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GauPro (version 0.2.4)

GauPro_kernel_model: GauPro model that uses kernels

Description

GauPro model that uses kernels

GauPro model that uses kernels

Arguments

Value

Object of R6Class with methods for fitting GP model.

Format

R6Class object.

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 with X and Z 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.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 predicted trend 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 standard deviation of each column.

optimizer

What algorithm should be used to optimize the parameters.

Methods

Public methods

Method new()

Create kernel_model object

Usage

GauPro_kernel_model$new(
  X,
  Z,
  kernel,
  trend,
  verbose = 0,
  useC = F,
  useGrad = T,
  parallel = FALSE,
  parallel_cores = "detect",
  nug = 1e-06,
  nug.min = 1e-08,
  nug.max = Inf,
  nug.est = TRUE,
  param.est = TRUE,
  restarts = 5,
  normalize = FALSE,
  optimizer = "L-BFGS-B",
  ...
)

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 optimization faster but uses more computer resources.

parallel_cores

When using parallel, how many cores should be 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 when estimating parameters?

normalize

Should the data be normalized?

optimizer

What algorithm should be used to optimize the parameters.

...

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)

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?

Method pred()

Predict for a matrix of points

Usage

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

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?

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
)

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 in a data frame?

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 cool1Dplot()

Make cool 1D plot

Usage

GauPro_kernel_model$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_kernel_model$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

xlab

x label

ylab

y label

xmin

xmin

xmax

xmax

ymin

ymin

ymax

ymax

Method plot2D()

Make 2D plot

Usage

GauPro_kernel_model$plot2D()

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 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$optim(
  restarts = 5,
  param_update = T,
  nug.update = self$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_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 value and 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 sample()

Sample at rows of XX

Usage

GauPro_kernel_model$sample(XX, n = 1)

Arguments

XX

Input matrix

n

Number of samples

Method print()

Print this object

Usage

GauPro_kernel_model$print()

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.

Details

Class providing object with methods for fitting a GP model. Allows for different kernel and trend functions to be used.

Examples

Run this code
# NOT RUN {
n <- 12
x <- 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)
# }

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