Package 'spareg' reference manual

Title:	Sparse Projected Averaged Regression
Description:	A flexible framework combining variable screening and random projection techniques for fitting ensembles of predictive generalized linear models to high-dimensional data. Designed for extensibility, the package implements key techniques as S3 classes with user-friendly constructors, enabling easy integration and development of new procedures for high-dimensional applications. For more details see Parzer et al (2024a) <doi:10.48550/arXiv.2312.00130> and Parzer et al (2024b) <doi:10.48550/arXiv.2410.00971>.
Authors:	Laura Vana-Gür [aut, cre] (ORCID: <https://orcid.org/0000-0002-9613-7604>), Roman Parzer [aut] (ORCID: <https://orcid.org/0000-0003-0893-3190>), Peter Filzmoser [aut] (ORCID: <https://orcid.org/0000-0002-8014-4682>)
Maintainer:	Laura Vana-Gür <[email protected]>
License:	GPL-3
Version:	1.1.1
Built:	2026-05-26 07:47:58 UTC
Source:	https://github.com/lauravana/spareg

Coef Method for `'spar'` Object

Description

Extracts coefficients from 'spar' bbject

Usage

## S3 method for class 'spar'
coef(
  object,
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median", "none"),
  ...
)
## S3 method for class 'spar'
coef(
  object,
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median", "none"),
  ...
)

Arguments

object

result of spar function of class 'spar'.

nummod

number of models used to form coefficients; value with minimal validation measure is used if not provided.

nu

threshold level used to form coefficients; value with minimal validation measure is used if not provided.

aggregate

character one of c("mean", "median", "none"). If set to "none" the coefficients are not aggregated over the marginal models, otherwise the coefficients are aggregated using the specified method (mean or median). Defaults to mean aggregation.

...

further arguments passed to or from other methods

Value

object of class 'coefspar' which is a list with elements

intercept intercept value
beta vector of length p of averaged coefficients
nummod number of models based on which the coefficient is computed
nu threshold based on which the coefficient is computed

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coef(spar_res)
coef(spar_res, aggregate = "median")
coef(spar_res, aggregate = "none")
coef(spar_res, nummod = 5, nu = 0)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coef(spar_res)
coef(spar_res, aggregate = "median")
coef(spar_res, aggregate = "none")
coef(spar_res, nummod = 5, nu = 0)

Coef Method for `'spar.cv'` Object

Description

Extract coefficients from 'spar.cv' object

Usage

## S3 method for class 'spar.cv'
coef(
  object,
  nummod = NULL,
  nu = NULL,
  opt_par = c("best", "1se"),
  aggregate = c("mean", "median", "none"),
  ...
)
## S3 method for class 'spar.cv'
coef(
  object,
  nummod = NULL,
  nu = NULL,
  opt_par = c("best", "1se"),
  aggregate = c("mean", "median", "none"),
  ...
)

Arguments

object

result of spar.cv function of class 'spar.cv'.

nummod

optional number of models used to form coefficients

nu

optional threshold level used to form coefficients

opt_par

one of c("1se","best"), chooses whether to select the best pair of nus and nummods according to cross-validated (CV) measure, or the sparsest solution within one sd of that optimal CV measure; ignored when nummod and nu are given

aggregate

...

further arguments passed to or from other methods

Value

List with elements

intercept intercept value
beta vector of length p of averaged coefficients
nummod number of models based on which the coefficient is computed
nu threshold based on which the coefficient is computed

Examples


example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  nummods = c(5, 10))
coef(spar_res)

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  nummods = c(5, 10))
coef(spar_res)

Constructor Function for Building `'randomprojection'` Object

Description

Creates an object class 'randomprojection' using arguments passed by user.

Usage

constructor_randomprojection(
  name,
  generate_fun,
  update_fun = NULL,
  update_rpm_w_data = NULL,
  control = list()
)
constructor_randomprojection(
  name,
  generate_fun,
  update_fun = NULL,
  update_rpm_w_data = NULL,
  control = list()
)

Arguments

name

character

generate_fun

function for generating the random projection matrix. This function should have with arguments rp, which is a 'randomprojection' object, m, the target dimension and a vector of indexes included_vector, x matrix of predictors and y matrix of predictors. Vector included_vector shows the column index of the original variables in the x matrix to be projected using the random projection. This is needed due to the fact that screening is employed pre-projection.

update_fun

function for updating the 'randomprojection' object with information from the data. This function should have arguments rp, which is a 'randomprojection' object and x (the matrix of predictors) and y (the vector of responses).

update_rpm_w_data

function for updating the random projection matrix with data. This can be used for the case where a list of random projection matrices is provided by argument RPMs. In this case, the random structure is kept fixed, but the data-dependent part gets updated with the provided data. Defaults to NULL. If not provided, the values of the provided RPMs do not change.

control

list of controls for random projection. Can include minimum and maximum dimension for the projection defaults to list(mslow = NULL, msup = NULL)

Value

a function which in turn creates an object of class 'randomprojection'

Examples

generate_cauchy <- function(rp, m, included_vector, x = NULL, y = NULL) {
  p <- length(included_vector)
  control_rcauchy <- c(rp$control[names(rp$control) %in% names(formals(rcauchy))],
    attributes(rp)[names(attributes(rp)) %in% names(formals(rcauchy))])
  control_rcauchy <-  control_rcauchy[!duplicated(names(control_rcauchy))]
vals <- do.call(function(...)
  rcauchy(m * p, ...), control_rcauchy)
 RM <- matrix(vals, nrow = m, ncol = p)
 return(RM)
}
rp_cauchy <- constructor_randomprojection("rp_cauchy",
  generate_fun = generate_cauchy)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, rp = rp_cauchy(scale = 1/400))
spar_res
generate_cauchy <- function(rp, m, included_vector, x = NULL, y = NULL) {
  p <- length(included_vector)
  control_rcauchy <- c(rp$control[names(rp$control) %in% names(formals(rcauchy))],
    attributes(rp)[names(attributes(rp)) %in% names(formals(rcauchy))])
  control_rcauchy <-  control_rcauchy[!duplicated(names(control_rcauchy))]
vals <- do.call(function(...)
  rcauchy(m * p, ...), control_rcauchy)
 RM <- matrix(vals, nrow = m, ncol = p)
 return(RM)
}
rp_cauchy <- constructor_randomprojection("rp_cauchy",
  generate_fun = generate_cauchy)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, rp = rp_cauchy(scale = 1/400))
spar_res

Constructor Function for Building `'screencoef'` Objects

Description

The created function will return a object of class 'screencoef' which constitutes of a list. The attributes of the generating object will include by default type, which can take one of two values "prob" (indicating probabilistic screening should be employed), "fixed" (indicating that the top nscreen variables should be employed).

Usage

constructor_screencoef(name, generate_fun)
constructor_screencoef(name, generate_fun)

Arguments

name

character

generate_fun

function for generating the screening coefficient. This function should have arguments and y (vector of responses – standardized for Gaussian family), x (the matrix of standardized predictors) and a 'screencoef' object.

Details

Creates an object class 'screencoef' using arguments passed by user.

Value

a function which in turn creates an object of class 'screencoef'

Examples

generate_scr_sirs <- function(y, x, object) {
  res_screen <- do.call(function(...)
    VariableScreening::screenIID(x, y, ...),
    object$control)
  coefs <- res_screen$measurement
  coefs
}
screen_sirs <- constructor_screencoef("screen_sirs",
  generate_fun = generate_scr_sirs)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_example <- spar(example_data$x, example_data$y,
  screencoef = screen_sirs(control = list(method = "SIRS")),
  rp = rp_sparse())
spar_example
generate_scr_sirs <- function(y, x, object) {
  res_screen <- do.call(function(...)
    VariableScreening::screenIID(x, y, ...),
    object$control)
  coefs <- res_screen$measurement
  coefs
}
screen_sirs <- constructor_screencoef("screen_sirs",
  generate_fun = generate_scr_sirs)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_example <- spar(example_data$x, example_data$y,
  screencoef = screen_sirs(control = list(method = "SIRS")),
  rp = rp_sparse())
spar_example

Constructor Function for Building `'sparmodel'` Object

Description

The created function will return a object of class 'sparmodel' which constitutes of a list.

Usage

constructor_sparmodel(name, model_fun, update_fun = NULL)
constructor_sparmodel(name, model_fun, update_fun = NULL)

Arguments

name

character

model_fun

function for estimating the marginal models which returns the function should have arguments and y (vector of responses – standardized for Gaussian family), z (the matrix of projected predictors) and a 'sparmodel' object.

update_fun

optional function for updating the 'sparmodel' object before the start of the algorithm.

Details

Creates an object of class 'sparmodel' using arguments passed by user.

Value

a function which in turn creates an object of class 'sparmodel'.

Examples

model_glmrob <- function(y, z, object) {
  requireNamespace("robustbase")
  fam <- object$control$family
  glmrob_res <- do.call(function(...)
    robustbase::glmrob(y ~ as.matrix(z), ...),
    object$control)
  intercept <- coef(glmrob_res)[1]
  gammas <- coef(glmrob_res)[-1]
  list(gammas = gammas, intercept = intercept)
}
spar_glmrob <- constructor_sparmodel(name = "glmrob",
  model_fun = model_glmrob)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest,
  model = spar_glmrob())
spar_res
model_glmrob <- function(y, z, object) {
  requireNamespace("robustbase")
  fam <- object$control$family
  glmrob_res <- do.call(function(...)
    robustbase::glmrob(y ~ as.matrix(z), ...),
    object$control)
  intercept <- coef(glmrob_res)[1]
  gammas <- coef(glmrob_res)[-1]
  list(gammas = gammas, intercept = intercept)
}
spar_glmrob <- constructor_sparmodel(name = "glmrob",
  model_fun = model_glmrob)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest,
  model = spar_glmrob())
spar_res

Extractor for Model Coefficients from `'coefspar'` Object

Description

Extractor for Model Coefficients from 'coefspar' Object

Usage

get_coef(x)
get_coef(x)

Arguments

x

A 'coefspar' object.

Value

A numeric vector or matrix of coefficients.

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coefs <- coef(spar_res)
get_coef(coefs)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coefs <- coef(spar_res)
get_coef(coefs)

Extractor for Model Intercept from `'coefspar'` Object

Description

Extractor for Model Intercept from 'coefspar' Object

Usage

get_intercept(x)
get_intercept(x)

Arguments

x

A 'coefspar' object.

Value

Intercept (numeric or vector).

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coefs <- coef(spar_res)
get_coef(coefs)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coefs <- coef(spar_res)
get_coef(coefs)

Extractor for (Cross-)Validation Measure from '`spar`' or '`spar.cv`' Object

Description

Extractor for (Cross-)Validation Measure from 'spar' or 'spar.cv' Object

Usage

get_measure(object)
get_measure(object)

Arguments

object

A fitted 'spar' or 'spar.cv' model

Value

data.frame containing the (cross-)validation measure for the considered threshold and number of model combinations. For 'spar' objects it contains information about the measure calculated on the validation set (or on the training sample if xval and yval are missing) and the number of active variables. For 'spar.cv' objects it contains information on the average measure obtained across folds together with the standard deviation across the folds and the average number of active variables. the nfolds of the training set.

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
get_measure(spar_res)

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
get_measure(spar_res)

Extractor of Specific Model from `'spar'` and `'spar.cv'` Object

Description

Extractor of Specific Model from 'spar' and 'spar.cv' Object

Usage

get_model(object, opt_par = c("best", "1se"))
get_model(object, opt_par = c("best", "1se"))

Arguments

object

A fitted 'spar' or 'spar.cv' model

opt_par

One of "best", "1se"

Value

A 'spar' or 'spar.cv' object where the beta and intercept elements are the ones which correspond to the best or the 1se model.

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, screencoef = screen_cor(),
  rp = rp_gaussian(), nummods=c(5, 10))
best_model <- get_model(spar_res, opt_par = "best")

spar_cv <- spar.cv(example_data$x, example_data$y,
  screencoef = screen_cor(),
  rp = rp_gaussian(), nummods = c(5, 10), nfolds = 4L)
best_model_cv <- get_model(spar_cv, opt_par = "best")
onese_model_cv <- get_model(spar_cv, opt_par = "1se")

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, screencoef = screen_cor(),
  rp = rp_gaussian(), nummods=c(5, 10))
best_model <- get_model(spar_res, opt_par = "best")

spar_cv <- spar.cv(example_data$x, example_data$y,
  screencoef = screen_cor(),
  rp = rp_gaussian(), nummods = c(5, 10), nfolds = 4L)
best_model_cv <- get_model(spar_cv, opt_par = "best")
onese_model_cv <- get_model(spar_cv, opt_par = "1se")

Plot Method for `'spar'` Object

Description

Plot values of validation measure or number of active variables over different thresholds or number of models for 'spar' object, or residuals vs fitted

Usage

## S3 method for class 'spar'
plot(
  x,
  plot_type = c("val_measure", "val_numactive", "res_vs_fitted", "coefs"),
  plot_along = c("nu", "nummod"),
  nummod = NULL,
  nu = NULL,
  xfit = NULL,
  yfit = NULL,
  prange = NULL,
  coef_order = NULL,
  digits = 2L,
  ...
)
## S3 method for class 'spar'
plot(
  x,
  plot_type = c("val_measure", "val_numactive", "res_vs_fitted", "coefs"),
  plot_along = c("nu", "nummod"),
  nummod = NULL,
  nu = NULL,
  xfit = NULL,
  yfit = NULL,
  prange = NULL,
  coef_order = NULL,
  digits = 2L,
  ...
)

Arguments

x

result of spar function of class 'spar'.

plot_type

one of c("val_measure", "val_numactive", "res_vs_fitted", "coefs").

plot_along

one of c("nu","nummod"); ignored when plot_type = "res_vs_fitted".

nummod

fixed value for number of models when plot_along = "nu" for plot_type = "val_measure" or "val_numactive"; same as for predict.spar when plot_type="res_vs_fitted".

nu

fixed value for $\nu$ when plot_along="nummod" for plot_type = "val_measure" or "val_numactive"; same as for predict.spar when plot_type="res_vs_fitted".

xfit

data used for predictions in "res_vs_fitted".

yfit

data used for predictions in "res_vs_fitted".

prange

optional vector of length 2 for "coefs"-plot to give the limits of the predictors' plot range; defaults to c(1, p).

coef_order

optional index vector of length p for plot_type = "coefs" to give the order of the predictors; defaults to 1 : p.

digits

number of significant digits to be displayed in the axis; defaults to 2L.

...

further arguments passed to or from other methods

Value

'ggplot2::ggplot' object

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest)
plot(spar_res, plot_type = "coefs", prange = c(1,400))
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest)
plot(spar_res, plot_type = "coefs", prange = c(1,400))

Plot Method for `'spar.cv'` Object

Description

Plot cross-validation measure or number of active variables over different thresholds or number of models of 'spar.cv' object, produce a residuals vs fitted plot, or a plot of the estimated coefficients in each marginal model, sorted by their absolute value.

Usage

## S3 method for class 'spar.cv'
plot(
  x,
  plot_type = c("val_measure", "val_numactive", "res_vs_fitted", "coefs"),
  plot_along = c("nu", "nummod"),
  nummod = NULL,
  nu = NULL,
  xfit = NULL,
  yfit = NULL,
  opt_par = c("best", "1se"),
  prange = NULL,
  coef_order = NULL,
  digits = 2,
  ...
)
## S3 method for class 'spar.cv'
plot(
  x,
  plot_type = c("val_measure", "val_numactive", "res_vs_fitted", "coefs"),
  plot_along = c("nu", "nummod"),
  nummod = NULL,
  nu = NULL,
  xfit = NULL,
  yfit = NULL,
  opt_par = c("best", "1se"),
  prange = NULL,
  coef_order = NULL,
  digits = 2,
  ...
)

Arguments

x

result of spar.cv function of class 'spar.cv'.

plot_type

one of c("val_measure","val_numactive","res_vs_fitted","coefs").

plot_along

one of c("nu","nummod"); ignored when plot_type="res_vs_fitted".

nummod

fixed value for nummod when plot_along="nu" for plot_type="val_measure" or "val_numactive"; same as for predict.spar.cv when plot_type="res_vs_fitted".

nu

fixed value for $\nu$ when plot_along="nummod" for plot_type="val_measure" or "val_numactive"; same as for predict.spar.cv when plot_type="res_vs_fitted".

xfit

data used for predictions in "res_vs_fitted".

yfit

data used for predictions in "res_vs_fitted".

opt_par

one of c("best","1se"), only needed for plot_type="res_vs_fitted" to set type of predictions, see predict.spar.cv.

prange

optional vector of length 2 for "coefs"-plot to give the limits of the predictors' plot range; defaults to c(1, p).

coef_order

optional index vector of length p for "coefs"-plot to give the order of the predictors; defaults to 1 : p.

digits

number of significant digits to be displayed in the axis; defaults to 2L.

...

further arguments passed to or from other methods

Value

'ggplot2::ggplot' object

Examples


example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  screencoef = screen_cor(), rp = rp_gaussian(), nummods = c(5, 10))
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest, opt_par = "1se")
plot(spar_res, "coefs", prange = c(1, 400))

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  screencoef = screen_cor(), rp = rp_gaussian(), nummods = c(5, 10))
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest, opt_par = "1se")
plot(spar_res, "coefs", prange = c(1, 400))

Predict Method for `'spar.cv'` Object

Description

Predict responses for new predictors from 'spar' object

Usage

## S3 method for class 'spar'
predict(
  object,
  xnew = NULL,
  type = c("response", "link"),
  avg_type = c("link", "response"),
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median"),
  ...
)
## S3 method for class 'spar'
predict(
  object,
  xnew = NULL,
  type = c("response", "link"),
  avg_type = c("link", "response"),
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median"),
  ...
)

Arguments

object

result of spar function of class 'spar'.

xnew

matrix of new predictor variables; must have same number of columns as x.

type

the type of required predictions; either on response level (default) or on link level

avg_type

type of averaging the marginal models; either on link (default) or on response level

nummod

number of models used to form coefficients; value with minimal validation measure is used if not provided.

nu

threshold level used to form coefficients; value with minimal validation measure is used if not provided.

aggregate

character one of c("mean", "median"); the aggregation over the ensembles is done using the specified method (mean or median). Defaults to mean aggregation.

...

further arguments passed to or from other methods

Value

Vector of predictions

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
pred <- predict(spar_res, xnew = example_data$xtest)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
pred <- predict(spar_res, xnew = example_data$xtest)

Predict Method for `'spar.cv'` Object

Description

Predict responses for new predictors from 'spar.cv' object

Usage

## S3 method for class 'spar.cv'
predict(
  object,
  xnew = NULL,
  type = c("response", "link"),
  avg_type = c("link", "response"),
  opt_par = c("best", "1se"),
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median"),
  ...
)
## S3 method for class 'spar.cv'
predict(
  object,
  xnew = NULL,
  type = c("response", "link"),
  avg_type = c("link", "response"),
  opt_par = c("best", "1se"),
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median"),
  ...
)

Arguments

object

result of spar function of class 'spar.cv'.

xnew

matrix of new predictor variables; must have same number of columns as x.

type

the type of required predictions; either on response level (default) or on link level

avg_type

type of averaging the marginal models; either on link (default) or on response level

opt_par

one of c("best","1se"), chooses whether to select the best pair of nus and nummods according to CV measure, or the sparsest solution within one sd of that optimal CV measure; ignored when nummod and nu, or coef are given

nummod

number of models used to form coefficients; value with minimal validation Meas is used if not provided.

nu

threshold level used to form coefficients; value with minimal validation Meas is used if not provided.

aggregate

character one of c("mean", "median"); the aggregation over the ensembles is done using the specified method (mean or median). Defaults to mean aggregation.

...

further arguments passed to or from other methods

Value

Vector of predictions

Examples


example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  rp = rp_gaussian(), nummods = c(5, 10))
pred <- predict(spar_res, example_data$x)

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  rp = rp_gaussian(), nummods = c(5, 10))
pred <- predict(spar_res, example_data$x)

Print Method for `'coefspar'` Object

Description

Print method showing the basic components of a 'coefspar' object.

Usage

## S3 method for class 'coefspar'
print(x, digits = 4L, show = 6L, ...)
## S3 method for class 'coefspar'
print(x, digits = 4L, show = 6L, ...)

Arguments

x

An object of class 'coefspar', typically created by a custom model function.

digits

integer digits to be printed, defaults to 4L.

show

integer number of coefficients to be shown, defaults to 6L.

...

Additional arguments passed to or from other methods (ignored here).

Value

Invisibly returns the input object x.

Examples

example_data <- simulate_spareg_data(n = 100, p = 2000, ntest = 100)
spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coef(spar_res)
coef(spar_res, aggregate = "median")
coef(spar_res, aggregate = "none")
print(coef(spar_res), show = 10L, digits = 6L)
example_data <- simulate_spareg_data(n = 100, p = 2000, ntest = 100)
spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
coef(spar_res)
coef(spar_res, aggregate = "median")
coef(spar_res, aggregate = "none")
print(coef(spar_res), show = 10L, digits = 6L)

Print Method for a `'randomprojection'` Object

Description

Print method for a 'randomprojection' object

Usage

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

Arguments

x

object of class 'randomprojection'

...

further arguments passed to or from other methods

Value

text summary

Print Method for `'screencoef'` Object

Description

Print method for a 'screencoef' object

Usage

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

Arguments

x

description

...

further arguments passed to or from other methods

Value

text summary

Summary of `'spar'` Object

Description

Print summary of 'spar' object

Usage

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

Arguments

x

result of spar function of class 'spar'.

...

further arguments passed to or from other methods

Value

text summary

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
print(spar_res)
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
print(spar_res)

Print Method for `'spar.cv'` Object

Description

Print summary of 'spar.cv' object

Usage

## S3 method for class 'spar.cv'
print(x, ...)
## S3 method for class 'spar.cv'
print(x, ...)

Arguments

x

result of spar.cv function of class 'spar.cv'.

...

further arguments passed to or from other methods

Value

text summary

Examples


example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spareg.cv(example_data$x, example_data$y, nfolds = 3L,
  screencoef = screen_cor(), rp = rp_gaussian(), nummods = c(5, 10))
print(spar_res)

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spareg.cv(example_data$x, example_data$y, nfolds = 3L,
  screencoef = screen_cor(), rp = rp_gaussian(), nummods = c(5, 10))
print(spar_res)

Sparse Embedding Matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a sparse embedding matrix as in (Clarkson and Woodruff 2013).

Usage

rp_cw(..., control = list())
rp_cw(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the random projection matrix

control

list of arguments to be used in functions generate_fun, update_fun, update_rpm_w_data

Details

The entries of the matrix are generated based on (Clarkson and Woodruff 2013). This matrix is constructed as $\Phi=BD\in \mathbb{R}^{m\times p}$ , where $B$ is a $(p\times p)$ binary matrix, where for each column $j$ an index is uniformly sampled from $\{1,\ldots,m\}$ and the corresponding entry is set to one, and $D$ is a $(p\times p)$ diagonal matrix, with entries $d_j \sim \text{Unif}(\{-1, 1\})$ . If specified as rp_cw(data = TRUE), the random elements on the diagonal are replaced by the ridge coefficients with a small penalty, as introduced in (Parzer et al. 2024).

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

References

Clarkson KL, Woodruff DP (2013). “Low Rank Approximation and Regression in Input Sparsity Time.” In Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC '13, 81–90. ISBN 9781450320290. doi:10.1145/2488608.2488620.

Parzer R, Filzmoser P, Vana-Gür L (2024). “Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models.” Technical Report 2410.00971, arXiv.org E-Print Archive. doi:10.48550/arXiv.2410.00971..

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_cw(data = TRUE))

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_cw(data = TRUE))

Gaussian Random Projection Matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a random matrix with normally distributed entries (mean 0 and standard deviation 1 by default).

Usage

rp_gaussian(..., control = list())
rp_gaussian(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the random projection matrix

control

list of arguments to be used in functions generate_fun, update_fun, update_rpm_w_data

Details

Arguments related to the random projection procedure can be passed to the rp_gaussian() function through ..., and will be saved as attributes of the 'randomprojection' object. The following attributes are relevant for spar and spar.cv:

mslow: integer giving the minimum dimension to which the predictors should be projected; defaults to $\log(p)$ .
msup: integer giving the maximum dimension to which the predictors should be projected; defaults to $n/2$ .

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_gaussian(control = list(sd = 1/sqrt(ncol(example_data$x)))))

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_gaussian(control = list(sd = 1/sqrt(ncol(example_data$x)))))

Sparse Random Projection Matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a sparse embedding matrix as in (Achlioptas 2003).

Usage

rp_sparse(..., control = list())
rp_sparse(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the random projection matrix.

control

list of arguments to be used in functions generate_fun, update_fun, update_rpm_w_data

Details

The sparse matrix used in (Achlioptas 2003) with entries equal to $\Psi_{ij} = \pm 1/\sqrt{\psi}$ with probability $\psi/2$ and zero otherwise for $\psi\in (0,1]$ . Default is psi = 1.

mslow: integer giving the minimum dimension to which the predictors should be projected; defaults to $\log(p)$ .
msup: integer giving the maximum dimension to which the predictors should be projected; defaults to $n/2$ .

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

References

Achlioptas D (2003). “Database-Friendly Random Projections: Johnson-Lindenstrauss with Binary Coins.” Journal of Computer and System Sciences, 66(4), 671-687. ISSN 0022-0000. doi:10.1016/S0022-0000(03)00025-4. Special Issue on PODS 2001.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_sparse(control = list(psi = 1/3)))

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_sparse(control = list(psi = 1/3)))

Screening Coefficient Based on Correlation

Description

Creates an object class 'screencoef' using arguments passed by user, where the screening coefficient should be computed based on the correlation coefficient of response and each predictor separately.

Usage

screen_cor(..., control = list())
screen_cor(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the 'screencoef' object

control

list of controls to be passed to the screening function

Details

Creates an object class 'screencoef' using arguments passed by user.

The function generate_fun relies on cor.

Arguments related to the screening procedure can be passed to the screen_cor() function through ..., and will be saved as attributes of the 'screencoef' object. The following attributes are relevant for spar and spar.cv:

nscreen integer giving the number of variables to be retained after screening; if not specified, defaults to $2n$.
split_data_prop, double between 0 and 1 which indicates the proportion of the data that should be used for computing the screening coefficient. The remaining data will be used for estimating the marginal models in the SPAR algorithm; if not specified, the whole data will be used for estimating the screening coefficient and the marginal models.
type character - either "prob" (indicating that probabilistic screening should be employed) or "fixed" (indicating that a fixed set of nscreen variables should be employed across the ensemble); defaults to type = "prob".
reuse_in_rp logical - indicates whether the screening coefficient should be reused at a later stage in the construction of the random projection. Defaults to FALSE.

Value

object of class 'screencoef' which is a list with elements

name (character)
control (list of controls passed as an argument)
generate_fun for generating the screening coefficient. This function should have arguments and y (vector of (standardized for Gaussian) responses), x (the matrix of standardized predictors) and a 'screencoef' object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_cor(control = list(method = "kendall")))

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_cor(control = list(method = "kendall")))

Screening Coefficient Based on glmnet Coefficients

Description

Creates an object class 'screencoef' using arguments passed by user, where the screening coefficient should be computed based on penalized coefficients.

Usage

screen_glmnet(..., control = list())
screen_glmnet(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the 'screencoef' object

control

list of controls to be passed to the screening function

Details

Creates an object class 'screencoef' using arguments passed by user.

The function generate_fun relies on glmnet.

Arguments related to the screening procedure can be passed to the screen_glmnet() function through ..., and will be saved as attributes of the 'screencoef' object. The following attributes are relevant for spar and spar.cv:

nscreen integer giving the number of variables to be retained after screening; if not specified, defaults to $2n$.
split_data_prop, double between 0 and 1 which indicates the proportion of the data that should be used for computing the screening coefficient. The remaining data will be used for estimating the marginal models in the SPAR algorithm; if not specified, the whole data will be used for estimating the screening coefficient and the marginal models.
type character - either "prob" (indicating that probabilistic screening should be employed) or "fixed" (indicating that a fixed set of nscreen variables should be employed across the ensemble); defaults to type = "prob".
reuse_in_rp logical - indicates whether the screening coefficient should be reused at a later stage in the construction of the random projection. Defaults to FALSE.

Value

object of class 'screencoef' which is a list with elements

name (character)
control (list of controls passed as an argument)
generate_fun for generating the screening coefficient. This function should have arguments and y (vector of (standardized for Gaussian) responses), x (the matrix of standardized predictors) and a 'screencoef' object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_glmnet(control = list(alpha = 0.1)))

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_glmnet(control = list(alpha = 0.1)))

Screening Coefficient Based on Marginal GLMs

Description

Creates an object class 'screencoef' using arguments passed by user, where the screening coefficient should be computed based on the marginal likelihood of the univariate GLM where the response is regressed on each predictor separately.

Usage

screen_marglik(..., control = list())
screen_marglik(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the 'screencoef' object

control

list of controls to be passed to the screening function

Details

The function generate_fun relies on glm.

Arguments related to the screening procedure can be passed to the screen_marglik() function through ..., and will be saved as attributes of the 'screencoef' object. The following attributes are relevant for spar and spar.cv:

nscreen integer giving the number of variables to be retained after screening; if not specified, defaults to $2n$.
split_data_prop, double between 0 and 1 which indicates the proportion of the data that should be used for computing the screening coefficient. The remaining data will be used for estimating the marginal models in the SPAR algorithm; if not specified, the whole data will be used for estimating the screening coefficient and the marginal models.
type character - either "prob" (indicating that probabilistic screening should be employed) or "fixed" (indicating that a fixed set of nscreen variables should be employed across the ensemble); defaults to type = "prob".
reuse_in_rp logical - indicates whether the screening coefficient should be reused at a later stage in the construction of the random projection. Defaults to FALSE.

Value

object of class 'screencoef' which is a list with elements:

name (character)
control (list of controls passed as an argument)
generate_fun for generating the screening coefficient. This function should have arguments and y (vector of (standardized for Gaussian) responses), x (the matrix of standardized predictors) and a 'screencoef' object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_marglik(nscreen = 500))

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_marglik(nscreen = 500))

Simulate Sparse Regression Data

Description

Generates synthetic data for sparse linear regression problems. Returns training and test sets along with model parameters.

Usage

simulate_spareg_data(
  n,
  p,
  ntest,
  a = min(100, p/4),
  snr = 10,
  rho = 0.5,
  mu = 1,
  beta_vals = NULL,
  seed = NULL
)
simulate_spareg_data(
  n,
  p,
  ntest,
  a = min(100, p/4),
  snr = 10,
  rho = 0.5,
  mu = 1,
  beta_vals = NULL,
  seed = NULL
)

Arguments

n

Integer. Number of training samples.

p

Integer. Number of predictors (features).

ntest

Integer. Number of test samples.

a

Integer. Number of non-zero coefficients in the true beta vector. Default is min(100, p/4).

snr

Numeric. Signal-to-noise ratio. Default is 10.

rho

Numeric between 0 and 1. Pairwise correlation coefficient among predictors. Default is 0.5. A compound symmetry correlation matrix is used. The variance of the predictors is fixed to 1.

mu

Numeric. Intercept term (mean of response). Default is 1.

beta_vals

Numeric. Possible values for non-zero coefficients in the true beta vector. Default to NULL, in which case the values -3, -2, -1, 1, 2, 3 will be used.

seed

Integer. Random seed for reproducibility. Default is NULL.

Value

A list with the following components:

x: Training design matrix (n x p).
y: Training response vector (length n).
xtest: Test design matrix (ntest x p).
ytest: Test response vector (length ntest).
mu: Intercept used in data generation.
beta: True coefficient vector (length p).
sigma2: Noise variance used in data generation. Equals beta' Sigma beta / snr.

Examples

set.seed(123)
data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
str(data)

set.seed(123)
data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
str(data)

Sparse Projected Averaged Regression

Description

Apply Sparse Projected Averaged Regression to high-dimensional data by building an ensemble of generalized linear models, where the high-dimensional predictors can be screened using a screening coefficient and then projected using data-agnostic or data-informed random projection matrices. This function performs the procedure for a given grid of thresholds $\nu$ and a grid of the number of marginal models to be employed in the ensemble. This function is also used in the cross-validated procedure spar.cv.

Usage

spar(
  x,
  y,
  family = gaussian("identity"),
  model = NULL,
  rp = NULL,
  screencoef = NULL,
  xval = NULL,
  yval = NULL,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  inds = NULL,
  RPMs = NULL,
  seed = NULL,
  ...
)

spareg(
  x,
  y,
  family = gaussian("identity"),
  model = NULL,
  rp = NULL,
  screencoef = NULL,
  xval = NULL,
  yval = NULL,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  inds = NULL,
  RPMs = NULL,
  seed = NULL,
  ...
)
spar(
  x,
  y,
  family = gaussian("identity"),
  model = NULL,
  rp = NULL,
  screencoef = NULL,
  xval = NULL,
  yval = NULL,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  inds = NULL,
  RPMs = NULL,
  seed = NULL,
  ...
)

spareg(
  x,
  y,
  family = gaussian("identity"),
  model = NULL,
  rp = NULL,
  screencoef = NULL,
  xval = NULL,
  yval = NULL,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  inds = NULL,
  RPMs = NULL,
  seed = NULL,
  ...
)

Arguments

x

n x p numeric matrix of predictor variables.

y

quantitative response vector of length n.

family

a family object used for the marginal generalized linear model, default gaussian("identity").

model

function creating a 'sparmodel' object; defaults to spar_glm() for gaussian family with identity link and to spar_glmnet() for all other family-link combinations.

rp

function creating a 'randomprojection' object. Defaults to NULL. In this case rp_cw(data = TRUE) is used.

screencoef

function creating a 'screeningcoef' object. Defaults to NULL. In this case no screening is used is used.

xval

optional matrix of predictor variables observations used for validation of threshold nu and number of models; x is used if not provided.

yval

optional response observations used for validation of threshold nu and number of models; y is used if not provided.

nnu

number of different threshold values $\nu$ to consider for thresholding; ignored when nus are given; defaults to 20.

nus

optional vector of $\nu$ 's to consider for thresholding; if not provided, nnu values ranging from 0 to the maximum absolute marginal coefficient are used.

nummods

vector of numbers of marginal models to consider for validation; defaults to c(20).

measure

loss to use for validation; defaults to "deviance" available for all families. Other options are "mse" or "mae" (between responses and predicted means, for all families), "class" (misclassification error) and "1-auc" (one minus area under the ROC curve) both just for binomial family.

avg_type

type of averaging the marginal models; either on link (default) or on response level. This is used in computing the validation measure.

parallel

assuming a parallel backend is loaded and available, a logical indicating whether the function should use it in parallelizing the estimation of the marginal models. Defaults to FALSE.

inds

optional list of index-vectors corresponding to variables kept after screening in each marginal model of length max(nummods); dimensions need to fit those of RPMs.

RPMs

optional list of projection matrices used in each marginal model of length max(nummods), diagonal elements will be overwritten with a coefficient only depending on the given x and y.

seed

integer seed to be set at the beginning of the SPAR algorithm. Default to NULL, in which case no seed is set.

...

further arguments mainly to ensure back-compatibility

Value

object of class 'spar' with elements

betas p x max(nummods) sparse matrix of class 'Matrix::dgCMatrix' containing the standardized coefficients from each marginal model
intercepts used in each marginal model
scr_coef vector of length p with coefficients used for screening the standardized predictors
inds list of index-vectors corresponding to variables kept after screening in each marginal model of length max(nummods)
RPMs list of projection matrices used in each marginal model of length max(nummods)
val_res data.frame with validation results (validation measure and number of active variables) for each element of nus and nummods
val_set logical flag, whether validation data were provided; if FALSE, training data were used for validation
family a character corresponding to family object used for the marginal generalized linear model e.g., "gaussian(identity)"
nus vector of $\nu$ 's considered for thresholding
nummods vector of numbers of marginal models considered for validation
ycenter empirical mean of initial response vector
yscale empirical standard deviation of initial response vector
xcenter p-vector of empirical means of initial predictor variables
xscale p-vector of empirical standard deviations of initial predictor variables
avg_type character, averaging type for computing the validation measure
measure character, type of validation measure used
rp an object of class "randomprojection"
screencoef an object of class "screeningcoef"
x_rows_for_fitting_marginal_models vector of row indicators from x which were used for fitting the marginal models, if screening was performed using screencoef with split_data_prop argument. Is NULL otherwise.

If a parallel backend is registered and parallel = TRUE, the foreach function is used to estimate the marginal models in parallel.

References

Parzer R, Filzmoser P, Vana-Gür L (2024). “Sparse Data-Driven Random Projection in Regression for High-Dimensional Data.” Technical Report 2312.00130, arXiv.org E-Print Archive. doi:10.48550/arXiv.2312.00130.

Examples

example_data <- simulate_spareg_data(n = 200, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
coefs <- coef(spar_res)
pred <- predict(spar_res, xnew = example_data$x)
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest)
plot(spar_res, plot_type = "coefs", prange = c(1,400))

spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
example_data <- simulate_spareg_data(n = 200, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
coefs <- coef(spar_res)
pred <- predict(spar_res, xnew = example_data$x)
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest)
plot(spar_res, plot_type = "coefs", prange = c(1,400))

spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))

GLM Marginal `'sparmodel'`

Description

Creates an object class 'sparmodel' using arguments passed by user.

Usage

spar_glm(..., control = list())
spar_glm(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the 'sparmodel' object

control

list of controls to be passed to the model function

Details

Relies on glm.

Value

object of class 'sparmodel' which is a list with elements

name (character)
control (list of controls passed as an argument)
model_fun function for estimating the model coefficients and the intercept. This function should have arguments y, vector of standardized responses, z, a matrix of projected predictors in each marginal model, and object, which is a 'sparmodel' object. Returns a list with two elements: gammas which is the vector of regression coefficients for the projected predictors and intercept which is the intercept of the model

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y,
  xval = example_data$xtest, yval = example_data$ytest,
  model = spar_glm())
example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y,
  xval = example_data$xtest, yval = example_data$ytest,
  model = spar_glm())

Penalized GLM Marginal `'sparmodel'`

Description

Creates an object class 'sparmodel' using arguments passed by user.

Usage

spar_glmnet(..., control = list())
spar_glmnet(..., control = list())

Arguments

...

includes arguments which can be passed as attributes to the 'sparmodel' object

control

list of controls to be passed to the model function

Details

Relies on glmnet.

Value

object of class 'sparmodel' which is a list with elements

name (character)
control (list of controls passed as an argument)
model_fun for generating the screening coefficient. This function should have arguments y, vector of standardized responses, z, a matrix of projected predictors in each marginal model, and object, which is a 'sparmodel' object. Returns a list with two elements: gammas which is the vector of regression coefficients for the projected predictors and intercept which is the intercept of the model.
update_fun optional function for updating the 'sparmodel' object before the start of the algorithm.

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y,
  xval = example_data$xtest, yval = example_data$ytest,
  model = spar_glmnet(alpha = 0.1))

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y,
  xval = example_data$xtest, yval = example_data$ytest,
  model = spar_glmnet(alpha = 0.1))

Sparse Projected Averaged Regression with Cross-Validation

Description

Apply Sparse Projected Averaged Regression to High-Dimensional Data, where the number of models and the threshold parameter is chosen using a cross-validation procedure.

Usage

spar.cv(
  x,
  y,
  family = gaussian("identity"),
  model = spar_glmnet(),
  rp = NULL,
  screencoef = NULL,
  nfolds = 10,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  seed = NULL,
  ...
)

spareg.cv(
  x,
  y,
  family = gaussian("identity"),
  model = spar_glmnet(),
  rp = NULL,
  screencoef = NULL,
  nfolds = 10,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  seed = NULL,
  ...
)
spar.cv(
  x,
  y,
  family = gaussian("identity"),
  model = spar_glmnet(),
  rp = NULL,
  screencoef = NULL,
  nfolds = 10,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  seed = NULL,
  ...
)

spareg.cv(
  x,
  y,
  family = gaussian("identity"),
  model = spar_glmnet(),
  rp = NULL,
  screencoef = NULL,
  nfolds = 10,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  seed = NULL,
  ...
)

Arguments

x

n x p numeric matrix of predictor variables.

y

quantitative response vector of length n.

family

a 'family' object used for the marginal generalized linear model; defaults to gaussian("identity").

model

function creating a 'sparmodel' object; defaults to spar_glm() for gaussian family with identity link and to spar_glmnet() for all other family-link combinations.

rp

function creating a 'randomprojection' object.

screencoef

function creating a 'screeningcoef' object

nfolds

number of folds to use for cross-validation; should be at least 2, defaults to 10.

nnu

number of different threshold values $\nu$ to consider for thresholding; ignored when nus is provided; defaults to 20.

nus

optional vector of $\nu$ 's to consider for thresholding; if not provided, nnu values ranging from 0 to the maximum absolute marginal coefficient are used.

nummods

vector of numbers of marginal models to consider for validation; defaults to c(20).

measure

avg_type

type of averaging the marginal models; either on link (default) or on response level. This is used in computing the validation measure.

parallel

assuming a parallel backend is loaded and available, a logical indicating whether the function should use it in parallelizing the estimation of the marginal models. Defaults to FALSE.

seed

integer seed to be set at the beginning of the SPAR algorithm. Default to NULL, in which case no seed is set.

...

further arguments mainly to ensure back-compatibility

Value

object of class 'spar.cv' with elements

betas p x max(nummods) sparse matrix of class 'Matrix::dgCMatrix' containing the standardized coefficients from each marginal model computed with the spar algorithm on the whole training data.
intercepts used in each marginal model, vector of length max(nummods) computed with the spar algorithm on the whole training data.
scr_coef p-vector of coefficients used for screening for standardized predictors
inds list of index-vectors corresponding to variables kept after screening in each marginal model of length max(nummods)
RPMs list of projection matrices used in each marginal model of length max(nummods)
val_res a data.frame with CV results for each fold and for each element of nus and nummods
nus vector of $\nu$ 's considered for thresholding
nummods vector of numbers of marginal models considered for validation
family a character corresponding to family object used for the marginal generalized linear model e.g., "gaussian(identity)"
measure character, type of validation measure used
avg_type character, averaging type for computing the validation measure
rp an object of class 'randomprojection'
screencoef an object of class 'screeningcoef'
model an object of class 'sparmodel'
ycenter empirical mean of initial response vector
yscale empirical standard deviation of initial response vector .
xcenter p-vector of empirical means of initial predictor variables
xscale p-vector of empirical standard deviations of initial predictor variables

Examples


example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  rp = rp_gaussian(), nummods = c(5, 10))
spar_res
coefs <- coef(spar_res)
pred <- predict(spar_res, example_data$x)
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest, opt_par = "1se")
plot(spar_res, "coefs", prange = c(1, 400))


spar_res <- spareg.cv(example_data$x, example_data$y,
  nummods=c(5, 10, 15, 20, 25, 30))

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  rp = rp_gaussian(), nummods = c(5, 10))
spar_res
coefs <- coef(spar_res)
pred <- predict(spar_res, example_data$x)
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest, opt_par = "1se")
plot(spar_res, "coefs", prange = c(1, 400))


spar_res <- spareg.cv(example_data$x, example_data$y,
  nummods=c(5, 10, 15, 20, 25, 30))

Summary Method for `'coefspar'` Object

Description

Provides a summary of a coefspar object.

Usage

## S3 method for class 'coefspar'
summary(object, digits = 4L, ...)
## S3 method for class 'coefspar'
summary(object, digits = 4L, ...)

Arguments

object

An object of class coefspar.

digits

integer digits to be printed, defaults to 4L.

...

Additional arguments (ignored).

Value

Invisibly returns object.

Examples

example_data <- simulate_spareg_data(n = 100, p = 2000, ntest = 100)
spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
summary(coef(spar_res))
summary(coef(spar_res, aggregate = "none"))
example_data <- simulate_spareg_data(n = 100, p = 2000, ntest = 100)
spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10))
summary(coef(spar_res))
summary(coef(spar_res, aggregate = "none"))

Package 'spareg'

Help Index

Coef Method for 'spar' Object

Description

Usage

Arguments

Value

See Also

Examples

Coef Method for 'spar.cv' Object

Description

Usage

Arguments

Value

Examples

Constructor Function for Building 'randomprojection' Object

Description

Usage

Arguments

Value

Examples

Constructor Function for Building 'screencoef' Objects

Description

Usage

Arguments

Details

Value

Examples

Constructor Function for Building 'sparmodel' Object

Description

Usage

Arguments

Details

Value

Examples

Extractor for Model Coefficients from 'coefspar' Object

Description

Usage

Arguments

Value

See Also

Examples

Extractor for Model Intercept from 'coefspar' Object

Description

Usage

Arguments

Value

Examples

Extractor for (Cross-)Validation Measure from 'spar' or 'spar.cv' Object

Description

Usage

Arguments

Value

See Also

Examples

Extractor of Specific Model from 'spar' and 'spar.cv' Object

Description

Usage

Arguments

Value

Examples

Plot Method for 'spar' Object

Description

Usage

Arguments

Value

Examples

Plot Method for 'spar.cv' Object

Description

Usage

Arguments

Value

Examples

Predict Method for 'spar.cv' Object

Description

Usage

Arguments

Value

Examples

Predict Method for 'spar.cv' Object

Coef Method for `'spar'` Object

Coef Method for `'spar.cv'` Object

Constructor Function for Building `'randomprojection'` Object

Constructor Function for Building `'screencoef'` Objects

Constructor Function for Building `'sparmodel'` Object

Extractor for Model Coefficients from `'coefspar'` Object

Extractor for Model Intercept from `'coefspar'` Object

Extractor for (Cross-)Validation Measure from '`spar`' or '`spar.cv`' Object

Extractor of Specific Model from `'spar'` and `'spar.cv'` Object

Plot Method for `'spar'` Object

Plot Method for `'spar.cv'` Object

Predict Method for `'spar.cv'` Object

Predict Method for `'spar.cv'` Object

Print Method for `'coefspar'` Object

Print Method for a `'randomprojection'` Object

Print Method for `'screencoef'` Object

Summary of `'spar'` Object

Print Method for `'spar.cv'` Object