
xlab: x label
ylab: y label
xmin: xmin
xmax: xmax
ymin: ymin
ymax: ymax
gg: Should ggplot2 be used to make plot?

Method`plot2D()`

Make 2D plot

Usage

GauPro_kernel_model$plot2D(se = FALSE, mean = TRUE, horizontal = TRUE, n = 50)

Arguments

se: Should the standard error of prediction be plotted?
mean: Should the mean be plotted?
horizontal: If plotting mean and se, should they be next to eachother?
n: Number of points along each dimension

Method`plotmarginal()`

Plot marginal. For each input, hold all others at a constantvalue and adjust it along it's range to see how the prediction changes.

Usage

GauPro_kernel_model$plotmarginal(npt = 5, ncol = NULL)

Arguments

npt: Number of lines to make. Each line represents changing asingle variable while holding the others at the same values.
ncol: Number of columnsfor the plot

Method`plotmarginalrandom()`

Plot marginal prediction for random sample of inputs

Usage

GauPro_kernel_model$plotmarginalrandom(npt = 100, ncol = NULL)

Arguments

npt: Number of random points to evaluate
ncol: Number of columns in the plot

Method`plotkernel()`

Plot the kernel

Usage

GauPro_kernel_model$plotkernel(X = self$X)

Arguments

X: X matrix for kernel plot

Method`plotLOO()`

Plot leave one out predictions for design points

Usage

GauPro_kernel_model$plotLOO()

Method`plot_track_optim()`

If track_optim, this will plot the parametersin the order they were evaluated.

Usage

GauPro_kernel_model$plot_track_optim(minindex = NULL)

Arguments

minindex: Minimum index to plot.

Method`loglikelihood()`

Calculate loglikelihood of parameters

Usage

GauPro_kernel_model$loglikelihood(mu = self$mu_hatX, s2 = self$s2_hat)

Arguments

mu: Mean parameters
s2: Variance parameter

Method`AIC()`

AIC (Akaike information criterion)

Usage

GauPro_kernel_model$AIC()

Method`get_optim_functions()`

Get optimization functions

Usage

GauPro_kernel_model$get_optim_functions(param_update, nug.update)

Arguments

param_update: Should parameters be updated?
nug.update: Should nugget be updated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

GauPro_kernel_model$param_optim_lower(nug.update)

Arguments

nug.update: Is the nugget being updated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

GauPro_kernel_model$param_optim_upper(nug.update)

Arguments

nug.update: Is the nugget being updated?

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

GauPro_kernel_model$param_optim_start(nug.update, jitter)

Arguments

nug.update: Is nugget being updated?
jitter: Should there be a jitter?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

GauPro_kernel_model$param_optim_start0(nug.update, jitter)

Arguments

nug.update: Is nugget being updated?
jitter: Should there be a jitter?

Method`param_optim_start_mat()`

Get matrix for starting points of optimization

Usage

GauPro_kernel_model$param_optim_start_mat(restarts, nug.update, l)

Arguments

restarts: Number of restarts to use
nug.update: Is nugget being updated?
l: Not used

Method`optim()`

Optimize parameters

Usage

GauPro_kernel_model$optim(  restarts = self$restarts,  n0 = 5 * self$D,  param_update = T,  nug.update = self$nug.est,  parallel = self$parallel,  parallel_cores = self$parallel_cores)

Arguments

restarts: Number of restarts to do
n0: This many starting parameters are chosen and evaluated.The best ones are used as the starting points for optimization.
param_update: Should parameters be updated?
nug.update: Should nugget be updated?
parallel: Should restarts be done in parallel?
parallel_cores: If running parallel, how many cores should be used?

Method`optimRestart()`

Run a single optimization restart.

Usage

GauPro_kernel_model$optimRestart(  start.par,  start.par0,  param_update,  nug.update,  optim.func,  optim.grad,  optim.fngr,  lower,  upper,  jit = T,  start.par.i)

Arguments

start.par: Starting parameters
start.par0: Starting parameters
param_update: Should parameters be updated?
nug.update: Should nugget be updated?
optim.func: Function to optimize.
optim.grad: Gradient of function to optimize.
optim.fngr: Function that returns the function valueand its gradient.
lower: Lower bounds for optimization
upper: Upper bounds for optimization
jit: Is jitter being used?
start.par.i: Starting parameters for this restart

Method`update()`

Update the model. Should only give in(Xnew and Znew) or (Xall and Zall).

Usage

GauPro_kernel_model$update(  Xnew = NULL,  Znew = NULL,  Xall = NULL,  Zall = NULL,  restarts = self$restarts,  param_update = self$param.est,  nug.update = self$nug.est,  no_update = FALSE)

Arguments

Xnew: New X values to add.
Znew: New Z values to add.
Xall: All X values to be used. Will replace existing X.
Zall: All Z values to be used. Will replace existing Z.
restarts: Number of optimization restarts.
param_update: Are the parameters being updated?
nug.update: Is the nugget being updated?
no_update: Are no parameters being updated?

Method`update_fast()`

Fast update when adding new data.

Usage

GauPro_kernel_model$update_fast(Xnew = NULL, Znew = NULL)

Arguments

Xnew: New X values to add.
Znew: New Z values to add.

Method`update_params()`

Update the parameters.

Usage

GauPro_kernel_model$update_params(..., nug.update)

Arguments

...: Passed to optim.
nug.update: Is the nugget being updated?

Method`update_data()`

Update the data. Should only give in(Xnew and Znew) or (Xall and Zall).

Usage

GauPro_kernel_model$update_data(  Xnew = NULL,  Znew = NULL,  Xall = NULL,  Zall = NULL)

Arguments

Xnew: New X values to add.
Znew: New Z values to add.
Xall: All X values to be used. Will replace existing X.
Zall: All Z values to be used. Will replace existing Z.

Method`update_corrparams()`

Update correlation parameters. Not the nugget.

Usage

GauPro_kernel_model$update_corrparams(...)

Arguments

...: Passed to self$update()

Method`update_nugget()`

Update nugget Not the correlation parameters.

Usage

GauPro_kernel_model$update_nugget(...)

Arguments

...: Passed to self$update()

Method`deviance()`

Calculate the deviance.

Usage

GauPro_kernel_model$deviance(  params = NULL,  nug = self$nug,  nuglog,  trend_params = NULL)

Arguments

params: Kernel parameters
nug: Nugget
nuglog: Log of nugget. Only give in nug or nuglog.
trend_params: Parameters for the trend.

Method`deviance_grad()`

Calculate the gradient of the deviance.

Usage

GauPro_kernel_model$deviance_grad(  params = NULL,  kernel_update = TRUE,  X = self$X,  nug = self$nug,  nug.update,  nuglog,  trend_params = NULL,  trend_update = TRUE)

Arguments

params: Kernel parameters
kernel_update: Is the kernel being updated? If yes,it's part of the gradient.
X: Input matrix
nug: Nugget
nug.update: Is the nugget being updated? If yes,it's part of the gradient.
nuglog: Log of the nugget.
trend_params: Trend parameters
trend_update: Is the trend being updated? If yes,it's part of the gradient.

Method`deviance_fngr()`

Calculate the deviance along with its gradient.

Usage

GauPro_kernel_model$deviance_fngr(  params = NULL,  kernel_update = TRUE,  X = self$X,  nug = self$nug,  nug.update,  nuglog,  trend_params = NULL,  trend_update = TRUE)

Arguments

params: Kernel parameters
kernel_update: Is the kernel being updated? If yes,it's part of the gradient.
X: Input matrix
nug: Nugget
nug.update: Is the nugget being updated? If yes,it's part of the gradient.
nuglog: Log of the nugget.
trend_params: Trend parameters
trend_update: Is the trend being updated? If yes,it's part of the gradient.

Method`grad()`

Calculate gradient

Usage

GauPro_kernel_model$grad(XX, X = self$X, Z = self$Z)

Arguments

XX: points to calculate at
X: X points
Z: output points

Method`grad_norm()`

Calculate norm of gradient

Usage

GauPro_kernel_model$grad_norm(XX)

Arguments

XX: points to calculate at

Method`grad_dist()`

Calculate distribution of gradient

Usage

GauPro_kernel_model$grad_dist(XX)

Arguments

XX: points to calculate at

Method`grad_sample()`

Sample gradient at points

Usage

GauPro_kernel_model$grad_sample(XX, n)

Arguments

XX: points to calculate at
n: Number of samples

Method`grad_norm2_mean()`

Calculate mean of gradient norm squared

Usage

GauPro_kernel_model$grad_norm2_mean(XX)

Arguments

XX: points to calculate at

Method`grad_norm2_dist()`

Calculate distribution of gradient norm squared

Usage

GauPro_kernel_model$grad_norm2_dist(XX)

Arguments

XX: points to calculate at

Method`grad_norm2_sample()`

Get samples of squared norm of gradient

Usage

GauPro_kernel_model$grad_norm2_sample(XX, n)

Arguments

XX: points to sample at
n: Number of samples

Method`hessian()`

Calculate Hessian

Usage

GauPro_kernel_model$hessian(XX, as_array = FALSE)

Arguments

XX: Points to calculate Hessian at
as_array: Should result be an array?

Method`gradpredvar()`

Calculate gradient of the predictive variance

Usage

GauPro_kernel_model$gradpredvar(XX)

Arguments

XX: points to calculate at

Method`sample()`

Sample at rows of XX

Usage

GauPro_kernel_model$sample(XX, n = 1)

Arguments

XX: Input matrix
n: Number of samples

Method`optimize_fn()`

Optimize any function of the GP prediction over thevalid input space.If there are inputs that should only be optimized over a discrete setof values, specify 'mopar' for all parameters.Factor inputs will be handled automatically.

Usage

GauPro_kernel_model$optimize_fn(  fn = NULL,  lower = apply(self$X, 2, min),  upper = apply(self$X, 2, max),  n0 = 100,  minimize = FALSE,  fn_args = NULL,  gr = NULL,  fngr = NULL,  mopar = NULL,  groupeval = FALSE)

Arguments

fn: Function to optimize
lower: Lower bounds to search within
upper: Upper bounds to search within
n0: Number of points to evaluate in initial stage
minimize: Are you trying to minimize the output?
fn_args: Arguments to pass to the function fn.
gr: Gradient of function to optimize.
fngr: Function that returns list with names elements "fn" for thefunction value and "gr" for the gradient. Useful when it is slow toevaluate and fn/gr would duplicate calculations if done separately.
mopar: List of parameters using mixopt
groupeval: Can a matrix of points be evaluated? Otherwise justa single point at a time.

Method`EI()`

Calculate expected improvement

Usage

GauPro_kernel_model$EI(x, minimize = FALSE, eps = 0, return_grad = FALSE, ...)

Arguments

x: Vector to calculate EI of, or matrix for whose rows it shouldbe calculated
minimize: Are you trying to minimize the output?
eps: Exploration parameter
return_grad: Should the gradient be returned?
...: Additional args

Method`maxEI()`

Find the point that maximizes the expected improvement.If there are inputs that should only be optimized over a discrete setof values, specify 'mopar' for all parameters.

Usage

GauPro_kernel_model$maxEI(  lower = apply(self$X, 2, min),  upper = apply(self$X, 2, max),  n0 = 100,  minimize = FALSE,  eps = 0,  dontconvertback = FALSE,  EItype = "corrected",  mopar = NULL,  usegrad = FALSE)

Arguments

lower: Lower bounds to search within
upper: Upper bounds to search within
n0: Number of points to evaluate in initial stage
minimize: Are you trying to minimize the output?
eps: Exploration parameter
dontconvertback: If data was given in with a formula, shouldit converted back to the original scale?
EItype: Type of EI to calculate. One of "EI", "Augmented",or "Corrected"
mopar: List of parameters using mixopt
usegrad: Should the gradient be used when optimizing?Can make it faster.

Method`maxqEI()`

Find the multiple points that maximize the expectedimprovement. Currently only implements the constant liar method.

Usage

GauPro_kernel_model$maxqEI(  npoints,  method = "pred",  lower = apply(self$X, 2, min),  upper = apply(self$X, 2, max),  n0 = 100,  minimize = FALSE,  eps = 0,  EItype = "corrected",  dontconvertback = FALSE,  mopar = NULL)

Arguments

npoints: Number of points to add
method: Method to use for setting the output value for the pointschosen as a placeholder.Can be one of: "CL" for constant liar,which uses the best value seen yet; or "pred", which uses the predictedvalue, also called the Believer method in literature.
lower: Lower bounds to search within
upper: Upper bounds to search within
n0: Number of points to evaluate in initial stage
minimize: Are you trying to minimize the output?
eps: Exploration parameter
EItype: Type of EI to calculate. One of "EI", "Augmented",or "Corrected"
dontconvertback: If data was given in with a formula, shouldit converted back to the original scale?
mopar: List of parameters using mixopt

Method`KG()`

Calculate Knowledge Gradient

Usage

GauPro_kernel_model$KG(x, minimize = FALSE, eps = 0, current_extreme = NULL)

Arguments

x: Point to calculate at
minimize: Is the objective to minimize?
eps: Exploration parameter
current_extreme: Used for recursive solving

Method`AugmentedEI()`

Calculated Augmented EI

Usage

GauPro_kernel_model$AugmentedEI(  x,  minimize = FALSE,  eps = 0,  return_grad = F,  ...)

Arguments

x: Vector to calculate EI of, or matrix for whose rows it shouldbe calculated
minimize: Are you trying to minimize the output?
eps: Exploration parameter
return_grad: Should the gradient be returned?
...: Additional args
f: The reference max, user shouldn't change this.

Method`CorrectedEI()`

Calculated Augmented EI

Usage

GauPro_kernel_model$CorrectedEI(  x,  minimize = FALSE,  eps = 0,  return_grad = F,  ...)

Arguments

x: Vector to calculate EI of, or matrix for whose rows it shouldbe calculated
minimize: Are you trying to minimize the output?
eps: Exploration parameter
return_grad: Should the gradient be returned?
...: Additional args

Method`importance()`

Feature importance

Usage

GauPro_kernel_model$importance(plot = TRUE, print_bars = TRUE)

Arguments

plot: Should the plot be made?
print_bars: Should the importances be printed as bars?

Method`print()`

Print this object

Usage

GauPro_kernel_model$print()

Method`summary()`

Summary

Usage

GauPro_kernel_model$summary(...)

Arguments

...: Additional arguments

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_kernel_model$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

References

https://scikit-learn.org/stable/modules/permutation_importance.html#id2

Examples

n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel="gauss")gp$predict(.454)gp$plot1D()gp$cool1Dplot()n <- 200d <- 7x <- matrix(runif(n*d), ncol=d)f <- function(x) {x[1]*x[2] + cos(x[3]) + x[4]^2}y <- apply(x, 1, f)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Gaussian)

Corr Gauss GP using inherited optim

Description

Corr Gauss GP using inherited optim

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro ->GauPro_kernel_model_LOO

Public fields

tmod: A second GP model for the t-values of leave-one-out predictions
use_LOO: Should the leave-one-out error corrections be used?

Methods

Public methods

Inherited methods

Method`new()`

Create a kernel model that uses a leave-one-out GP modelto fix the standard error predictions.

Usage

GauPro_kernel_model_LOO$new(..., LOO_kernel, LOO_options = list())

Arguments

...: Passed to super$initialize.
LOO_kernel: The kernel that should be used for theleave-one-out model. Shouldn't be too smooth.
LOO_options: Options passed to the leave-one-out model.

Method`update()`

Update the model. Should only give in(Xnew and Znew) or (Xall and Zall).

Usage

GauPro_kernel_model_LOO$update(  Xnew = NULL,  Znew = NULL,  Xall = NULL,  Zall = NULL,  restarts = 5,  param_update = self$param.est,  nug.update = self$nug.est,  no_update = FALSE)

Arguments

Xnew: New X values to add.
Znew: New Z values to add.
Xall: All X values to be used. Will replace existing X.
Zall: All Z values to be used. Will replace existing Z.
restarts: Number of optimization restarts.
param_update: Are the parameters being updated?
nug.update: Is the nugget being updated?
no_update: Are no parameters being updated?

Method`pred_one_matrix()`

Predict for a matrix of points

Usage

GauPro_kernel_model_LOO$pred_one_matrix(  XX,  se.fit = F,  covmat = F,  return_df = FALSE,  mean_dist = FALSE)

Arguments

XX: points to predict at
se.fit: Should standard error be returned?
covmat: Should covariance matrix be returned?
return_df: When returning se.fit, should it be returned ina data frame?
mean_dist: Should mean distribution be returned?

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_kernel_model_LOO$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model_LOO$new(X=x, Z=y, kernel=Gaussian)y <- x^2 * sin(2*pi*x) + rnorm(n,0,1e-3)gp <- GauPro_kernel_model_LOO$new(X=x, Z=y, kernel=Matern52)y <- exp(-1.4*x)*cos(7*pi*x/2)gp <- GauPro_kernel_model_LOO$new(X=x, Z=y, kernel=Matern52)

Trend R6 class

Description

Trend R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Public fields

D: Number of input dimensions of data

Methods

Public methods

GauPro_trend$clone()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GauPro_trend$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

#k <- GauPro_trend$new()

Gaussian Kernel R6 class

Description

Gaussian Kernel R6 class

Usage

k_Gaussian(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_Gaussian

Methods

Public methods

Inherited methods

Method`k()`

Calculate covariance between two points

Usage

Gaussian$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Gaussian$kone(x, y, beta, theta, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Gaussian$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

Gaussian$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Gaussian$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`d2C_dx2()`

Second derivative of covariance with respect to X

Usage

Gaussian$d2C_dx2(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`d2C_dudv()`

Second derivative of covariance with respect toX and XX each once.

Usage

Gaussian$d2C_dudv(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`d2C_dudv_ueqvrows()`

Second derivative of covariance with respect to X and XXwhen they equal the same value

Usage

Gaussian$d2C_dudv_ueqvrows(XX, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`print()`

Print this object

Usage

Gaussian$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Gaussian$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Gaussian$new(beta=0)plot(k1)k1 <- Gaussian$new(beta=c(0,-1, 1))plot(k1)n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Gaussian$new(1),                              parallel=FALSE)gp$predict(.454)gp$plot1D()gp$cool1Dplot()

Calculate the Gaussian deviance in C

Description

Calculate the Gaussian deviance in C

Usage

Gaussian_devianceC(theta, nug, X, Z)

Arguments

theta

Theta vector

nug

Nugget

X

Matrix X

Z

Matrix Z

Value

Correlation matrix

Examples

Gaussian_devianceC(c(1,1), 1e-8, matrix(c(1,0,0,1),2,2), matrix(c(1,0),2,1))

Calculate Hessian for a GP with Gaussian correlation

Description

Calculate Hessian for a GP with Gaussian correlation

Usage

Gaussian_hessianC(XX, X, Z, Kinv, mu_hat, theta)

Arguments

XX

The vector at which to calculate the Hessian

X

The input points

Z

The output values

Kinv

The inverse of the correlation matrix

mu_hat

Estimate of mu

theta

Theta parameters for the correlation

Value

Matrix, the Hessian at XX

Examples

set.seed(0)n <- 40x <- matrix(runif(n*2), ncol=2)f1 <- function(a) {sin(2*pi*a[1]) + sin(6*pi*a[2])}y <- apply(x,1,f1) + rnorm(n,0,.01)gp <- GauPro(x,y, verbose=2, parallel=FALSE);gp$thetagp$hessian(c(.2,.75), useC=TRUE) # Should be -38.3, -5.96, -5.96, -389.4 as 2x2 matrix

Gaussian hessian in C

Description

Gaussian hessian in C

Usage

Gaussian_hessianCC(XX, X, Z, Kinv, mu_hat, theta)

Arguments

XX

point to find Hessian at

X

matrix of data points

Z

matrix of output

Kinv

inverse of correlation matrix

mu_hat

mean estimate

theta

correlation parameters

Value

Hessian matrix

Calculate Hessian for a GP with Gaussian correlation

Description

Calculate Hessian for a GP with Gaussian correlation

Usage

Gaussian_hessianR(XX, X, Z, Kinv, mu_hat, theta)

Arguments

XX

The vector at which to calculate the Hessian

X

The input points

Z

The output values

Kinv

The inverse of the correlation matrix

mu_hat

Estimate of mu

theta

Theta parameters for the correlation

Value

Matrix, the Hessian at XX

Examples

set.seed(0)n <- 40x <- matrix(runif(n*2), ncol=2)f1 <- function(a) {sin(2*pi*a[1]) + sin(6*pi*a[2])}y <- apply(x,1,f1) + rnorm(n,0,.01)gp <- GauPro(x,y, verbose=2, parallel=FALSE);gp$thetagp$hessian(c(.2,.75), useC=FALSE) # Should be -38.3, -5.96, -5.96, -389.4 as 2x2 matrix

Gower factor Kernel R6 class

Description

Gower factor Kernel R6 class

Usage

k_GowerFactorKernel(  s2 = 1,  D,  nlevels,  xindex,  p_lower = 0,  p_upper = 0.9,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  p,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2

Initial variance

D

Number of input dimensions of data

nlevels

Number of levels for the factor

xindex

Index of the factor (which column of X)

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

p

Vector of correlations

useC

Should C code used? Not implemented for FactorKernel yet.

offdiagequal

What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Format

R6Class object.

Details

For a factor that has been converted to its indices.Each factor will need a separate kernel.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_GowerFactorKernel

Public fields

p: Parameter for correlation
p_est: Should p be estimated?
p_lower: Lower bound of p
p_upper: Upper bound of p
s2: variance
s2_est: Is s2 estimated?
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2
xindex: Index of the factor (which column of X)
nlevels: Number of levels for the factor
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

GowerFactorKernel$new(  s2 = 1,  D,  nlevels,  xindex,  p_lower = 0,  p_upper = 0.9,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  p,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2: Initial variance
D: Number of input dimensions of data
nlevels: Number of levels for the factor
xindex: Index of the factor (which column of X)
p_lower: Lower bound for p
p_upper: Upper bound for p
p_est: Should p be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
p: Vector of correlations
useC: Should C code used? Not implemented for FactorKernel yet.
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`k()`

Calculate covariance between two points

Usage

GowerFactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
p: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

GowerFactorKernel$kone(  x,  y,  p,  s2,  isdiag = TRUE,  offdiagequal = self$offdiagequal)

Arguments

x: vector
y: vector
p: correlation parameters on regular scale
s2: Variance parameter
isdiag: Is this on the diagonal of the covariance?
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

GowerFactorKernel$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

GowerFactorKernel$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

GowerFactorKernel$dC_dx(XX, X, ...)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
...: Additional args, not used

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

GowerFactorKernel$param_optim_start(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?
alpha_est: Is alpha being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

GowerFactorKernel$param_optim_start0(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?
alpha_est: Is alpha being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

GowerFactorKernel$param_optim_lower(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?
alpha_est: Is alpha being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

GowerFactorKernel$param_optim_upper(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?
alpha_est: Is alpha being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

GowerFactorKernel$set_params_from_optim(  optim_out,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
p_est: Is p being estimated?
s2_est: Is s2 being estimated?
alpha_est: Is alpha being estimated?

Method`s2_from_params()`

Get s2 from params vector

Usage

GowerFactorKernel$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

GowerFactorKernel$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

GowerFactorKernel$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

kk <- GowerFactorKernel$new(D=1, nlevels=5, xindex=1, p=.2)kmat <- outer(1:5, 1:5, Vectorize(kk$k))kmatkk$plot()# 2D, Gaussian on 1D, index on 2nd dimif (requireNamespace("dplyr", quietly=TRUE)) {library(dplyr)n <- 20X <- cbind(matrix(runif(n,2,6), ncol=1),           matrix(sample(1:2, size=n, replace=TRUE), ncol=1))X <- rbind(X, c(3.3,3))n <- nrow(X)Z <- X[,1] - (X[,2]-1.8)^2 + rnorm(n,0,.1)tibble(X=X, Z) %>% arrange(X,Z)k2a <- IgnoreIndsKernel$new(k=Gaussian$new(D=1), ignoreinds = 2)k2b <- GowerFactorKernel$new(D=2, nlevels=3, xind=2)k2 <- k2a * k2bk2b$p_upper <- .65*k2b$p_uppergp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,                              nug.min=1e-2, restarts=0)gp$kernel$k1$kernel$betagp$kernel$k2$pgp$kernel$k(x = gp$X)tibble(X=X, Z=Z, pred=gp$predict(X)) %>% arrange(X, Z)tibble(X=X[,2], Z) %>% group_by(X) %>% summarize(n=n(), mean(Z))curve(gp$pred(cbind(matrix(x,ncol=1),1)),2,6, ylim=c(min(Z), max(Z)))points(X[X[,2]==1,1], Z[X[,2]==1])curve(gp$pred(cbind(matrix(x,ncol=1),2)), add=TRUE, col=2)points(X[X[,2]==2,1], Z[X[,2]==2], col=2)curve(gp$pred(cbind(matrix(x,ncol=1),3)), add=TRUE, col=3)points(X[X[,2]==3,1], Z[X[,2]==3], col=3)legend(legend=1:3, fill=1:3, x="topleft")# See which points affect (5.5, 3 themost)data.frame(X, cov=gp$kernel$k(X, c(5.5,3))) %>% arrange(-cov)plot(k2b)}

Kernel R6 class

Description

Kernel R6 class

Usage

k_IgnoreIndsKernel(k, ignoreinds, useC = TRUE)

Arguments

k

Kernel to use on the non-ignored indices

ignoreinds

Indices of columns of X to ignore.

useC

Should C code used? Not implemented for IgnoreInds.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_IgnoreInds

Public fields

D: Number of input dimensions of data
kernel: Kernel to use on indices that aren't ignored
ignoreinds: Indices to ignore. For a matrix X, these are the columnsto ignore. For example, when those dimensions will be given a differentkernel, such as for factors.

Active bindings

s2_est: Is s2 being estimated?
s2: Value of s2 (variance)

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

IgnoreIndsKernel$new(k, ignoreinds, useC = TRUE)

Arguments

k: Kernel to use on the non-ignored indices
ignoreinds: Indices of columns of X to ignore.
useC: Should C code used? Not implemented for IgnoreInds.

Method`k()`

Calculate covariance between two points

Usage

IgnoreIndsKernel$k(x, y = NULL, ...)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
...: Passed to kernel

Method`kone()`

Find covariance of two points

Usage

IgnoreIndsKernel$kone(x, y, ...)

Arguments

x: vector
y: vector
...: Passed to kernel

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

IgnoreIndsKernel$dC_dparams(params = NULL, X, ...)

Arguments

params: Kernel parameters
X: matrix of points in rows
...: Passed to kernel

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

IgnoreIndsKernel$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

IgnoreIndsKernel$dC_dx(XX, X, ...)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
...: Additional arguments passed on to the kernel

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

IgnoreIndsKernel$param_optim_start(...)

Arguments

...: Passed to kernel

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

IgnoreIndsKernel$param_optim_start0(...)

Arguments

...: Passed to kernel

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

IgnoreIndsKernel$param_optim_lower(...)

Arguments

...: Passed to kernel

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

IgnoreIndsKernel$param_optim_upper(...)

Arguments

...: Passed to kernel

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

IgnoreIndsKernel$set_params_from_optim(...)

Arguments

...: Passed to kernel

Method`s2_from_params()`

Get s2 from params vector

Usage

IgnoreIndsKernel$s2_from_params(...)

Arguments

...: Passed to kernel

Method`print()`

Print this object

Usage

IgnoreIndsKernel$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

IgnoreIndsKernel$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

kg <- Gaussian$new(D=3)kig <- GauPro::IgnoreIndsKernel$new(k = Gaussian$new(D=3), ignoreinds = 2)Xtmp <- as.matrix(expand.grid(1:2, 1:2, 1:2))cbind(Xtmp, kig$k(Xtmp))cbind(Xtmp, kg$k(Xtmp))

Latent Factor Kernel R6 class

Description

Latent Factor Kernel R6 class

Usage

k_LatentFactorKernel(  s2 = 1,  D,  nlevels,  xindex,  latentdim,  p_lower = 0,  p_upper = 1,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2

Initial variance

D

Number of input dimensions of data

nlevels

Number of levels for the factor

xindex

Index of X to use the kernel on

latentdim

Dimension of embedding space

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

offdiagequal

What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Format

R6Class object.

Details

Used for factor variables, a single dimension.Each level of the factor gets mapped into a latent space,then the distances in that space determine their correlations.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_LatentFactorKernel

Public fields

p: Parameter for correlation
p_est: Should p be estimated?
p_lower: Lower bound of p
p_upper: Upper bound of p
p_length: length of p
s2: variance
s2_est: Is s2 estimated?
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2
xindex: Index of the factor (which column of X)
nlevels: Number of levels for the factor
latentdim: Dimension of embedding space
pf_to_p_log: Logical vector used to convert pf to p
p_to_pf_inds: Vector of indexes used to convert p to pf
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

LatentFactorKernel$new(  s2 = 1,  D,  nlevels,  xindex,  latentdim,  p_lower = 0,  p_upper = 1,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2: Initial variance
D: Number of input dimensions of data
nlevels: Number of levels for the factor
xindex: Index of X to use the kernel on
latentdim: Dimension of embedding space
p_lower: Lower bound for p
p_upper: Upper bound for p
p_est: Should p be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster.
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`k()`

Calculate covariance between two points

Usage

LatentFactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
p: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

LatentFactorKernel$kone(  x,  y,  pf,  s2,  isdiag = TRUE,  offdiagequal = self$offdiagequal)

Arguments

x: vector
y: vector
pf: correlation parameters on regular scale, includes zeroesfor first level.
s2: Variance parameter
isdiag: Is this on the diagonal of the covariance?
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

LatentFactorKernel$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

LatentFactorKernel$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

LatentFactorKernel$dC_dx(XX, X, ...)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
...: Additional args, not used

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

LatentFactorKernel$param_optim_start(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

LatentFactorKernel$param_optim_start0(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

LatentFactorKernel$param_optim_lower(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

LatentFactorKernel$param_optim_upper(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

LatentFactorKernel$set_params_from_optim(  optim_out,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`p_to_pf()`

Convert p (short parameter vector) to pf (long parametervector with zeros).

Usage

LatentFactorKernel$p_to_pf(p)

Arguments

p: Parameter vector

Method`s2_from_params()`

Get s2 from params vector

Usage

LatentFactorKernel$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`plotLatent()`

Plot the points in the latent space

Usage

LatentFactorKernel$plotLatent()

Method`print()`

Print this object

Usage

LatentFactorKernel$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

LatentFactorKernel$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

References

https://stackoverflow.com/questions/27086195/linear-index-upper-triangular-matrix

Examples

# Create a new kernel for a single factor with 5 levels,#  mapped into two latent dimensions.kk <- LatentFactorKernel$new(D=1, nlevels=5, xindex=1, latentdim=2)# Random initial parameter valueskk$p# Plots to understandkk$plotLatent()kk$plot()# 5 levels, 1/4 are similar and 2/3/5 are similarn <- 30x <- matrix(sample(1:5, n, TRUE))y <- c(ifelse(x == 1 | x == 4, 4, -3) + rnorm(n,0,.1))plot(c(x), y)m5 <- GauPro_kernel_model$new(  X=x, Z=y,  kernel=LatentFactorKernel$new(D=1, nlevels = 5, xindex = 1, latentdim = 2))m5$kernel$p# We should see 1/4 and 2/3/4 in separate clustersm5$kernel$plotLatent()if (requireNamespace("dplyr", quietly=TRUE)) {library(dplyr)n <- 20X <- cbind(matrix(runif(n,2,6), ncol=1),           matrix(sample(1:2, size=n, replace=TRUE), ncol=1))X <- rbind(X, c(3.3,3), c(3.7,3))n <- nrow(X)Z <- X[,1] - (4-X[,2])^2 + rnorm(n,0,.1)plot(X[,1], Z, col=X[,2])tibble(X=X, Z) %>% arrange(X,Z)k2a <- IgnoreIndsKernel$new(k=Gaussian$new(D=1), ignoreinds = 2)k2b <- LatentFactorKernel$new(D=2, nlevels=3, xind=2, latentdim=2)k2 <- k2a * k2bk2b$p_upper <- .65*k2b$p_uppergp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,  nug.min=1e-2, restarts=1)gp$kernel$k1$kernel$betagp$kernel$k2$pgp$kernel$k(x = gp$X)tibble(X=X, Z=Z, pred=gp$predict(X)) %>% arrange(X, Z)tibble(X=X[,2], Z) %>% group_by(X) %>% summarize(n=n(), mean(Z))curve(gp$pred(cbind(matrix(x,ncol=1),1)),2,6, ylim=c(min(Z), max(Z)))points(X[X[,2]==1,1], Z[X[,2]==1])curve(gp$pred(cbind(matrix(x,ncol=1),2)), add=TRUE, col=2)points(X[X[,2]==2,1], Z[X[,2]==2], col=2)curve(gp$pred(cbind(matrix(x,ncol=1),3)), add=TRUE, col=3)points(X[X[,2]==3,1], Z[X[,2]==3], col=3)legend(legend=1:3, fill=1:3, x="topleft")# See which points affect (5.5, 3 themost)data.frame(X, cov=gp$kernel$k(X, c(5.5,3))) %>% arrange(-cov)plot(k2b)}

Matern 3/2 Kernel R6 class

Description

Matern 3/2 Kernel R6 class

Usage

k_Matern32(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_Matern32

Public fields

sqrt3: Saved value of square root of 3

Methods

Public methods

Inherited methods

Method`k()`

Calculate covariance between two points

Usage

Matern32$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Matern32$kone(x, y, beta, theta, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Matern32$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Matern32$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`print()`

Print this object

Usage

Matern32$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Matern32$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Matern32$new(beta=0)plot(k1)n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Matern32$new(1),                              parallel=FALSE)gp$predict(.454)gp$plot1D()gp$cool1Dplot()

Matern 5/2 Kernel R6 class

Description

Matern 5/2 Kernel R6 class

Usage

k_Matern52(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Format

R6Class object.

Details

k(x, y) = s2 * (1 + t1 + t1^2 / 3) * exp(-t1)wheret1 = sqrt(5) * sqrt(sum(theta * (x-y)^2))

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_Matern52

Public fields

sqrt5: Saved value of square root of 5

Methods

Public methods

Inherited methods

Method`k()`

Calculate covariance between two points

Usage

Matern52$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Matern52$kone(x, y, beta, theta, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Matern52$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Matern52$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`print()`

Print this object

Usage

Matern52$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Matern52$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Matern52$new(beta=0)plot(k1)n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Matern52$new(1),                              parallel=FALSE)gp$predict(.454)gp$plot1D()gp$cool1Dplot()

Ordered Factor Kernel R6 class

Description

Ordered Factor Kernel R6 class

Usage

k_OrderedFactorKernel(  s2 = 1,  D,  nlevels,  xindex,  p_lower = 1e-08,  p_upper = 5,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2

Initial variance

D

Number of input dimensions of data

nlevels

Number of levels for the factor

xindex

Index of the factor (which column of X)

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Not implemented for FactorKernel yet.

offdiagequal

What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Format

R6Class object.

Details

Use for factor inputs that are considered to have an ordering

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_OrderedFactorKernel

Public fields

p: Parameter for correlation
p_est: Should p be estimated?
p_lower: Lower bound of p
p_upper: Upper bound of p
p_length: length of p
s2: variance
s2_est: Is s2 estimated?
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2
xindex: Index of the factor (which column of X)
nlevels: Number of levels for the factor
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

OrderedFactorKernel$new(  s2 = 1,  D = NULL,  nlevels,  xindex,  p_lower = 1e-08,  p_upper = 5,  p_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  offdiagequal = 1 - 1e-06)

Arguments

s2: Initial variance
D: Number of input dimensions of data
nlevels: Number of levels for the factor
xindex: Index of X to use the kernel on
p_lower: Lower bound for p
p_upper: Upper bound for p
p_est: Should p be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster.
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.
p: Vector of distances in latent space

Method`k()`

Calculate covariance between two points

Usage

OrderedFactorKernel$k(x, y = NULL, p = self$p, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
p: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

OrderedFactorKernel$kone(  x,  y,  p,  s2,  isdiag = TRUE,  offdiagequal = self$offdiagequal)

Arguments

x: vector
y: vector
p: correlation parameters on regular scale
s2: Variance parameter
isdiag: Is this on the diagonal of the covariance?
offdiagequal: What should offdiagonal values be set to when theindices are the same? Use to avoid decomposition errors, similar toadding a nugget.

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

OrderedFactorKernel$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

OrderedFactorKernel$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

OrderedFactorKernel$dC_dx(XX, X, ...)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
...: Additional args, not used

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

OrderedFactorKernel$param_optim_start(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

OrderedFactorKernel$param_optim_start0(  jitter = F,  y,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

OrderedFactorKernel$param_optim_lower(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

OrderedFactorKernel$param_optim_upper(p_est = self$p_est, s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

OrderedFactorKernel$set_params_from_optim(  optim_out,  p_est = self$p_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
p_est: Is p being estimated?
s2_est: Is s2 being estimated?

Method`s2_from_params()`

Get s2 from params vector

Usage

OrderedFactorKernel$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`plotLatent()`

Plot the points in the latent space

Usage

OrderedFactorKernel$plotLatent()

Method`print()`

Print this object

Usage

OrderedFactorKernel$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

OrderedFactorKernel$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

References

https://stackoverflow.com/questions/27086195/linear-index-upper-triangular-matrix

Examples

kk <- OrderedFactorKernel$new(D=1, nlevels=5, xindex=1)kk$p <- (1:10)/100kmat <- outer(1:5, 1:5, Vectorize(kk$k))kmatif (requireNamespace("dplyr", quietly=TRUE)) {library(dplyr)n <- 20X <- cbind(matrix(runif(n,2,6), ncol=1),           matrix(sample(1:2, size=n, replace=TRUE), ncol=1))X <- rbind(X, c(3.3,3), c(3.7,3))n <- nrow(X)Z <- X[,1] - (4-X[,2])^2 + rnorm(n,0,.1)plot(X[,1], Z, col=X[,2])tibble(X=X, Z) %>% arrange(X,Z)k2a <- IgnoreIndsKernel$new(k=Gaussian$new(D=1), ignoreinds = 2)k2b <- OrderedFactorKernel$new(D=2, nlevels=3, xind=2)k2 <- k2a * k2bk2b$p_upper <- .65*k2b$p_uppergp <- GauPro_kernel_model$new(X=X, Z=Z, kernel = k2, verbose = 5,  nug.min=1e-2, restarts=0)gp$kernel$k1$kernel$betagp$kernel$k2$pgp$kernel$k(x = gp$X)tibble(X=X, Z=Z, pred=gp$predict(X)) %>% arrange(X, Z)tibble(X=X[,2], Z) %>% group_by(X) %>% summarize(n=n(), mean(Z))curve(gp$pred(cbind(matrix(x,ncol=1),1)),2,6, ylim=c(min(Z), max(Z)))points(X[X[,2]==1,1], Z[X[,2]==1])curve(gp$pred(cbind(matrix(x,ncol=1),2)), add=TRUE, col=2)points(X[X[,2]==2,1], Z[X[,2]==2], col=2)curve(gp$pred(cbind(matrix(x,ncol=1),3)), add=TRUE, col=3)points(X[X[,2]==3,1], Z[X[,2]==3], col=3)legend(legend=1:3, fill=1:3, x="topleft")# See which points affect (5.5, 3 themost)data.frame(X, cov=gp$kernel$k(X, c(5.5,3))) %>% arrange(-cov)plot(k2b)}

Periodic Kernel R6 class

Description

Periodic Kernel R6 class

Usage

k_Periodic(  p,  alpha = 1,  s2 = 1,  D,  p_lower = 0,  p_upper = 100,  p_est = TRUE,  alpha_lower = 0,  alpha_upper = 100,  alpha_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

p

Periodic parameter

alpha

Periodic parameter

s2

Initial variance

D

Number of input dimensions of data

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p be estimated?

alpha_lower

Lower bound for alpha

alpha_upper

Upper bound for alpha

alpha_est

Should alpha be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster if implemented.

Format

R6Class object.

Details

p is the period for each dimension, a is a single number for scaling

k(x, y) = s2 * exp(-sum(alpha*sin(p * (x-y))^2))

k(x, y) = \sigma^2 * \exp(-\sum(\alpha_i*sin(p * (x_i-y_i))^2))

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_Periodic

Public fields

p: Parameter for correlation
p_est: Should p be estimated?
logp: Log of p
logp_lower: Lower bound of logp
logp_upper: Upper bound of logp
p_length: length of p
alpha: Parameter for correlation
alpha_est: Should alpha be estimated?
logalpha: Log of alpha
logalpha_lower: Lower bound of logalpha
logalpha_upper: Upper bound of logalpha
s2: variance
s2_est: Is s2 estimated?
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

Periodic$new(  p,  alpha = 1,  s2 = 1,  D,  p_lower = 0,  p_upper = 100,  p_est = TRUE,  alpha_lower = 0,  alpha_upper = 100,  alpha_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

p: Periodic parameter
alpha: Periodic parameter
s2: Initial variance
D: Number of input dimensions of data
p_lower: Lower bound for p
p_upper: Upper bound for p
p_est: Should p be estimated?
alpha_lower: Lower bound for alpha
alpha_upper: Upper bound for alpha
alpha_est: Should alpha be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster if implemented.

Method`k()`

Calculate covariance between two points

Usage

Periodic$k(  x,  y = NULL,  logp = self$logp,  logalpha = self$logalpha,  s2 = self$s2,  params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
logp: Correlation parameters.
logalpha: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Periodic$kone(x, y, logp, p, alpha, s2)

Arguments

x: vector
y: vector
logp: correlation parameters on log scale
p: correlation parameters on regular scale
alpha: correlation parameter
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Periodic$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

Periodic$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Periodic$dC_dx(XX, X, logp = self$logp, logalpha = self$logalpha, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
logp: log of p
logalpha: log of alpha
s2: Variance parameter

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

Periodic$param_optim_start(  jitter = F,  y,  p_est = self$p_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

Periodic$param_optim_start0(  jitter = F,  y,  p_est = self$p_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
p_est: Is p being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

Periodic$param_optim_lower(  p_est = self$p_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

Periodic$param_optim_upper(  p_est = self$p_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

p_est: Is p being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

Periodic$set_params_from_optim(  optim_out,  p_est = self$p_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
p_est: Is p being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`s2_from_params()`

Get s2 from params vector

Usage

Periodic$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

Periodic$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Periodic$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Periodic$new(p=1, alpha=1)plot(k1)n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Periodic$new(D=1),                              parallel=FALSE)gp$predict(.454)gp$plot1D()gp$cool1Dplot()plot(gp$kernel)

Power Exponential Kernel R6 class

Description

Power Exponential Kernel R6 class

Usage

k_PowerExp(  alpha = 1.95,  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  alpha_lower = 1e-08,  alpha_upper = 2,  alpha_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

alpha

Initial alpha value (the exponent). Between 0 and 2.

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

alpha_lower

Lower bound for alpha

alpha_upper

Upper bound for alpha

alpha_est

Should alpha be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster if implemented.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_PowerExp

Public fields

alpha: alpha value (the exponent). Between 0 and 2.
alpha_lower: Lower bound for alpha
alpha_upper: Upper bound for alpha
alpha_est: Should alpha be estimated?

Methods

Public methods

Inherited methods

Method`new()`

Initialize kernel object

Usage

PowerExp$new(  alpha = 1.95,  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  alpha_lower = 1e-08,  alpha_upper = 2,  alpha_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

alpha: Initial alpha value (the exponent). Between 0 and 2.
beta: Initial beta value
s2: Initial variance
D: Number of input dimensions of data
beta_lower: Lower bound for beta
beta_upper: Upper bound for beta
beta_est: Should beta be estimated?
alpha_lower: Lower bound for alpha
alpha_upper: Upper bound for alpha
alpha_est: Should alpha be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster if implemented.

Method`k()`

Calculate covariance between two points

Usage

PowerExp$k(  x,  y = NULL,  beta = self$beta,  alpha = self$alpha,  s2 = self$s2,  params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
alpha: alpha value (the exponent). Between 0 and 2.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

PowerExp$kone(x, y, beta, theta, alpha, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
alpha: alpha value (the exponent). Between 0 and 2.
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

PowerExp$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

PowerExp$dC_dx(  XX,  X,  theta,  beta = self$beta,  alpha = self$alpha,  s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
alpha: alpha value (the exponent). Between 0 and 2.
s2: Variance parameter

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

PowerExp$param_optim_start(  jitter = F,  y,  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

PowerExp$param_optim_start0(  jitter = F,  y,  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

PowerExp$param_optim_lower(  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

PowerExp$param_optim_upper(  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

PowerExp$set_params_from_optim(  optim_out,  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
beta_est: Is beta estimate?
alpha_est: Is alpha estimated?
s2_est: Is s2 estimated?

Method`print()`

Print this object

Usage

PowerExp$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

PowerExp$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- PowerExp$new(beta=0, alpha=0)

Rational Quadratic Kernel R6 class

Description

Rational Quadratic Kernel R6 class

Usage

k_RatQuad(  beta,  alpha = 1,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  alpha_lower = 1e-08,  alpha_upper = 100,  alpha_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

beta

Initial beta value

alpha

Initial alpha value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

alpha_lower

Lower bound for alpha

alpha_upper

Upper bound for alpha

alpha_est

Should alpha be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster if implemented.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_RatQuad

Public fields

alpha: alpha value (the exponent). Between 0 and 2.
logalpha: Log of alpha
logalpha_lower: Lower bound for log of alpha
logalpha_upper: Upper bound for log of alpha
alpha_est: Should alpha be estimated?

Methods

Public methods

Inherited methods

Method`new()`

Initialize kernel object

Usage

RatQuad$new(  beta,  alpha = 1,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  alpha_lower = 1e-08,  alpha_upper = 100,  alpha_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

beta: Initial beta value
alpha: Initial alpha value
s2: Initial variance
D: Number of input dimensions of data
beta_lower: Lower bound for beta
beta_upper: Upper bound for beta
beta_est: Should beta be estimated?
alpha_lower: Lower bound for alpha
alpha_upper: Upper bound for alpha
alpha_est: Should alpha be estimated?
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Much faster if implemented.

Method`k()`

Calculate covariance between two points

Usage

RatQuad$k(  x,  y = NULL,  beta = self$beta,  logalpha = self$logalpha,  s2 = self$s2,  params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
logalpha: A correlation parameter
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

RatQuad$kone(x, y, beta, theta, alpha, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
alpha: A correlation parameter
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

RatQuad$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

RatQuad$dC_dx(XX, X, theta, beta = self$beta, alpha = self$alpha, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
alpha: parameter
s2: Variance parameter

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

RatQuad$param_optim_start(  jitter = F,  y,  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

RatQuad$param_optim_start0(  jitter = F,  y,  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

RatQuad$param_optim_lower(  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

RatQuad$param_optim_upper(  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

RatQuad$set_params_from_optim(  optim_out,  beta_est = self$beta_est,  alpha_est = self$alpha_est,  s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
beta_est: Is beta being estimated?
alpha_est: Is alpha being estimated?
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

RatQuad$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

RatQuad$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- RatQuad$new(beta=0, alpha=0)

Triangle Kernel R6 class

Description

Triangle Kernel R6 class

Usage

k_Triangle(  beta,  s2 = 1,  D,  beta_lower = -8,  beta_upper = 6,  beta_est = TRUE,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE,  isotropic = FALSE)

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for alldimensions. If not (anisotropic) then a separate beta/beta is used foreach dimension.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel ->GauPro::GauPro_kernel_beta ->GauPro_kernel_Triangle

Methods

Public methods

Inherited methods

Method`k()`

Calculate covariance between two points

Usage

Triangle$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
beta: Correlation parameters.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

Triangle$kone(x, y, beta, theta, s2)

Arguments

x: vector
y: vector
beta: correlation parameters on log scale
theta: correlation parameters on regular scale
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

Triangle$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

Triangle$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
theta: Correlation parameters
beta: log of theta
s2: Variance parameter

Method`print()`

Print this object

Usage

Triangle$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

Triangle$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Triangle$new(beta=0)plot(k1)n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Triangle$new(1),                              parallel=FALSE)gp$predict(.454)gp$plot1D()gp$cool1Dplot()

White noise Kernel R6 class

Description

Initialize kernel object

Usage

k_White(  s2 = 1,  D,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

s2

Initial variance

D

Number of input dimensions of data

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Not implemented for White.

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_White

Public fields

s2: variance
logs2: Log of s2
logs2_lower: Lower bound of logs2
logs2_upper: Upper bound of logs2
s2_est: Should s2 be estimated?

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel object

Usage

White$new(  s2 = 1,  D,  s2_lower = 1e-08,  s2_upper = 1e+08,  s2_est = TRUE,  useC = TRUE)

Arguments

s2: Initial variance
D: Number of input dimensions of data
s2_lower: Lower bound for s2
s2_upper: Upper bound for s2
s2_est: Should s2 be estimated?
useC: Should C code used? Not implemented for White.

Method`k()`

Calculate covariance between two points

Usage

White$k(x, y = NULL, s2 = self$s2, params = NULL)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
s2: Variance parameter.
params: parameters to use instead of beta and s2.

Method`kone()`

Find covariance of two points

Usage

White$kone(x, y, s2)

Arguments

x: vector
y: vector
s2: Variance parameter

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

White$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
C: Covariance with nugget
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

White$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

White$dC_dx(XX, X, s2 = self$s2)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to
s2: Variance parameter
theta: Correlation parameters
beta: log of theta

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

White$param_optim_start(jitter = F, y, s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
s2_est: Is s2 being estimated?

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

White$param_optim_start0(jitter = F, y, s2_est = self$s2_est)

Arguments

jitter: Should there be a jitter?
y: Output
s2_est: Is s2 being estimated?

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

White$param_optim_lower(s2_est = self$s2_est)

Arguments

s2_est: Is s2 being estimated?

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

White$param_optim_upper(s2_est = self$s2_est)

Arguments

s2_est: Is s2 being estimated?

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

White$set_params_from_optim(optim_out, s2_est = self$s2_est)

Arguments

optim_out: Output from optimization
s2_est: s2 estimate

Method`s2_from_params()`

Get s2 from params vector

Usage

White$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

White$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

White$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- White$new(s2=1e-8)

Cube multiply over first dimension

Description

The result is transposed since that is what apply will give you

Usage

arma_mult_cube_vec(cub, v)

Arguments

cub

A cube (3D array)

v

A vector

Value

Transpose of multiplication over first dimension of cub time v

Examples

d1 <- 10d2 <- 1e2d3 <- 2e2aa <- array(data = rnorm(d1*d2*d3), dim = c(d1, d2, d3))bb <- rnorm(d3)t1 <- apply(aa, 1, function(U) {U%*%bb})t2 <- arma_mult_cube_vec(aa, bb)dd <- t1 - t2summary(dd)image(dd)table(dd)# microbenchmark::microbenchmark(apply(aa, 1, function(U) {U%*%bb}),#                                arma_mult_cube_vec(aa, bb))

Correlation Cubic matrix in C (symmetric)

Description

Correlation Cubic matrix in C (symmetric)

Usage

corr_cubic_matrix_symC(x, theta)

Arguments

x

Matrix x

theta

Theta vector

Value

Correlation matrix

Examples

corr_cubic_matrix_symC(matrix(c(1,0,0,1),2,2),c(1,1))

Correlation Gaussian matrix in C (symmetric)

Description

Correlation Gaussian matrix in C (symmetric)

Usage

corr_exponential_matrix_symC(x, theta)

Arguments

x

Matrix x

theta

Theta vector

Value

Correlation matrix

Examples

corr_gauss_matrix_symC(matrix(c(1,0,0,1),2,2),c(1,1))

Correlation Gaussian matrix gradient in C using Armadillo

Description

Correlation Gaussian matrix gradient in C using Armadillo

Usage

corr_gauss_dCdX(XX, X, theta, s2)

Arguments

XX

Matrix XX to get gradient for

X

Matrix X GP was fit to

theta

Theta vector

s2

Variance parameter

Value

3-dim array of correlation derivative

Examples

# corr_gauss_dCdX(matrix(c(1,0,0,1),2,2),c(1,1))

Gaussian correlation

Description

Gaussian correlation

Usage

corr_gauss_matrix(x, x2 = NULL, theta)

Arguments

x

First data matrix

x2

Second data matrix

theta

Correlation parameter

Value

Correlation matrix

Examples

corr_gauss_matrix(matrix(1:10,ncol=1), matrix(6:15,ncol=1), 1e-2)

Correlation Gaussian matrix in C using Rcpp

Description

Correlation Gaussian matrix in C using Rcpp

Usage

corr_gauss_matrixC(x, y, theta)

Arguments

x

Matrix x

y

Matrix y, must have same number of columns as x

theta

Theta vector

Value

Correlation matrix

Examples

corr_gauss_matrixC(matrix(c(1,0,0,1),2,2), matrix(c(1,0,1,1),2,2), c(1,1))

Correlation Gaussian matrix in C using Armadillo

Description

20-25

Usage

corr_gauss_matrix_armaC(x, y, theta, s2 = 1)

Arguments

x

Matrix x

y

Matrix y, must have same number of columns as x

theta

Theta vector

s2

Variance to multiply matrix by

Value

Correlation matrix

Examples

corr_gauss_matrix_armaC(matrix(c(1,0,0,1),2,2),matrix(c(1,0,1,1),2,2),c(1,1))x1 <- matrix(runif(100*6), nrow=100, ncol=6)x2 <- matrix(runif(1e4*6), ncol=6)th <- runif(6)t1 <- corr_gauss_matrixC(x1, x2, th)t2 <- corr_gauss_matrix_armaC(x1, x2, th)identical(t1, t2)# microbenchmark::microbenchmark(corr_gauss_matrixC(x1, x2, th),#                                corr_gauss_matrix_armaC(x1, x2, th))

Correlation Gaussian matrix in C (symmetric)

Description

Correlation Gaussian matrix in C (symmetric)

Usage

corr_gauss_matrix_symC(x, theta)

Arguments

x

Matrix x

theta

Theta vector

Value

Correlation matrix

Examples

corr_gauss_matrix_symC(matrix(c(1,0,0,1),2,2),c(1,1))

Correlation Gaussian matrix in C using Armadillo (symmetric)

Description

About 30

Usage

corr_gauss_matrix_sym_armaC(x, theta)

Arguments

x

Matrix x

theta

Theta vector

Value

Correlation matrix

Examples

corr_gauss_matrix_sym_armaC(matrix(c(1,0,0,1),2,2),c(1,1))x3 <- matrix(runif(1e3*6), ncol=6)th <- runif(6)t3 <- corr_gauss_matrix_symC(x3, th)t4 <- corr_gauss_matrix_sym_armaC(x3, th)identical(t3, t4)# microbenchmark::microbenchmark(corr_gauss_matrix_symC(x3, th),#                     corr_gauss_matrix_sym_armaC(x3, th), times=50)

Correlation Latent factor matrix in C (symmetric)

Description

Correlation Latent factor matrix in C (symmetric)

Usage

corr_latentfactor_matrix_symC(x, theta, xindex, latentdim, offdiagequal)

Arguments

x

Matrix x

theta

Theta vector

xindex

Index to use

latentdim

Number of latent dimensions

offdiagequal

What to set off-diagonal values with matching values to.

Value

Correlation matrix

Examples

corr_latentfactor_matrix_symC(matrix(c(1,.5, 2,1.6, 1,0),ncol=2,byrow=TRUE),                              c(1.5,1.8), 1, 1, 1-1e-6)corr_latentfactor_matrix_symC(matrix(c(0,0,0,1,0,0,0,2,0,0,0,3,0,0,0,4),                                     ncol=4, byrow=TRUE),  c(0.101, -0.714, 0.114, -0.755, 0.117, -0.76, 0.116, -0.752),  4, 2, 1-1e-6) * 6.85

Correlation Latent factor matrix in C (symmetric)

Description

Correlation Latent factor matrix in C (symmetric)

Usage

corr_latentfactor_matrixmatrixC(x, y, theta, xindex, latentdim, offdiagequal)

Arguments

x

Matrix x

y

Matrix y

theta

Theta vector

xindex

Index to use

latentdim

Number of latent dimensions

offdiagequal

What to set off-diagonal values with matching values to.

Value

Correlation matrix

Examples

corr_latentfactor_matrixmatrixC(matrix(c(1,.5, 2,1.6, 1,0),ncol=2,byrow=TRUE),                                matrix(c(2,1.6, 1,0),ncol=2,byrow=TRUE),                                c(1.5,1.8), 1, 1, 1-1e-6)corr_latentfactor_matrixmatrixC(matrix(c(0,0,0,1,0,0,0,2,0,0,0,3,0,0,0,4),                                  ncol=4, byrow=TRUE),                                matrix(c(0,0,0,2,0,0,0,4,0,0,0,1),                                  ncol=4, byrow=TRUE),  c(0.101, -0.714, 0.114, -0.755, 0.117, -0.76, 0.116, -0.752),  4, 2, 1-1e-6) * 6.85

Correlation Matern 3/2 matrix in C (symmetric)

Description

Correlation Matern 3/2 matrix in C (symmetric)

Usage

corr_matern32_matrix_symC(x, theta)

Arguments

x

Matrix x

theta

Theta vector

Value

Correlation matrix

Examples

corr_gauss_matrix_symC(matrix(c(1,0,0,1),2,2),c(1,1))

Correlation Gaussian matrix in C (symmetric)

Description

Correlation Gaussian matrix in C (symmetric)

Usage

corr_matern52_matrix_symC(x, theta)

Arguments

x

Matrix x

theta

Theta vector

Value

Correlation matrix

Examples

corr_matern52_matrix_symC(matrix(c(1,0,0,1),2,2),c(1,1))

Correlation ordered factor matrix in C (symmetric)

Description

Correlation ordered factor matrix in C (symmetric)

Usage

corr_orderedfactor_matrix_symC(x, theta, xindex, offdiagequal)

Arguments

x

Matrix x

theta

Theta vector

xindex

Index to use

offdiagequal

What to set off-diagonal values with matching values to.

Value

Correlation matrix

Examples

corr_orderedfactor_matrix_symC(matrix(c(1,.5, 2,1.6, 1,0),ncol=2,byrow=TRUE),                              c(1.5,1.8), 1, 1-1e-6)corr_orderedfactor_matrix_symC(matrix(c(0,0,0,1,0,0,0,2,0,0,0,3,0,0,0,4),                                     ncol=4, byrow=TRUE),  c(0.101, -0.714, 0.114, -0.755, 0.117, -0.76, 0.116, -0.752),  4, 1-1e-6) * 6.85

Correlation ordered factor matrix in C (symmetric)

Description

Correlation ordered factor matrix in C (symmetric)

Usage

corr_orderedfactor_matrixmatrixC(x, y, theta, xindex, offdiagequal)

Arguments

x

Matrix x

y

Matrix y

theta

Theta vector

xindex

Index to use

offdiagequal

What to set off-diagonal values with matching values to.

Value

Correlation matrix

Examples

corr_orderedfactor_matrixmatrixC(matrix(c(1,.5, 2,1.6, 1,0),ncol=2,byrow=TRUE),                                matrix(c(2,1.6, 1,0),ncol=2,byrow=TRUE),                                c(1.5,1.8), 1, 1-1e-6)corr_orderedfactor_matrixmatrixC(matrix(c(0,0,0,1,0,0,0,2,0,0,0,3,0,0,0,4),                                  ncol=4, byrow=TRUE),                                matrix(c(0,0,0,2,0,0,0,4,0,0,0,1),                                  ncol=4, byrow=TRUE),  c(0.101, -0.714, 0.114, -0.755, 0.117, -0.76, 0.116, -0.752),  4, 1-1e-6) * 6.85

Gaussian process regression model

Description

Fits a Gaussian process regression model to data.

An R6 object is returned with many methods.

'gpkm()' is an alias for 'GauPro_kernel_model$new()'.For full documentation, see documentation for 'GauPro_kernel_model'.

Standard methods that work include 'plot()', 'summary()', and 'predict()'.

Usage

gpkm(  X,  Z,  kernel,  trend,  verbose = 0,  useC = TRUE,  useGrad = TRUE,  parallel = FALSE,  parallel_cores = "detect",  nug = 1e-06,  nug.min = 1e-08,  nug.max = 100,  nug.est = TRUE,  param.est = TRUE,  restarts = 0,  normalize = FALSE,  optimizer = "L-BFGS-B",  track_optim = FALSE,  formula,  data,  ...)

Arguments

X

Matrix whose rows are the input points

Z

Output points corresponding to X

kernel

The kernel to use. E.g., Gaussian$new().

trend

Trend to use. E.g., trend_constant$new().

verbose

Amount of stuff to print. 0 is little, 2 is a lot.

useC

Should C code be used when possible? Should be faster.

useGrad

Should the gradient be used?

parallel

Should code be run in parallel? Make optimizationfaster but uses more computer resources.

parallel_cores

When using parallel, how many cores shouldbe used?

nug

Value for the nugget. The starting value if estimating it.

nug.min

Minimum allowable value for the nugget.

nug.max

Maximum allowable value for the nugget.

nug.est

Should the nugget be estimated?

param.est

Should the kernel parameters be estimated?

restarts

How many optimization restarts should be used whenestimating parameters?

normalize

Should the data be normalized?

optimizer

What algorithm should be used to optimize theparameters.

track_optim

Should it track the parameters evaluatedwhile optimizing?

formula

Formula for the data if giving in a data frame.

data

Data frame of data. Use in conjunction with formula.

...

Not used

Details

The default kernel is a Matern 5/2 kernel, but factor/character inputswill be given factor kernels.

Calculate gradfunc in optimization to speed up.NEEDS TO APERM dC_dparamsDoesn't need to be exported, should only be useful in functions.

Description

Calculate gradfunc in optimization to speed up.NEEDS TO APERM dC_dparamsDoesn't need to be exported, should only be useful in functions.

Usage

gradfuncarray(dC_dparams, Cinv, Cinv_yminusmu)

Arguments

dC_dparams

Derivative matrix for covariance function wrt kernel parameters

Cinv

Inverse of covariance matrix

Cinv_yminusmu

Vector that is the inverse of C times y minus the mean.

Value

Vector, one value for each parameter

Examples

gradfuncarray(array(dim=c(2,4,4), data=rnorm(32)), matrix(rnorm(16),4,4), rnorm(4))

Calculate gradfunc in optimization to speed up.NEEDS TO APERM dC_dparamsDoesn't need to be exported, should only be useful in functions.

Description

Calculate gradfunc in optimization to speed up.NEEDS TO APERM dC_dparamsDoesn't need to be exported, should only be useful in functions.

Usage

gradfuncarrayR(dC_dparams, Cinv, Cinv_yminusmu)

Arguments

dC_dparams

Derivative matrix for covariance function wrt kernel parameters

Cinv

Inverse of covariance matrix

Cinv_yminusmu

Vector that is the inverse of C times y minus the mean.

Value

Vector, one value for each parameter

Examples

a1 <- array(dim=c(2,4,4), data=rnorm(32))a2 <- matrix(rnorm(16),4,4)a3 <- rnorm(4)#gradfuncarray(a1, a2, a3)#gradfuncarrayR(a1, a2, a3)

Derivative of cubic kernel covariance matrix in C

Description

Derivative of cubic kernel covariance matrix in C

Usage

kernel_cubic_dC(x, theta, C_nonug, s2_est, beta_est, lenparams_D, s2_nug, s2)

Arguments

x

Matrix x

theta

Theta vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

beta_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

s2

Value

Correlation matrix

Derivative of Matern 5/2 kernel covariance matrix in C

Description

Derivative of Matern 5/2 kernel covariance matrix in C

Usage

kernel_exponential_dC(  x,  theta,  C_nonug,  s2_est,  beta_est,  lenparams_D,  s2_nug,  s2)

Arguments

x

Matrix x

theta

Theta vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

beta_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

s2

s2 parameter

Value

Correlation matrix

Derivative of Gaussian kernel covariance matrix in C

Description

Derivative of Gaussian kernel covariance matrix in C

Usage

kernel_gauss_dC(x, theta, C_nonug, s2_est, beta_est, lenparams_D, s2_nug)

Arguments

x

Matrix x

theta

Theta vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

beta_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

Value

Correlation matrix

Derivative of covariance matrix of X with respect to kernelparameters for the Latent Factor Kernel

Description

Derivative of covariance matrix of X with respect to kernelparameters for the Latent Factor Kernel

Usage

kernel_latentFactor_dC(  x,  pf,  C_nonug,  s2_est,  p_est,  lenparams_D,  s2_nug,  latentdim,  xindex,  nlevels,  s2)

Arguments

x

Matrix x

pf

pf vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

p_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

latentdim

Number of latent dimensions

xindex

Which column of x is the indexing variable

nlevels

Number of levels

s2

Value of s2

Value

Correlation matrix

Derivative of Matern 5/2 kernel covariance matrix in C

Description

Derivative of Matern 5/2 kernel covariance matrix in C

Usage

kernel_matern32_dC(x, theta, C_nonug, s2_est, beta_est, lenparams_D, s2_nug)

Arguments

x

Matrix x

theta

Theta vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

beta_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

Value

Correlation matrix

Derivative of Matern 5/2 kernel covariance matrix in C

Description

Derivative of Matern 5/2 kernel covariance matrix in C

Usage

kernel_matern52_dC(x, theta, C_nonug, s2_est, beta_est, lenparams_D, s2_nug)

Arguments

x

Matrix x

theta

Theta vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

beta_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

Value

Correlation matrix

Derivative of covariance matrix of X with respect to kernelparameters for the Ordered Factor Kernel

Description

Derivative of covariance matrix of X with respect to kernelparameters for the Ordered Factor Kernel

Usage

kernel_orderedFactor_dC(  x,  pf,  C_nonug,  s2_est,  p_est,  lenparams_D,  s2_nug,  xindex,  nlevels,  s2)

Arguments

x

Matrix x

pf

pf vector

C_nonug

cov mat without nugget

s2_est

whether s2 is being estimated

p_est

Whether theta/beta is being estimated

lenparams_D

Number of parameters the derivative is being calculated for

s2_nug

s2 times the nug

xindex

Which column of x is the indexing variable

nlevels

Number of levels

s2

Value of s2

Value

Correlation matrix

Gaussian Kernel R6 class

Description

Gaussian Kernel R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_product

Public fields

k1: kernel 1
k2: kernel 2
s2: Variance

Active bindings

k1pl: param length of kernel 1
k2pl: param length of kernel 2
s2_est: Is s2 being estimated?

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Is s2 being estimated?

Length of the parameters of k1

Length of the parameters of k2

Initialize kernel

Usage

kernel_product$new(k1, k2, useC = TRUE)

Arguments

k1: Kernel 1
k2: Kernel 2
useC: Should C code used? Not applicable for kernel product.

Method`k()`

Calculate covariance between two points

Usage

kernel_product$k(x, y = NULL, params, ...)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
params: parameters to use instead of beta and s2.
...: Not used

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

kernel_product$param_optim_start(jitter = F, y)

Arguments

jitter: Should there be a jitter?
y: Output

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

kernel_product$param_optim_start0(jitter = F, y)

Arguments

jitter: Should there be a jitter?
y: Output

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

kernel_product$param_optim_lower()

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

kernel_product$param_optim_upper()

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

kernel_product$set_params_from_optim(optim_out)

Arguments

optim_out: Output from optimization

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

kernel_product$dC_dparams(params = NULL, C, X, C_nonug, nug)

Arguments

params: Kernel parameters
C: Covariance with nugget
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

kernel_product$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

kernel_product$dC_dx(XX, X)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to

Method`s2_from_params()`

Get s2 from params vector

Usage

kernel_product$s2_from_params(params, s2_est = self$s2_est)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

kernel_product$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

kernel_product$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Exponential$new(beta=1)k2 <- Matern32$new(beta=2)k <- k1 * k2k$k(matrix(c(2,1), ncol=1))

Gaussian Kernel R6 class

Description

Gaussian Kernel R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel ->GauPro_kernel_sum

Public fields

k1: kernel 1
k2: kernel 2
k1_param_length: param length of kernel 1
k2_param_length: param length of kernel 2
k1pl: param length of kernel 1
k2pl: param length of kernel 2
s2: variance
s2_est: Is s2 being estimated?

Methods

Public methods

Inherited methods

GauPro::GauPro_kernel$plot()

Method`new()`

Initialize kernel

Usage

kernel_sum$new(k1, k2, useC = TRUE)

Arguments

k1: Kernel 1
k2: Kernel 2
useC: Should C code used? Not applicable for kernel sum.

Method`k()`

Calculate covariance between two points

Usage

kernel_sum$k(x, y = NULL, params, ...)

Arguments

x: vector.
y: vector, optional. If excluded, find correlationof x with itself.
params: parameters to use instead of beta and s2.
...: Not used

Method`param_optim_start()`

Starting point for parameters for optimization

Usage

kernel_sum$param_optim_start(jitter = F, y)

Arguments

jitter: Should there be a jitter?
y: Output

Method`param_optim_start0()`

Starting point for parameters for optimization

Usage

kernel_sum$param_optim_start0(jitter = F, y)

Arguments

jitter: Should there be a jitter?
y: Output

Method`param_optim_lower()`

Lower bounds of parameters for optimization

Usage

kernel_sum$param_optim_lower()

Method`param_optim_upper()`

Upper bounds of parameters for optimization

Usage

kernel_sum$param_optim_upper()

Method`set_params_from_optim()`

Set parameters from optimization output

Usage

kernel_sum$set_params_from_optim(optim_out)

Arguments

optim_out: Output from optimization

Method`dC_dparams()`

Derivative of covariance with respect to parameters

Usage

kernel_sum$dC_dparams(params = NULL, C, X, C_nonug, nug)

Arguments

params: Kernel parameters
C: Covariance with nugget
X: matrix of points in rows
C_nonug: Covariance without nugget added to diagonal
nug: Value of nugget

Method`C_dC_dparams()`

Calculate covariance matrix and its derivativewith respect to parameters

Usage

kernel_sum$C_dC_dparams(params = NULL, X, nug)

Arguments

params: Kernel parameters
X: matrix of points in rows
nug: Value of nugget

Method`dC_dx()`

Derivative of covariance with respect to X

Usage

kernel_sum$dC_dx(XX, X)

Arguments

XX: matrix of points
X: matrix of points to take derivative with respect to

Method`s2_from_params()`

Get s2 from params vector

Usage

kernel_sum$s2_from_params(params)

Arguments

params: parameter vector
s2_est: Is s2 being estimated?

Method`print()`

Print this object

Usage

kernel_sum$print()

Method`clone()`

The objects of this class are cloneable with this method.

Usage

kernel_sum$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

k1 <- Exponential$new(beta=1)k2 <- Matern32$new(beta=2)k <- k1 + k2k$k(matrix(c(2,1), ncol=1))

Predict for class GauPro

Description

Predict for class GauPro

Usage

## S3 method for class 'GauPro'predict(object, XX, se.fit = F, covmat = F, split_speed = T, ...)

Arguments

object

Object of class GauPro

XX

new points to predict

se.fit

Should standard error be returned (and variance)?

covmat

Should the covariance matrix be returned?

split_speed

Should the calculation be split up to speed it up?

...

Additional parameters

Value

Prediction from object at XX

Examples

n <- 12x <- matrix(seq(0,1,length.out = n), ncol=1)y <- sin(2*pi*x) + rnorm(n,0,1e-1)gp <- GauPro(X=x, Z=y, parallel=FALSE)predict(gp, .448)

Predict for class GauPro_base

Description

Predict mean and se for given matrix

Usage

## S3 method for class 'GauPro_base'predict(object, XX, se.fit = F, covmat = F, split_speed = T, ...)

Arguments

object

Object of class GauPro_base

XX

Points to predict at

se.fit

Should the se be returned?

covmat

Should the covariance matrix be returned?

split_speed

Should the predictions be split up for speed

...

Additional parameters

Value

Prediction from object at XX

Print summary.GauPro

Description

Print summary.GauPro

Usage

## S3 method for class 'summary.GauPro'print(x, ...)

Arguments

x

summary.GauPro object

...

Additional args

Value

prints, returns invisible object

Find the square root of a matrix

Description

Same thing as 'expm::sqrtm', but faster.

Usage

sqrt_matrix(mat, symmetric)

Arguments

mat

Matrix to find square root matrix of

symmetric

Is it symmetric? Passed to eigen.

Value

Square root of mat

Examples

mat <- matrix(c(1,.1,.1,1), 2, 2)smat <- sqrt_matrix(mat=mat, symmetric=TRUE)smat %*% smat

Summary for GauPro object

Description

Summary for GauPro object

Usage

## S3 method for class 'GauPro'summary(object, ...)

Arguments

object

GauPro R6 object

...

Additional arguments passed to summary

Value

Summary

Trend R6 class

Description

Trend R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_trend ->GauPro_trend_0

Public fields

m: Trend parameters
m_lower: m lower bound
m_upper: m upper bound
m_est: Should m be estimated?

Methods

Public methods

Method`new()`

Initialize trend object

Usage

trend_0$new(m = 0, m_lower = 0, m_upper = 0, m_est = FALSE, D = NA)

Arguments

m: trend initial parameters
m_lower: trend lower bounds
m_upper: trend upper bounds
m_est: Logical of whether each param should be estimated
D: Number of input dimensions of data

Method`Z()`

Get trend value for given matrix X

Usage

trend_0$Z(X, m = self$m, params = NULL)

Arguments

X: matrix of points
m: trend parameters
params: trend parameters

Method`dZ_dparams()`

Derivative of trend with respect to trend parameters

Usage

trend_0$dZ_dparams(X, m = m$est, params = NULL)

Arguments

X: matrix of points
m: trend values
params: overrides m

Method`dZ_dx()`

Derivative of trend with respect to X

Usage

trend_0$dZ_dx(X, m = self$m, params = NULL)

Arguments

X: matrix of points
m: trend values
params: overrides m

Method`param_optim_start()`

Get parameter initial point for optimization

Usage

trend_0$param_optim_start(jitter, trend_est)

Arguments

jitter: Not used
trend_est: If the trend should be estimate.

Method`param_optim_start0()`

Get parameter initial point for optimization

Usage

trend_0$param_optim_start0(jitter, trend_est)

Arguments

jitter: Not used
trend_est: If the trend should be estimate.

Method`param_optim_lower()`

Get parameter lower bounds for optimization

Usage

trend_0$param_optim_lower(jitter, trend_est)

Arguments

jitter: Not used
trend_est: If the trend should be estimate.

Method`param_optim_upper()`

Get parameter upper bounds for optimization

Usage

trend_0$param_optim_upper(jitter, trend_est)

Arguments

jitter: Not used
trend_est: If the trend should be estimate.

Method`set_params_from_optim()`

Set parameters after optimization

Usage

trend_0$set_params_from_optim(optim_out)

Arguments

optim_out: Output from optim

Method`clone()`

The objects of this class are cloneable with this method.

Usage

trend_0$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

t1 <- trend_0$new()

Trend R6 class

Description

Trend R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_trend ->GauPro_trend_LM

Public fields

m: Trend parameters
m_lower: m lower bound
m_upper: m upper bound
m_est: Should m be estimated?
b: trend parameter
b_lower: trend lower bounds
b_upper: trend upper bounds
b_est: Should b be estimated?

Methods

Public methods

Method`new()`

Initialize trend object

Usage

trend_LM$new(  D,  m = rep(0, D),  m_lower = rep(-Inf, D),  m_upper = rep(Inf, D),  m_est = rep(TRUE, D),  b = 0,  b_lower = -Inf,  b_upper = Inf,  b_est = TRUE)

Arguments

D: Number of input dimensions of data
m: trend initial parameters
m_lower: trend lower bounds
m_upper: trend upper bounds
m_est: Logical of whether each param should be estimated
b: trend parameter
b_lower: trend lower bounds
b_upper: trend upper bounds
b_est: Should b be estimated?

Method`Z()`

Get trend value for given matrix X

Usage

trend_LM$Z(X, m = self$m, b = self$b, params = NULL)

Arguments

X: matrix of points
m: trend parameters
b: trend parameters (slopes)
params: trend parameters

Method`dZ_dparams()`

Derivative of trend with respect to trend parameters

Usage

trend_LM$dZ_dparams(X, m = self$m_est, b = self$b_est, params = NULL)

Arguments

X: matrix of points
m: trend values
b: trend intercept
params: overrides m

Method`dZ_dx()`

Derivative of trend with respect to X

Usage

trend_LM$dZ_dx(X, m = self$m, params = NULL)

Arguments

X: matrix of points
m: trend values
params: overrides m

Method`param_optim_start()`

Get parameter initial point for optimization

Usage

trend_LM$param_optim_start(  jitter = FALSE,  b_est = self$b_est,  m_est = self$m_est)

Arguments

jitter: Not used
b_est: If the mean should be estimated.
m_est: If the linear terms should be estimated.

Method`param_optim_start0()`

Get parameter initial point for optimization

Usage

trend_LM$param_optim_start0(  jitter = FALSE,  b_est = self$b_est,  m_est = self$m_est)

Arguments

jitter: Not used
b_est: If the mean should be estimated.
m_est: If the linear terms should be estimated.

Method`param_optim_lower()`

Get parameter lower bounds for optimization

Usage

trend_LM$param_optim_lower(b_est = self$b_est, m_est = self$m_est)

Arguments

b_est: If the mean should be estimated.
m_est: If the linear terms should be estimated.

Method`param_optim_upper()`

Get parameter upper bounds for optimization

Usage

trend_LM$param_optim_upper(b_est = self$b_est, m_est = self$m_est)

Arguments

b_est: If the mean should be estimated.
m_est: If the linear terms should be estimated.

Method`set_params_from_optim()`

Set parameters after optimization

Usage

trend_LM$set_params_from_optim(optim_out)

Arguments

optim_out: Output from optim

Method`clone()`

The objects of this class are cloneable with this method.

Usage

trend_LM$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

t1 <- trend_LM$new(D=2)

Trend R6 class

Description

Trend R6 class

Format

R6Class object.

Value

Object ofR6Class with methods for fitting GP model.

Super class

GauPro::GauPro_trend ->GauPro_trend_c

Public fields

m: Trend parameters
m_lower: m lower bound
m_upper: m upper bound
m_est: Should m be estimated?

Methods

Public methods

Method`new()`

Initialize trend object

Usage

trend_c$new(m = 0, m_lower = -Inf, m_upper = Inf, m_est = TRUE, D = NA)

Arguments

m: trend initial parameters
m_lower: trend lower bounds
m_upper: trend upper bounds
m_est: Logical of whether each param should be estimated
D: Number of input dimensions of data

Method`Z()`

Get trend value for given matrix X

Usage

trend_c$Z(X, m = self$m, params = NULL)

Arguments

X: matrix of points
m: trend parameters
params: trend parameters

Method`dZ_dparams()`

Derivative of trend with respect to trend parameters

Usage

trend_c$dZ_dparams(X, m = self$m, params = NULL)

Arguments

X: matrix of points
m: trend values
params: overrides m

Method`dZ_dx()`

Derivative of trend with respect to X

Usage

trend_c$dZ_dx(X, m = self$m, params = NULL)

Arguments

X: matrix of points
m: trend values
params: overrides m

Method`param_optim_start()`

Get parameter initial point for optimization

Usage

trend_c$param_optim_start(jitter = F, m_est = self$m_est)

Arguments

jitter: Not used
m_est: If the trend should be estimate.

Method`param_optim_start0()`

Get parameter initial point for optimization

Usage

trend_c$param_optim_start0(jitter = F, m_est = self$m_est)

Arguments

jitter: Not used
m_est: If the trend should be estimate.

Method`param_optim_lower()`

Get parameter lower bounds for optimization

Usage

trend_c$param_optim_lower(m_est = self$m_est)

Arguments

m_est: If the trend should be estimate.

Method`param_optim_upper()`

Get parameter upper bounds for optimization

Usage

trend_c$param_optim_upper(m_est = self$m_est)

Arguments

m_est: If the trend should be estimate.

Method`set_params_from_optim()`

Set parameters after optimization

Usage

trend_c$set_params_from_optim(optim_out)

Arguments

optim_out: Output from optim

Method`clone()`

The objects of this class are cloneable with this method.

Usage

trend_c$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

t1 <- trend_c$new()

Movatterモバイル変換

Kernel product

Description

Usage

Arguments

Value

Examples

Kernel sum

Description

Usage

Arguments

Value

Examples

Cubic Kernel R6 class

Description

Usage

Arguments

Format

Value

Super classes

Methods

Public methods

Methodk()

Usage

Arguments

Methodkone()

Usage

Arguments

MethoddC_dparams()

Usage

Arguments

MethoddC_dx()

Usage

Arguments

Methodprint()

Usage

Methodclone()

Usage

Arguments

Examples

Exponential Kernel R6 class

Description

Usage

Arguments

Format

Value

Super classes

Methods

Public methods

Methodk()

Usage

Arguments

Methodkone()

Usage

Arguments

MethoddC_dparams()

Usage

Arguments

MethoddC_dx()

Usage

Arguments

Methodprint()

Usage

Methodclone()

Usage

Arguments

Examples

Factor Kernel R6 class

Description

Usage

Arguments

Format

Details

Value

Super class

Public fields

Methods

Public methods

Methodnew()

Usage

Method`k()`

Method`kone()`

Method`dC_dparams()`

Method`dC_dx()`

Method`print()`

Method`clone()`

Method`k()`

Method`kone()`

Method`dC_dparams()`

Method`dC_dx()`

Method`print()`

Method`clone()`

Method`new()`

Method`k()`

Method`kone()`

Method`dC_dparams()`

Method`C_dC_dparams()`

Method`dC_dx()`

Method`param_optim_start()`

Method`param_optim_start0()`

Method`param_optim_lower()`

Method`param_optim_upper()`

Method`set_params_from_optim()`

Method`s2_from_params()`

Method`print()`

Method`clone()`

Method`new()`

Method`corr_func()`

Method`deviance_theta()`

Method`deviance_theta_log()`

Method`deviance()`