Title: 'SelectBoost'-Style Variable Selection for Quantile Regression
Date: 2026-04-07
Version: 0.3.1
Author: Frederic Bertrand ORCID iD [cre, aut]
Maintainer: Frederic Bertrand <frederic.bertrand@lecnam.net>
Description: A 'SelectBoost'-inspired workflow for sparse quantile regression. The package builds correlation neighborhoods, perturbs correlated predictors with a directional sampler inspired by the original 'SelectBoost' internals, refits penalized quantile regression models on the perturbed designs, and aggregates variable-selection frequencies across a path of correlation thresholds.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.3.3
Imports: graphics, movMF, quantreg, stats, utils, withr
Suggests: knitr, pkgload, rmarkdown, testthat (≥ 3.0.0)
URL: https://fbertran.github.io/SelectBoost.quantile/, https://github.com/fbertran/SelectBoost.quantile
BugReports: https://github.com/fbertran/SelectBoost.quantile/issues
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2026-04-07 10:36:30 UTC; bertran7
Repository: CRAN
Date/Publication: 2026-04-13 11:40:08 UTC

SelectBoost.quantile

Description

A small, installable sketch of a SelectBoost-style algorithm for quantile regression. The implementation mirrors the broad structure of the original SelectBoost package while keeping the perturbation step compact and easy to inspect.

Author(s)

Maintainer: Frederic Bertrand frederic.bertrand@lecnam.net (ORCID)

See Also

Useful links:

Benchmark quantile-selection methods on correlated designs

Description

benchmark_quantile_selection() runs a reproducible simulation study over a set of scenarios and compares three selectors:

Usage

benchmark_quantile_selection(
  scenarios = default_quantile_benchmark_scenarios(),
  methods = c("lasso", "lasso_tuned", "selectboost"),
  replications = 20,
  threshold = 0.55,
  selection_metric = c("hybrid", "frequency"),
  selectboost_args = list(B = 20, step_num = 0.25, screen = "auto", tune_lambda = "cv",
    lambda_rule = "one_se", lambda_inflation = 1.25, nlambda = 12, folds = 5, repeats =
    1, subsamples = 25, sample_fraction = 0.5, complementary_pairs = TRUE, max_group_size
    = 15, verbose = FALSE),
  tuned_args = list(method = "cv", rule = "one_se", lambda_inflation = 1.25, nlambda =
    12, folds = 5, repeats = 1, verbose = FALSE),
  lasso_args = list(),
  standardize = TRUE,
  eps = 1e-06,
  seed = NULL,
  verbose = interactive()
)

Arguments

scenarios

Named list of scenario specifications. Each entry is passed to simulate_quantile_data(). Use default_quantile_benchmark_scenarios() for a ready-made validation grid.

methods

Methods to benchmark. Supported values are "lasso", "lasso_tuned", and "selectboost".

replications

Number of Monte Carlo replications per scenario.

threshold

Selection-frequency threshold used when extracting the stable support from selectboost_quantile().

selection_metric

Summary score used when extracting the stable support from selectboost_quantile(). "hybrid" combines stability and fitted effect size, while "frequency" uses mean path frequency alone.

selectboost_args

Additional named arguments passed to selectboost_quantile() for the "selectboost" method.

tuned_args

Additional named arguments passed to tune_lambda_quantile() for the "lasso_tuned" method.

lasso_args

Additional named arguments passed to quantile_lasso_selector() for the "lasso" method.

standardize

Should the lasso baselines use the same standardized design as selectboost_quantile()?

eps

Numerical tolerance used to turn coefficients into selections.

seed

Optional random seed.

verbose

Should progress messages be emitted?

Details

Each row in the returned benchmark table records support recovery, false discoveries, runtime, and failure status for one scenario, replication, and method.

Value

An object of class "benchmark_quantile_selection" with raw per-replication results in results.

Examples

scenarios <- default_quantile_benchmark_scenarios(
  tau = 0.5,
  regimes = "moderate_corr"
)
bench <- benchmark_quantile_selection(
  scenarios = scenarios,
  replications = 1,
  selectboost_args = list(B = 2, step_num = 1, tune_lambda = "bic", nlambda = 3),
  tuned_args = list(method = "bic", nlambda = 3),
  verbose = FALSE,
  seed = 1
)
summary(bench)

Extract coefficients from a SelectBoost-style quantile fit

Description

Extract coefficients from a SelectBoost-style quantile fit

Usage

## S3 method for class 'selectboost_quantile'
coef(
  object,
  tau = NULL,
  c0 = min(object$c0_seq),
  threshold = NULL,
  include_intercept = TRUE,
  standardized = FALSE,
  ...
)

Arguments

object

A selectboost_quantile() fit.

tau

Optional quantile level to extract for multi-tau fits. When omitted, a named list is returned.

c0

Threshold along the perturbation path. The closest available c0 value is used when threshold is not NULL.

threshold

Optional minimum selection frequency required for inclusion. When NULL, all baseline coefficients are returned.

include_intercept

Should the intercept be included?

standardized

Should coefficients be returned on the standardized model scale instead of the original predictor scale?

...

Unused.

Value

A named numeric vector or a named list of such vectors.

Default validation scenarios for quantile-selection benchmarks

Description

default_quantile_benchmark_scenarios() returns a named list of simulation scenarios covering moderate and strong correlation, block dependence, high-dimensional designs, and misspecified noise. The output is designed to feed directly into benchmark_quantile_selection().

Usage

default_quantile_benchmark_scenarios(
  tau = c(0.25, 0.5, 0.75),
  regimes = c("moderate_corr", "high_corr", "block_corr", "high_dim", "heavy_tail",
    "heteroskedastic")
)

Arguments

tau

Quantile levels to include in the validation grid. Each regime is expanded over these values.

regimes

Character vector selecting which regimes to include.

Value

A named list of scenario specifications.

Examples

scenarios <- default_quantile_benchmark_scenarios(
  tau = c(0.25, 0.5),
  regimes = c("moderate_corr", "heavy_tail")
)
names(scenarios)

Grouping functions for SelectBoost.quantile

Description

group_neighbors() reproduces the variable-wise neighborhood construction used by the original SelectBoost::group_func_1(): each variable is paired with the predictors whose absolute correlation exceeds c0.

Usage

group_neighbors(abs_corr, c0)

group_components(abs_corr, c0)

Arguments

abs_corr

Absolute correlation matrix.

c0

Correlation threshold in ⁠[0, 1]⁠.

Details

group_components() maps each variable to the connected component induced by the thresholded absolute correlation graph. This is a coarser grouping rule that can be useful for stress-testing the perturbation stage.

Value

A list of integer vectors, one neighborhood per variable.

Plot selection-frequency paths

Description

Plot selection-frequency paths

Usage

## S3 method for class 'selectboost_quantile'
plot(x, tau = NULL, vars = NULL, ...)

Arguments

x

A selectboost_quantile() fit.

tau

Optional quantile level to plot for multi-tau fits. Defaults to the first available tau.

vars

Optional subset of variables to plot. Defaults to the six variables with the highest mean selection frequency.

...

Passed to graphics::matplot().

Value

Invisibly returns the plotted frequency matrix.

Predict from a SelectBoost-style quantile fit

Description

Predict from a SelectBoost-style quantile fit

Usage

## S3 method for class 'selectboost_quantile'
predict(
  object,
  newdata,
  tau = NULL,
  c0 = min(object$c0_seq),
  threshold = NULL,
  ...
)

Arguments

object

A selectboost_quantile() fit.

newdata

New data used for prediction. Required.

tau

Optional quantile level to predict for multi-tau fits. When omitted, predictions for all fitted tau values are returned.

c0

Threshold along the perturbation path. The closest available c0 value is used when threshold is not NULL.

threshold

Optional selection-frequency threshold used to zero-out unstable coefficients before prediction. When NULL, the full baseline fit is used.

...

Unused.

Value

A numeric vector for single-tau predictions or a matrix with one column per tau.

Sparse quantile-regression selector

Description

A thin wrapper around quantreg::rq.fit.lasso() that always includes an unpenalized intercept and returns a named coefficient vector.

Usage

quantile_lasso_selector(x, y, tau = 0.5, lambda = NULL, ...)

Arguments

x

Numeric design matrix.

y

Numeric response vector.

tau

Quantile level in ⁠(0, 1)⁠.

lambda

Optional lasso penalty. A scalar applies the same penalty to every slope, while a vector may be supplied either for the slopes alone or for the full coefficient vector including the intercept.

...

Reserved for future selector variants.

Value

A named coefficient vector.

SelectBoost-style quantile regression

Description

selectboost_quantile() adapts the core SelectBoost workflow to sparse quantile regression:

Usage

selectboost_quantile(
  x,
  y = NULL,
  tau = 0.5,
  B = 50,
  c0_seq = NULL,
  step_num = 0.1,
  group = group_neighbors,
  max_group_size = NULL,
  screen = c("auto", "none", "quantile_rank"),
  screen_size = NULL,
  lambda = NULL,
  tune_lambda = c("none", "cv", "bic"),
  lambda_rule = c("min", "one_se"),
  lambda_factors = NULL,
  lambda_inflation = 1,
  nlambda = 20,
  lambda_min_ratio = 0.05,
  folds = 5,
  repeats = 1,
  subsamples = 1,
  sample_fraction = 0.5,
  complementary_pairs = FALSE,
  selector = quantile_lasso_selector,
  standardize = TRUE,
  eps = 1e-06,
  seed = NULL,
  data = NULL,
  subset = NULL,
  na.action = stats::na.fail,
  verbose = interactive(),
  ...
)

Arguments

x

Numeric design matrix or a formula.

y

Numeric response vector when x is a matrix.

tau

Quantile level in ⁠(0, 1)⁠. Can be a vector.

B

Number of perturbation replicates for each c0 threshold.

c0_seq

Optional decreasing sequence of correlation thresholds. When NULL, it is computed from empirical correlation quantiles using step_num.

step_num

Step size used to build the default c0 path.

group

Grouping rule used to convert the absolute correlation matrix and threshold c0 into a list of neighborhoods, one per variable. Can be a function or the name of one. Functions must accept ⁠(abs_corr, c0)⁠.

max_group_size

Optional cap on the size of each correlation neighborhood. When supplied, only the strongest absolute correlations are retained within each variable's group.

screen

Screening rule applied before the SelectBoost loop. "auto" enables tau-aware rank screening when p > n, "none" disables screening, and "quantile_rank" always uses the built-in rank-score screen. Functions must accept ⁠(x, y, tau, screen_size)⁠.

screen_size

Optional number of predictors retained after screening.

lambda

Optional lasso penalty supplied to quantreg::rq.fit.lasso(). A scalar applies a common slope penalty, while a full penalty vector can also be supplied. When tau has length greater than one, lambda can also be a list with one entry per tau.

tune_lambda

One of "none", "cv", or "bic". When not "none", the package tunes a penalty profile once on the original design and reuses it for all perturbations.

lambda_rule

Selection rule used after tuning. "min" takes the best tuning score, while "one_se" applies the one-standard-error rule when tune_lambda = "cv".

lambda_factors

Optional positive multipliers applied to the default quantile-lasso penalty profile during tuning.

lambda_inflation

Optional multiplier applied after tuning to favor a stronger selection penalty.

nlambda

Number of tuning candidates when lambda_factors is NULL.

lambda_min_ratio

Smallest tuning multiplier used to generate the default tuning grid.

folds

Number of cross-validation folds when tune_lambda = "cv".

repeats

Number of repeated fold assignments when tune_lambda = "cv".

subsamples

Number of subsample draws used for stability selection. Values greater than one aggregate selection frequencies across subsamples.

sample_fraction

Fraction of observations drawn in each subsample when subsamples > 1.

complementary_pairs

Should subsamples be generated as complementary pairs?

selector

Function used to fit the sparse quantile model. It must accept ⁠(x, y, tau, lambda, ...)⁠ and return a named coefficient vector including an intercept.

standardize

Should the selector be fitted on the SelectBoost-normalized design? When TRUE, columns are centered and scaled to unit Euclidean norm before fitting, matching the original package. When FALSE, perturbations are still generated in the normalized space but mapped back to the original scale before model fitting.

eps

Numerical tolerance used to turn coefficients into selections.

seed

Optional random seed for reproducible perturbations and tuning.

data

Optional data frame used when x is a formula.

subset

Optional subset expression used with the formula interface.

na.action

Missing-data handler used with the formula interface.

verbose

Should the routine report progress?

...

Additional arguments forwarded to selector.

Details

  1. build a centered, unit-norm design as in SelectBoost::boost.normalize(),

  2. compute correlation neighborhoods along a c0 path,

  3. fit a directional distribution to each variable's sign-aligned neighborhood in the sample hyperplane,

  4. draw perturbed predictors from those fitted directional models,

  5. refit penalized quantile regression and aggregate selection frequencies.

This version keeps the public API stable while separating the internals into explicit preprocessing, grouping, directional perturbation, and tuning stages.

Value

An object of class "selectboost_quantile" with components: frequencies, baseline, baseline_standardized, c0_seq, tau, B, lambda, lambda_tuning, call, and preprocessing metadata.

Examples

sim <- simulate_quantile_data(n = 80, p = 12, active = 1:3, seed = 1)
fit <- selectboost_quantile(sim$x, sim$y, tau = 0.5, B = 8, seed = 1)
print(fit)
summary(fit, threshold = 0.6)

dat <- data.frame(y = sim$y, sim$x)
fit_formula <- selectboost_quantile(
  y ~ .,
  data = dat,
  tau = 0.5,
  B = 4,
  step_num = 0.5,
  seed = 1
)

Simulate a sparse quantile-regression problem

Description

Simulate a sparse quantile-regression problem

Usage

simulate_quantile_data(
  n = 200,
  p = 40,
  active = 1:5,
  beta = c(2, 1.5, -1.5, 1, -1),
  tau = 0.5,
  rho = 0.7,
  correlation = c("toeplitz", "block"),
  block_size = 5L,
  error = c("gaussian", "student", "laplace", "heteroskedastic"),
  error_df = 3,
  heteroskedastic_strength = 0.75,
  seed = NULL
)

Arguments

n

Number of observations.

p

Number of predictors.

active

Indices of active predictors.

beta

Coefficients for the active predictors. Recycled as needed.

tau

Quantile level whose conditional linear predictor is controlled.

rho

Toeplitz correlation parameter for the predictors.

correlation

Correlation structure. One of "toeplitz" or "block".

block_size

Block size used when correlation = "block".

error

Error distribution. One of "gaussian", "student", "laplace", or "heteroskedastic".

error_df

Degrees of freedom when error = "student".

heteroskedastic_strength

Positive scale multiplier used when error = "heteroskedastic".

seed

Optional random seed.

Value

A list containing x, y, beta, active, tau, and the simulation settings used to generate the data.

Examples

sim <- simulate_quantile_data(seed = 42)
str(sim, max.level = 1)

Summarize a quantile-selection benchmark

Description

Summarize a quantile-selection benchmark

Usage

## S3 method for class 'benchmark_quantile_selection'
summary(object, ...)

Arguments

object

A benchmark_quantile_selection() object.

...

Unused.

Value

A data frame with one row per scenario, quantile level, and method.

Summarize a SelectBoost-style quantile fit

Description

Summarize a SelectBoost-style quantile fit

Usage

## S3 method for class 'selectboost_quantile'
summary(
  object,
  threshold = 0.55,
  tau = NULL,
  enforce_monotone = TRUE,
  selection_metric = c("hybrid", "frequency"),
  ...
)

Arguments

object

A selectboost_quantile() fit.

threshold

Frequency threshold used to define the reported stable support.

tau

Optional quantile level to summarize when the fit contains multiple tau values. When omitted, a multi-summary is returned.

enforce_monotone

Should the frequency paths be post-processed into a non-increasing function of the perturbation strength?

selection_metric

Summary score used to define the stable support. "frequency" thresholds the pathwise mean selection frequency, while "hybrid" downweights frequently selected variables whose fitted baseline effect size remains weak.

...

Unused.

Value

An object of class "summary.selectboost_quantile" or "summary.selectboost_quantile_multi".

Extract selected support at a frequency threshold

Description

Extract selected support at a frequency threshold

Usage

support_selectboost_quantile(
  object,
  tau = NULL,
  c0 = min(object$c0_seq),
  threshold = 0.55,
  selection_metric = c("hybrid", "frequency"),
  include_intercept = FALSE
)

Arguments

object

A selectboost_quantile() fit.

tau

Optional quantile level to extract for multi-tau fits. When omitted, a named list is returned.

c0

Threshold along the perturbation path. The closest available c0 value is used when selection_metric = "frequency".

threshold

Minimum summary score required for inclusion.

selection_metric

Support score used to define the returned support. "hybrid" reuses the summary-level hybrid stability/effect-size score, while "frequency" applies the threshold directly to the selection frequency at the requested c0.

include_intercept

Should the intercept be included in the returned support?

Value

A character vector or a named list of character vectors.

Tune the lasso penalty for sparse quantile regression

Description

tune_lambda_quantile() tunes a penalty profile once on the original design and returns the selected penalty vector. The default grid rescales the quantreg::LassoLambdaHat() profile rather than using a single scalar, which keeps the tuning step aligned with the underlying quantile-lasso routine.

Usage

tune_lambda_quantile(
  x,
  y = NULL,
  tau = 0.5,
  method = c("cv", "bic"),
  rule = c("min", "one_se"),
  lambda_factors = NULL,
  lambda_inflation = 1,
  nlambda = 20,
  lambda_min_ratio = 0.05,
  folds = 5,
  repeats = 1,
  selector = quantile_lasso_selector,
  standardize = TRUE,
  eps = 1e-06,
  seed = NULL,
  data = NULL,
  subset = NULL,
  na.action = stats::na.fail,
  verbose = interactive(),
  ...
)

Arguments

x

Numeric design matrix or a formula.

y

Numeric response vector when x is a matrix.

tau

Quantile level in ⁠(0, 1)⁠. Can be a vector.

method

One of "cv" or "bic".

rule

Selection rule for choosing the tuned penalty from the candidate grid. "min" takes the minimizer of the tuning score, while "one_se" applies the one-standard-error rule when method = "cv".

lambda_factors

Optional positive multipliers applied to the default penalty profile.

lambda_inflation

Optional multiplier applied after tuning to enforce a stronger penalty for selection than for prediction.

nlambda

Number of tuning candidates when lambda_factors is NULL.

lambda_min_ratio

Smallest multiplier in the default grid.

folds

Number of folds when method = "cv".

repeats

Number of repeated fold assignments when method = "cv".

selector

Function used to fit the sparse quantile model.

standardize

Should tuning use the SelectBoost-normalized design?

eps

Numerical tolerance used to count active coefficients for the BIC heuristic.

seed

Optional random seed.

data

Optional data frame used when x is a formula.

subset

Optional subset expression used with the formula interface.

na.action

Missing-data handler used with the formula interface.

verbose

Should tuning report progress?

...

Additional arguments forwarded to selector.

Value

An object of class "tuned_lambda_quantile".

Examples

sim <- simulate_quantile_data(n = 60, p = 10, active = 1:3, seed = 2)
tuned <- tune_lambda_quantile(
  sim$x,
  sim$y,
  tau = 0.5,
  method = "bic",
  nlambda = 6
)
tuned$factor