| Title: | Best Orthogonalized Subset Selection (BOSS) |
|---|---|
| Description: | Best Orthogonalized Subset Selection (BOSS) is a least-squares (LS) based subset selection method, that performs best subset selection upon an orthogonalized basis of ordered predictors, with the computational effort of a single ordinary LS fit. This package provides a highly optimized implementation of BOSS and estimates a heuristic degrees of freedom for BOSS, which can be plugged into an information criterion (IC) such as AICc in order to select the subset from candidates. It provides various choices of IC, including AIC, BIC, AICc, Cp and GCV. It also implements the forward stepwise selection (FS) with no additional computational cost, where the subset of FS is selected via cross-validation (CV). CV is also an option for BOSS. For details see: Tian, Hurvich and Simonoff (2021), "On the Use of Information Criteria for Subset Selection in Least Squares Regression", <arXiv:1911.10191>. |
| Authors: | Sen Tian [aut, cre], Clifford Hurvich [aut], Jeffrey Simonoff [aut] |
| Maintainer: | Sen Tian <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.2.0 |
| Built: | 2024-10-31 06:44:27 UTC |
| Source: | CRAN |
Compute the solution path of BOSS and forward stepwise selection (FS).
Compute various information criteria based on a heuristic degrees of freedom (hdf) that can serve as the selection rule to choose the subset given by BOSS.
boss( x, y, maxstep = min(nrow(x) - intercept - 1, ncol(x)), intercept = TRUE, hdf.ic.boss = TRUE, mu = NULL, sigma = NULL, ... )boss( x, y, maxstep = min(nrow(x) - intercept - 1, ncol(x)), intercept = TRUE, hdf.ic.boss = TRUE, mu = NULL, sigma = NULL, ... )
x |
A matrix of predictors, with |
y |
A vector of response variable, with |
maxstep |
Maximum number of steps performed. Default is |
intercept |
Logical, whether to include an intercept term. Default is TRUE. |
hdf.ic.boss |
Logical, whether to calculate the heuristic degrees of freedom (hdf) and information criteria (IC) for BOSS. IC includes AIC, BIC, AICc, BICc, GCV, Cp. Default is TRUE. |
mu |
True mean vector, used in the calculation of hdf. Default is NULL, and is estimated via least-squares (LS) regression of y upon x for n>p, and 10-fold CV cross-validated lasso estimate for n<=p. |
sigma |
True standard deviation of the error, used in the calculation of hdf. Default is NULL, and is estimated via least-squares (LS) regression of y upon x for n>p, and 10-fold cross-validated lasso for n<=p. |
... |
Extra parameters to allow flexibility. Currently none allows or requires, just for the convinience of call from other parent functions like cv.boss. |
This function computes the full solution path given by BOSS and FS on a given dataset (x,y) with n observations and p predictors. It also calculates the heuristic degrees of freedom for BOSS, and various information criteria, which can further be used to select the subset from the candidates. Please refer to the Vignette for implementation details and Tian et al. (2021) for methodology details (links are given below).
beta_fs: A matrix of regression coefficients for all the subsets given by FS,
from a null model until stop, with nrow=p and ncol=min(n,p)+1, where min(n,p) is
the maximum number of steps performed.
beta_boss: A matrix of regression coefficients for all the subsets given by
BOSS, with nrow=p and ncol=min(n,p)+1. Note that unlike beta_fs and due to the nature of BOSS,
the number of non-zero components in columns of beta_boss may not be unique, i.e.
there maybe multiple columns corresponding to the same size of subset.
steps_x: A vector of numbers representing which predictor joins at each step,
with length(steps)=min(n,p). The ordering is determined by the partial correlation between a predictor
and the response y.
steps_q: A vector of numbers representing which predictor joins at each step in the orthogonal basis,
with length(steps)=min(n,p). BOSS takes the ordered predictors (ordering given in steps_x) and performs best
subset regression upon their orthogonal basis, which is essentially ordering the orthogonalized predictors by their
marginal correlations with the response y. For example, steps_q=c(2,1) indicates that the orthogonal basis of
x_2 joins first.
hdf_boss: A vector of heuristic degrees of freedom (hdf) for BOSS, with
length(hdf_boss)=p+1. Note that hdf_boss=NULL if n<=p or hdf.ic.boss=FALSE.
IC_boss: A list of information criteria (IC) for BOSS, where each element in the list is a vector representing values of a given IC for each candidate subset of BOSS (or each column in beta_boss). The output IC includes AIC, BIC, AICc, BICc, GCV and Mallows' Cp. Note that each IC is calculated by plugging in hdf_boss.
sigma: estimated error standard deviation. It is only returned when hdf is calculated, i.e. hdf.ic.boss=TRUE.
Sen Tian
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
Reid, S., Tibshirani, R. and Friedman, J. (2016), A Study of Error Variance Estimation in Lasso Regression. Statistica Sinica, P35-67, JSTOR.
BOSSreg Vignette https://github.com/sentian/BOSSreg/blob/master/r-package/vignettes/BOSSreg.pdf
predict and coef methods for "boss" object, and the cv.boss function
## 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(n, sd=0.01), center = TRUE, scale = FALSE) ## Fit the model boss_result = boss(x, y) ## Get the coefficient vector selected by AICc-hdf (S3 method for boss) beta_boss_aicc = coef(boss_result) # the above is equivalent to the following beta_boss_aicc = boss_result$beta_boss[, which.min(boss_result$IC_boss$aicc), drop=FALSE] ## Get the fitted values of BOSS-AICc-hdf (S3 method for boss) mu_boss_aicc = predict(boss_result, newx=x) # the above is equivalent to the following mu_boss_aicc = cbind(1,x) %*% beta_boss_aicc ## Repeat the above process, but using Cp-hdf instead of AICc-hdf ## coefficient vector beta_boss_cp = coef(boss_result, method.boss='cp') beta_boss_cp = boss_result$beta_boss[, which.min(boss_result$IC_boss$cp), drop=FALSE] ## fitted values of BOSS-Cp-hdf mu_boss_cp = predict(boss_result, newx=x, method.boss='cp') mu_boss_cp = cbind(1,x) %*% beta_boss_cp## 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(n, sd=0.01), center = TRUE, scale = FALSE) ## Fit the model boss_result = boss(x, y) ## Get the coefficient vector selected by AICc-hdf (S3 method for boss) beta_boss_aicc = coef(boss_result) # the above is equivalent to the following beta_boss_aicc = boss_result$beta_boss[, which.min(boss_result$IC_boss$aicc), drop=FALSE] ## Get the fitted values of BOSS-AICc-hdf (S3 method for boss) mu_boss_aicc = predict(boss_result, newx=x) # the above is equivalent to the following mu_boss_aicc = cbind(1,x) %*% beta_boss_aicc ## Repeat the above process, but using Cp-hdf instead of AICc-hdf ## coefficient vector beta_boss_cp = coef(boss_result, method.boss='cp') beta_boss_cp = boss_result$beta_boss[, which.min(boss_result$IC_boss$cp), drop=FALSE] ## fitted values of BOSS-Cp-hdf mu_boss_cp = predict(boss_result, newx=x, method.boss='cp') mu_boss_cp = cbind(1,x) %*% beta_boss_cp
Calculate a specified information criterion (IC) for an estimate or a group of estimates. The choices of IC include AIC, BIC, AICc, BICc, GCV and Mallows' Cp.
calc.ic( y_hat, y, ic = c("aicc", "bicc", "aic", "bic", "gcv", "cp"), df, sigma = NULL )calc.ic( y_hat, y, ic = c("aicc", "bicc", "aic", "bic", "gcv", "cp"), df, sigma = NULL )
y_hat |
A vector of fitted values with |
y |
A vector of response variable, with |
ic |
A specified IC to calculate. Default is AICc ('aicc'). Other choices include AIC ('aic'), BIC ('bic'), BICc ('bicc'), GCV ('gcv') and Mallows' Cp ('cp'). |
df |
A number if y_hat is a vector, or a vector with |
sigma |
Standard deviation of the error term. It only needs to be specified if the argument |
This function enables the computation of various common IC for model fits, which can further be used to choose the optimal fit. This allows user comparing the effect of different IC. In order to calculate an IC, degrees of freedoms (df) needs to be specified. To be more specific, here are the formulas used to calculate each IC:
The value(s) of the specified IC for each fit.
Sen Tian
## 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) ## Fit the model boss_result = boss(x, y) ## Print the values of AICc-hdf for all subsets given by BOSS print(boss_result$IC_boss$aicc) ## calculate them manually using the calc.ic function y_hat = cbind(rep(1,n),x)%*%boss_result$beta_boss print(calc.ic(y_hat, y, df=boss_result$hdf_boss))## 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) ## Fit the model boss_result = boss(x, y) ## Print the values of AICc-hdf for all subsets given by BOSS print(boss_result$IC_boss$aicc) ## calculate them manually using the calc.ic function y_hat = cbind(rep(1,n),x)%*%boss_result$beta_boss print(calc.ic(y_hat, y, df=boss_result$hdf_boss))
This function returns the optimal coefficient vector of BOSS selected by AICc (by default) or other types of information criterion.
## S3 method for class 'boss' coef( object, ic = c("aicc", "bicc", "aic", "bic", "gcv", "cp"), select.boss = NULL, ... )## S3 method for class 'boss' coef( object, ic = c("aicc", "bicc", "aic", "bic", "gcv", "cp"), select.boss = NULL, ... )
object |
The boss object, returned from calling the |
ic |
Which information criterion is used to select the optimal coefficient vector for BOSS. The default is AICc-hdf. |
select.boss |
The index (or indicies) of columns in the coefficient matrix for which one wants to select. By default (NULL) it's selected by the information criterion specified in 'ic'. |
... |
Extra arguments (unused for now) |
If select.boss is specified, the function returns
corresponding column(s) in the coefficient matrix.
If select.boss is unspecified, the function returns the optimal coefficient
vector selected by AICc-hdf (other choice of IC can be specified in the argument ic).
The chosen coefficient vector(s) for BOSS.
## 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(n, sd=0.01), center = TRUE, scale = FALSE) ## Fit the model boss_result = boss(x, y) ## Get the coefficient vector selected by AICc-hdf (S3 method for boss) beta_boss_aicc = coef(boss_result) # the above is equivalent to the following beta_boss_aicc = boss_result$beta_boss[, which.min(boss_result$IC_boss$aicc), drop=FALSE] ## Get the fitted values of BOSS-AICc-hdf (S3 method for boss) mu_boss_aicc = predict(boss_result, newx=x) # the above is equivalent to the following mu_boss_aicc = cbind(1,x) %*% beta_boss_aicc ## Repeat the above process, but using Cp-hdf instead of AICc-hdf ## coefficient vector beta_boss_cp = coef(boss_result, method.boss='cp') beta_boss_cp = boss_result$beta_boss[, which.min(boss_result$IC_boss$cp), drop=FALSE] ## fitted values of BOSS-Cp-hdf mu_boss_cp = predict(boss_result, newx=x, method.boss='cp') mu_boss_cp = cbind(1,x) %*% beta_boss_cp## 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(n, sd=0.01), center = TRUE, scale = FALSE) ## Fit the model boss_result = boss(x, y) ## Get the coefficient vector selected by AICc-hdf (S3 method for boss) beta_boss_aicc = coef(boss_result) # the above is equivalent to the following beta_boss_aicc = boss_result$beta_boss[, which.min(boss_result$IC_boss$aicc), drop=FALSE] ## Get the fitted values of BOSS-AICc-hdf (S3 method for boss) mu_boss_aicc = predict(boss_result, newx=x) # the above is equivalent to the following mu_boss_aicc = cbind(1,x) %*% beta_boss_aicc ## Repeat the above process, but using Cp-hdf instead of AICc-hdf ## coefficient vector beta_boss_cp = coef(boss_result, method.boss='cp') beta_boss_cp = boss_result$beta_boss[, which.min(boss_result$IC_boss$cp), drop=FALSE] ## fitted values of BOSS-Cp-hdf mu_boss_cp = predict(boss_result, newx=x, method.boss='cp') mu_boss_cp = cbind(1,x) %*% beta_boss_cp
This function returns coefficient vector that minimizes out-of-sample (OOS) cross validation score.
## S3 method for class 'cv.boss' coef(object, method = c("boss", "fs"), ...)## S3 method for class 'cv.boss' coef(object, method = c("boss", "fs"), ...)
object |
The cv.boss object, returned from calling |
method |
It can either be 'fs' or 'boss'. The default is 'boss'. |
... |
Extra arguments (unused for now). |
The chosen coefficient vector for BOSS or FS.
## 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$i.min.boss, drop=FALSE] ## Get the fitted values of BOSS-CV (S3 method for cv.boss) mu_boss_cv = predict(boss_cv_result, newx=x) # the above is equivalent to mu_boss_cv = cbind(1,x) %*% beta_boss_cv ## Get the coefficient vector of FS that gives minimum CV OSS score (S3 method for cv.boss) beta_fs_cv = coef(boss_cv_result, method='fs') ## Get the fitted values of FS-CV (S3 method for cv.boss) mu_fs_cv = predict(boss_cv_result, newx=x, method='fs')## Generate a trivial dataset, X has mean 0 and norm 1, y has mean 0 set.seed(11) n = 20 p = 5 x = matrix(rnorm(n*p), nrow=n, ncol=p) x = scale(x, center = colMeans(x)) x = scale(x, scale = sqrt(colSums(x^2))) beta = c(1, 1, 0, 0, 0) y = x%*%beta + scale(rnorm(20, sd=0.01), center = TRUE, scale = FALSE) ## Perform 10-fold CV without replication boss_cv_result = cv.boss(x, y) ## Get the coefficient vector of BOSS that gives minimum CV OSS score (S3 method for cv.boss) beta_boss_cv = coef(boss_cv_result) # the above is equivalent to boss_result = boss_cv_result$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')
Cross-validation for Best Orthogonalized Subset Selection (BOSS) and Forward Stepwise Selection (FS).
cv.boss( x, y, maxstep = min(nrow(x) - intercept - 1, ncol(x)), intercept = TRUE, n.folds = 10, n.rep = 1, show.warning = TRUE, ... )cv.boss( x, y, maxstep = min(nrow(x) - intercept - 1, ncol(x)), intercept = TRUE, n.folds = 10, n.rep = 1, show.warning = TRUE, ... )
x |
A matrix of predictors, see |
y |
A vector of response variable, see |
maxstep |
Maximum number of steps performed. Default is |
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 |
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.
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.
Sen Tian
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
predict and coef methods for cv.boss object, and the boss function
## 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$i.min.boss, drop=FALSE] ## Get the fitted values of BOSS-CV (S3 method for cv.boss) mu_boss_cv = predict(boss_cv_result, newx=x) # the above is equivalent to mu_boss_cv = cbind(1,x) %*% beta_boss_cv ## Get the coefficient vector of FS that gives minimum CV OSS score (S3 method for cv.boss) beta_fs_cv = coef(boss_cv_result, method='fs') ## Get the fitted values of FS-CV (S3 method for cv.boss) mu_fs_cv = predict(boss_cv_result, newx=x, method='fs')## Generate a trivial dataset, X has mean 0 and norm 1, y has mean 0 set.seed(11) n = 20 p = 5 x = matrix(rnorm(n*p), nrow=n, ncol=p) x = scale(x, center = colMeans(x)) x = scale(x, scale = sqrt(colSums(x^2))) beta = c(1, 1, 0, 0, 0) y = x%*%beta + scale(rnorm(20, sd=0.01), center = TRUE, scale = FALSE) ## Perform 10-fold CV without replication boss_cv_result = cv.boss(x, y) ## Get the coefficient vector of BOSS that gives minimum CV OSS score (S3 method for cv.boss) beta_boss_cv = coef(boss_cv_result) # the above is equivalent to boss_result = boss_cv_result$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')
This function returns the prediction(s) given new observation(s), for BOSS, where the optimal coefficient vector is chosen via certain selection rule.
## S3 method for class 'boss' predict(object, newx, ...)## S3 method for class 'boss' predict(object, newx, ...)
object |
The boss object, returned from calling 'boss' function. |
newx |
A new data entry or several entries. It can be a vector, or a matrix with
|
... |
Extra arguments to be plugged into |
The function basically calculates , where coef
is a coefficient vector chosen by a selection rule. See more details about the default
and available choices of the selection rule in the description of coef.boss.
The prediction(s) for BOSS.
## 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(n, sd=0.01), center = TRUE, scale = FALSE) ## Fit the model boss_result = boss(x, y) ## Get the coefficient vector selected by AICc-hdf (S3 method for boss) beta_boss_aicc = coef(boss_result) # the above is equivalent to the following beta_boss_aicc = boss_result$beta_boss[, which.min(boss_result$IC_boss$aicc), drop=FALSE] ## Get the fitted values of BOSS-AICc-hdf (S3 method for boss) mu_boss_aicc = predict(boss_result, newx=x) # the above is equivalent to the following mu_boss_aicc = cbind(1,x) %*% beta_boss_aicc ## Repeat the above process, but using Cp-hdf instead of AICc-hdf ## coefficient vector beta_boss_cp = coef(boss_result, method.boss='cp') beta_boss_cp = boss_result$beta_boss[, which.min(boss_result$IC_boss$cp), drop=FALSE] ## fitted values of BOSS-Cp-hdf mu_boss_cp = predict(boss_result, newx=x, method.boss='cp') mu_boss_cp = cbind(1,x) %*% beta_boss_cp## 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(n, sd=0.01), center = TRUE, scale = FALSE) ## Fit the model boss_result = boss(x, y) ## Get the coefficient vector selected by AICc-hdf (S3 method for boss) beta_boss_aicc = coef(boss_result) # the above is equivalent to the following beta_boss_aicc = boss_result$beta_boss[, which.min(boss_result$IC_boss$aicc), drop=FALSE] ## Get the fitted values of BOSS-AICc-hdf (S3 method for boss) mu_boss_aicc = predict(boss_result, newx=x) # the above is equivalent to the following mu_boss_aicc = cbind(1,x) %*% beta_boss_aicc ## Repeat the above process, but using Cp-hdf instead of AICc-hdf ## coefficient vector beta_boss_cp = coef(boss_result, method.boss='cp') beta_boss_cp = boss_result$beta_boss[, which.min(boss_result$IC_boss$cp), drop=FALSE] ## fitted values of BOSS-Cp-hdf mu_boss_cp = predict(boss_result, newx=x, method.boss='cp') mu_boss_cp = cbind(1,x) %*% beta_boss_cp
This function returns the prediction(s) given new observation(s) for BOSS or FS, where the optimal coefficient vector is chosen via cross-validation.
## S3 method for class 'cv.boss' predict(object, newx, ...)## S3 method for class 'cv.boss' predict(object, newx, ...)
object |
The cv.boss object, returned from calling |
newx |
A new data entry or several entries. It can be a vector, or a matrix with
|
... |
Extra arguments to be plugged into |
The prediction for BOSS or FS.
## 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$i.min.boss, drop=FALSE] ## Get the fitted values of BOSS-CV (S3 method for cv.boss) mu_boss_cv = predict(boss_cv_result, newx=x) # the above is equivalent to mu_boss_cv = cbind(1,x) %*% beta_boss_cv ## Get the coefficient vector of FS that gives minimum CV OSS score (S3 method for cv.boss) beta_fs_cv = coef(boss_cv_result, method='fs') ## Get the fitted values of FS-CV (S3 method for cv.boss) mu_fs_cv = predict(boss_cv_result, newx=x, method='fs')## Generate a trivial dataset, X has mean 0 and norm 1, y has mean 0 set.seed(11) n = 20 p = 5 x = matrix(rnorm(n*p), nrow=n, ncol=p) x = scale(x, center = colMeans(x)) x = scale(x, scale = sqrt(colSums(x^2))) beta = c(1, 1, 0, 0, 0) y = x%*%beta + scale(rnorm(20, sd=0.01), center = TRUE, scale = FALSE) ## Perform 10-fold CV without replication boss_cv_result = cv.boss(x, y) ## Get the coefficient vector of BOSS that gives minimum CV OSS score (S3 method for cv.boss) beta_boss_cv = coef(boss_cv_result) # the above is equivalent to boss_result = boss_cv_result$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')