SerialRegression: Stability selection in regression (internal)

In sharp: Stability-enHanced Approaches using Resampling Procedures

Stability selection in regression (internal)

Description

Runs stability selection regression models with different combinations of parameters controlling the sparsity of the underlying selection algorithm (e.g. penalty parameter for regularised models) and thresholds in selection proportions. These two parameters are jointly calibrated by maximising the stability score of the model (possibly under a constraint on the expected number of falsely stably selected features). This function uses a serial implementation and requires the grid of parameters controlling the underlying algorithm as input (for internal use only).

Usage

SerialRegression(
  xdata,
  ydata = NULL,
  Lambda,
  pi_list = seq(0.6, 0.9, by = 0.01),
  K = 100,
  tau = 0.5,
  seed = 1,
  n_cat = 3,
  family = "gaussian",
  implementation = PenalisedRegression,
  resampling = "subsampling",
  cpss = FALSE,
  PFER_method = "MB",
  PFER_thr = Inf,
  FDP_thr = Inf,
  group_x = NULL,
  group_penalisation = FALSE,
  output_data = FALSE,
  verbose = TRUE,
  ...
)

Arguments

xdata	matrix of predictors with observations as rows and variables as columns.
ydata	optional vector or matrix of outcome(s). If family is set to "binomial" or "multinomial", ydata can be a vector with character/numeric values or a factor.
Lambda	matrix of parameters controlling the level of sparsity in the underlying feature selection algorithm specified in implementation. With implementation="glmnet", Lambda contains penalty parameters.
pi_list	vector of thresholds in selection proportions. If n_cat=NULL or n_cat=2, these values must be >0 and <1. If n_cat=3, these values must be >0.5 and <1.
K	number of resampling iterations.
tau	subsample size. Only used if resampling="subsampling" and cpss=FALSE.
seed	value of the seed to initialise the random number generator and ensure reproducibility of the results (see set.seed).
n_cat	computation options for the stability score. Default is NULL to use the score based on a z test. Other possible values are 2 or 3 to use the score based on the negative log-likelihood.
family	type of regression model. This argument is defined as in glmnet. Possible values include "gaussian" (linear regression), "binomial" (logistic regression), "multinomial" (multinomial regression), and "cox" (survival analysis).
implementation	function to use for variable selection. Possible functions are: PenalisedRegression, SparsePLS, GroupPLS and SparseGroupPLS. Alternatively, a user-defined function can be provided.
resampling	resampling approach. Possible values are: "subsampling" for sampling without replacement of a proportion tau of the observations, or "bootstrap" for sampling with replacement generating a resampled dataset with as many observations as in the full sample. Alternatively, this argument can be a function to use for resampling. This function must use arguments named data and tau and return the IDs of observations to be included in the resampled dataset.
cpss	logical indicating if complementary pair stability selection should be done. For this, the algorithm is applied on two non-overlapping subsets of half of the observations. A feature is considered as selected if it is selected for both subsamples. With this method, the data is split K/2 times (K models are fitted). Only used if PFER_method="MB".
PFER_method	method used to compute the upper-bound of the expected number of False Positives (or Per Family Error Rate, PFER). If PFER_method="MB", the method proposed by Meinshausen and Bühlmann (2010) is used. If PFER_method="SS", the method proposed by Shah and Samworth (2013) under the assumption of unimodality is used.
PFER_thr	threshold in PFER for constrained calibration by error control. If PFER_thr=Inf and FDP_thr=Inf, unconstrained calibration is used (the default).
FDP_thr	threshold in the expected proportion of falsely selected features (or False Discovery Proportion) for constrained calibration by error control. If PFER_thr=Inf and FDP_thr=Inf, unconstrained calibration is used (the default).
group_x	vector encoding the grouping structure among predictors. This argument indicates the number of variables in each group. Only used for models with group penalisation (e.g. implementation=GroupPLS or implementation=SparseGroupPLS).
group_penalisation	logical indicating if a group penalisation should be considered in the stability score. The use of group_penalisation=TRUE strictly applies to group (not sparse-group) penalisation.
output_data	logical indicating if the input datasets xdata and ydata should be included in the output.
verbose	logical indicating if a loading bar and messages should be printed.
...	additional parameters passed to the functions provided in implementation or resampling.

Value

A list with:

S	a matrix of the best stability scores for different parameters controlling the level of sparsity in the underlying algorithm.
Lambda	a matrix of parameters controlling the level of sparsity in the underlying algorithm.
Q	a matrix of the average number of selected features by the underlying algorithm with different parameters controlling the level of sparsity.
Q_s	a matrix of the calibrated number of stably selected features with different parameters controlling the level of sparsity.
P	a matrix of calibrated thresholds in selection proportions for different parameters controlling the level of sparsity in the underlying algorithm.
PFER	a matrix of upper-bounds in PFER of calibrated stability selection models with different parameters controlling the level of sparsity.
FDP	a matrix of upper-bounds in FDP of calibrated stability selection models with different parameters controlling the level of sparsity.
S_2d	a matrix of stability scores obtained with different combinations of parameters. Columns correspond to different thresholds in selection proportions.
PFER_2d	a matrix of upper-bounds in FDP obtained with different combinations of parameters. Columns correspond to different thresholds in selection proportions.
FDP_2d	a matrix of upper-bounds in PFER obtained with different combinations of parameters. Columns correspond to different thresholds in selection proportions.
selprop	a matrix of selection proportions. Columns correspond to predictors from xdata.
Beta	an array of model coefficients. Columns correspond to predictors from xdata. Indices along the third dimension correspond to different resampling iterations. With multivariate outcomes, indices along the fourth dimension correspond to outcome-specific coefficients.
method	a list with type="variable_selection" and values used for arguments implementation, family, resampling, cpss and PFER_method.
params	a list with values used for arguments K, pi_list, tau, n_cat, pk, n (number of observations), PFER_thr, FDP_thr and seed. The datasets xdata and ydata are also included if output_data=TRUE.

For all matrices and arrays returned, the rows are ordered in the same way and correspond to parameter values stored in Lambda.

sharp documentation built on April 11, 2025, 5:44 p.m.