cv.boss {BOSSreg}

Cross-validation for Best Orthogonalized Subset Selection (BOSS) and Forward Stepwise Selection (FS).

Description

Cross-validation for Best Orthogonalized Subset Selection (BOSS) and Forward Stepwise Selection (FS).

Usage

cv.boss(
  x,
  y,
  maxstep = min(nrow(x) - intercept - 1, ncol(x)),
  intercept = TRUE,
  n.folds = 10,
  n.rep = 1,
  show.warning = TRUE,
  ...
)

Arguments

x

A matrix of predictors, see boss.

y

A vector of response variable, see boss.

maxstep

Maximum number of steps performed. Default is min(n-1,p) if intercept=FALSE, and it is min(n-2, p) otherwise.

intercept

Logical, whether to fit an intercept term. Default is TRUE.

n.folds

The number of cross validation folds. Default is 10.

n.rep

The number of replications of cross validation. Default is 1.

show.warning

Whether to display a warning if CV is only performed for a subset of candidates. e.g. when n<p and 10-fold. Default is TRUE.

...

Arguments to boss, such as hdf.ic.boss.

Details

This function fits BOSS and FS (boss) on the full dataset, and performs n.folds cross-validation. The cross-validation process can be repeated n.rep times to evaluate the out-of-sample (OOS) performance for the candidate subsets given by both methods.

Value

• boss: An object boss that fits on the full dataset.

• n.folds: The number of cross validation folds.

• cvm.fs: Mean OOS deviance for each candidate given by FS.

• cvm.boss: Mean OSS deviance for each candidate given by BOSS.

• i.min.fs: The index of minimum cvm.fs.

• i.min.boss: The index of minimum cvm.boss.

Author(s)

Sen Tian

References

• Tian, S., Hurvich, C. and Simonoff, J. (2021), On the Use of Information Criteria for Subset Selection in Least Squares Regression. https://arxiv.org/abs/1911.10191

• BOSSreg Vignette https://github.com/sentian/BOSSreg/blob/master/r-package/vignettes/BOSSreg.pdf

See Also

predict and coef methods for cv.boss object, and the boss function

Examples

## Generate a trivial dataset, X has mean 0 and norm 1, y has mean 0
set.seed(11)
n = 20
p = 5
x = matrix(rnorm(n*p), nrow=n, ncol=p)
x = scale(x, center = colMeans(x))
x = scale(x, scale = sqrt(colSums(x^2)))
beta = c(1, 1, 0, 0, 0)
y = x%*%beta + scale(rnorm(20, sd=0.01), center = TRUE, scale = FALSE)

## Perform 10-fold CV without replication
boss_cv_result = cv.boss(x, y)
## Get the coefficient vector of BOSS that gives minimum CV OSS score (S3 method for cv.boss)
beta_boss_cv = coef(boss_cv_result)
# the above is equivalent to
boss_result = boss_cv_result$boss
beta_boss_cv = boss_result$beta_boss[, boss_cv_result$i.min.boss, drop=FALSE]
## Get the fitted values of BOSS-CV (S3 method for cv.boss)
mu_boss_cv = predict(boss_cv_result, newx=x)
# the above is equivalent to
mu_boss_cv = cbind(1,x) %*% beta_boss_cv

## Get the coefficient vector of FS that gives minimum CV OSS score (S3 method for cv.boss)
beta_fs_cv = coef(boss_cv_result, method='fs')
## Get the fitted values of FS-CV (S3 method for cv.boss)
mu_fs_cv = predict(boss_cv_result, newx=x, method='fs')