iprior_cv {iprior}

Perform a cross-validation experiment with the iprior function

Description

A convenience function to perform a k-fold cross-validation experiment and obtain mean squared error of prediction. Most of the arguments are similar to iprior() and kernL().

Usage

## Default S3 method:
iprior_cv(
  y,
  ...,
  folds = 2,
  par.cv = TRUE,
  kernel = "linear",
  method = "direct",
  control = list(),
  interactions = NULL,
  est.lambda = TRUE,
  est.hurst = FALSE,
  est.lengthscale = FALSE,
  est.offset = FALSE,
  est.psi = TRUE,
  fixed.hyp = NULL,
  lambda = 1,
  psi = 1,
  nystrom = FALSE,
  nys.seed = NULL
)

## S3 method for class 'formula'
iprior_cv(
  formula,
  data,
  folds = 2,
  one.lam = FALSE,
  par.cv = TRUE,
  kernel = "linear",
  method = "direct",
  control = list(),
  est.lambda = TRUE,
  est.hurst = FALSE,
  est.lengthscale = FALSE,
  est.offset = FALSE,
  est.psi = TRUE,
  fixed.hyp = NULL,
  lambda = 1,
  psi = 1,
  nystrom = FALSE,
  nys.seed = NULL,
  ...
)

Arguments

y

Vector of response variables

...

Only used when fitting using non-formula, enter the variables (vectors or matrices) separated by commas.

folds

The number of cross-validation folds. Set equal to sample size or Inf to perform leave-one-out cross-validation.

par.cv

Logical. Multithreading to fit the models? Defaults to TRUE.

kernel

Character vector indicating the type of kernel for the variables. Available choices are:

• "linear" - (default) for the linear kernel

• "canonical" - alternative name for "linear"

• "fbm", "fbm,0.5" - for the fBm kernel with Hurst coefficient 0.5 (default)

• "se", "se,1" - for the SE kernel with lengthscale 1 (default)

• "poly", "poly2", "poly2,0" - for the polynomial kernel of degree 2 with offset 0 (default)

• "pearson" - for the Pearson kernel

The kernel argument can also be a vector of length equal to the number of variables, therefore it is possible to specify different kernels for each variables. Note that factor type variables are assigned the Pearson kernel by default, and that non-factor types can be forced to use the Pearson kernel (not recommended).

method

The estimation method. One of:

• "direct" - for the direct minimisation of the marginal deviance using optim()'s L-BFGS method

• "em" - for the EM algorithm

• "mixed" - combination of the direct and EM methods

• "fixed" - for just obtaining the posterior regression function with fixed hyperparameters (default method when setting fixed.hyp = TRUE)

• "canonical" - an efficient estimation method which takes advantage of the structure of the linear kernel

control

(Optional) A list of control options for the estimation procedure:

maxit

The maximum number of iterations for the quasi-Newton optimisation or the EM algorithm. Defaults to 100.

em.maxit

For method = "mixed", the number of EM steps before switching to direct optimisation. Defaults to 5.

stop.crit

The stopping criterion for the EM and L-BFGS algorithm, which is the difference in successive log-likelihood values. Defaults to 1e-8.

theta0

The initial values for the hyperparameters. Defaults to random starting values.

report

The interval of reporting for the optim() function.

restarts

The number of random restarts to perform. Defaults to 0. It's also possible to set it to TRUE, in which case the number of random restarts is set to the total number of available cores.

no.cores

The number of cores in which to do random restarts. Defaults to the total number of available cores.

omega

The overrelaxation parameter for the EM algorithm - a value between 0 and 1.

interactions

Character vector to specify the interaction terms. When using formulas, this is specified automatically, so is not required. Syntax is "a:b" to indicate variable a interacts with variable b.

est.lambda

Logical. Estimate the scale parameters? Defaults to TRUE.

est.hurst

Logical. Estimate the Hurst coefficients for fBm kernels? Defaults to FALSE.

est.lengthscale

Logical. Estimate the lengthscales for SE kernels? Defaults to FALSE.

est.offset

Logical. Estimate the offsets for polynomial kernels? Defaults to FALSE.

est.psi

Logical. Estimate the error precision? Defaults to TRUE.

fixed.hyp

Logical. If TRUE, then no hyperparameters are estimated, i.e. all of the above est.x are set to FALSE, and vice versa. If NULL (default) then all of the est.x defaults are respected.

lambda

Initial/Default scale parameters. Relevant especially if est.lambda = FALSE.

psi

Initial/Default value for error precision. Relevant especially if est.psi = FALSE.

nystrom

Either logical or an integer indicating the number of Nystrom samples to take. Defaults to FALSE. If TRUE, then approximately 10% of the sample size is used for the Nystrom approximation.

nys.seed

The random seed for the Nystrom sampling. Defaults to NULL, which means the random seed is not fixed.

formula

The formula to fit when using formula interface.

data

Data frame containing variables when using formula interface.

one.lam

Logical. When using formula input, this is a convenient way of letting the function know to treat all variables as a single variable (i.e. shared scale parameter). Defaults to FALSE.

Details

Uses a multicore loop to fit the folds by default, set par.cv = FALSE to not use multithreading.

Value

An iprior_xv object containing a data frame of the cross-validated values such as the log-likelihood, training MSE and test MSE.

Examples

## Not run: 

# 5-fold CV experiment
(mod.cv <- iprior_cv(y ~ X, gen_smooth(100), kernel = "se", folds = 5))

# LOOCV experiment
(mod.cv <- iprior_cv(y ~ X, gen_smooth(100), kernel = "se", folds = Inf))

# Can also get root MSE
print(mod.cv, "RMSE")

## End(Not run)