StabilityPath: Class StabilityPath

In quadrupen: Sparse and Group Sparse Linear Models

Class StabilityPath

Description

Class of object returned by the QuadrupenFit$cross_validate() method or the cross_validate() function. Owns print() and plot() methods.

Public fields

probabilities

a Matrix object containing the estimated probabilities of selection along the path of solutions.

regParam

a list with the levels of the regularizing parameters used

subsamples

a list that contains the folds used for each subsample.

Active bindings

nvar

number of variables (without intercept)

nobs

number of observation/sample size

nonzero

variables with a non-null probability of selection along the stability path

nonzeroprob

subset of the probabilities stability path on the nonzero variables

Methods

Public methods

• StabilityPath$new()

• StabilityPath$show()

• StabilityPath$print()

• StabilityPath$selection()

• StabilityPath$plot()

• StabilityPath$clone()

---

StabilityPath$new()

Constructor for a StabilityPath object Should be called internally by an object QuadrupenFit$stability()

Usage

StabilityPath$new(probabilities, regParam, subsamples)

Arguments

probabilities

a Matrix object containing the estimated probabilities of selection along the path of solutions.

regParam

a list with the levels of the regularizing parameters used

subsamples

a list that contains the folds used for each subsample.

---

StabilityPath$show()

User friendly print method

Usage

StabilityPath$show()

---

StabilityPath$print()

User friendly print method

Usage

StabilityPath$print()

---

StabilityPath$selection()

Perform variable selection based on the stability path

Usage

StabilityPath$selection(
  sel_mode = c("rank", "PFER"),
  cutoff = 0.75,
  PFER = 2,
  nvarsel = floor(self$nobs/log(self$nvar))
)

Arguments

sel_mode

a character string, either "rank" or "PFER". In the first case, the selection is based on the rank of total probabilities by variables along the path: the first nvarsel variables are selected (see below). In the second case, the PFER control is used as described in Meinshausen and Buhlmannn's paper. Default is "rank".

cutoff

value of the cutoff probability (only relevant when sel_mode equals "PFER").

PFER

value of the per-family error rate to control (only relevant when sel_mode equals "PFER").

nvarsel

number of variables selected (only relevant when sel_mode equals "rank". Default is floor(n/log(p)).

---

StabilityPath$plot()

Produce a plot of the stability path obtained by stability selection.

Usage

StabilityPath$plot(
  xvar = "lambda",
  title = "Stability path",
  labels = rep("unknown status", self$nvar),
  sel_mode = c("rank", "PFER"),
  cutoff = 0.75,
  PFER = 2,
  nvarsel = min(self$nvar, floor(self$nobs/log(self$nvar)))
)

Arguments

xvar

variable to plot on the X-axis: either "lambda" (first penalty level) or "fraction" (fraction of the penalty level applied tune by \lambda_1). Default is "lambda".

title

title title. If none given, a somewhat appropriate title is automatically generated.

labels

an optional vector of labels for each variable in the path (e.g., 'relevant'/'irrelevant'). See examples.

sel_mode

a character string, either "rank" or "PFER". In the first case, the selection is based on the rank of total probabilities by variables along the path: the first nvarsel variables are selected (see below). In the second case, the PFER control is used as described in Meinshausen and Buhlmannn's paper. Default is "rank".

cutoff

value of the cutoff probability (only relevant when sel_mode equals "PFER").

PFER

value of the per-family error rate to control (only relevant when sel_mode equals "PFER").

nvarsel

number of variables selected (only relevant when sel_mode equals "rank". Default is floor(n/log(p)).

plot

logical; indicates if the graph should be plotted. Default is TRUE. If FALSE, only the ggplot2 object is sent back.

Returns

a list with a ggplot2 object which can be plotted via the print method, and a vector of selected variables corresponding to method of choice ("rank" or "PFER").

Examples

## Simulating multivariate Gaussian with blockwise correlation
## and piecewise constant vector of parameters
beta <- rep(c(0,1,0,-1,0), c(25,10,25,10,25))
Soo  <- matrix(0.75,25,25) ## bloc correlation between zero variables
Sww  <- matrix(0.75,10,10) ## bloc correlation between active variables
Sigma <- Matrix::bdiag(Soo,Sww,Soo,Sww,Soo) + 0.2
diag(Sigma) <- 1
n <- 100
x <- as.matrix(matrix(rnorm(95*n),n,95) %*% chol(Sigma))
y <- 10 + x %*% beta + rnorm(n,0,10)

## Build a vector of label for true nonzeros
labels <- rep("irrelevant", length(beta))
labels[beta != 0] <- c("relevant")
labels <- factor(labels, ordered=TRUE, levels=c("relevant","irrelevant"))

enet <- elastic_net(x, y, lambda2 = 10, struct = solve(Sigma), minratio = 1e-2)
stab <- stability(enet, n_subsamples = 200)

## Build the plot an recover the selected variable
plot(stab, labels=labels)

cat("\nFalse positives for the randomized Elastic-net with stability selection: ",
     sum(labels[stab$selection()] != "relevant"))
cat("\nDONE.\n")

---

StabilityPath$clone()

The objects of this class are cloneable with this method.

Usage

StabilityPath$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

## ------------------------------------------------
## Method `StabilityPath$plot()`
## ------------------------------------------------

## Not run: 
## Simulating multivariate Gaussian with blockwise correlation
## and piecewise constant vector of parameters
beta <- rep(c(0,1,0,-1,0), c(25,10,25,10,25))
Soo  <- matrix(0.75,25,25) ## bloc correlation between zero variables
Sww  <- matrix(0.75,10,10) ## bloc correlation between active variables
Sigma <- Matrix::bdiag(Soo,Sww,Soo,Sww,Soo) + 0.2
diag(Sigma) <- 1
n <- 100
x <- as.matrix(matrix(rnorm(95*n),n,95) %*% chol(Sigma))
y <- 10 + x %*% beta + rnorm(n,0,10)

## Build a vector of label for true nonzeros
labels <- rep("irrelevant", length(beta))
labels[beta != 0] <- c("relevant")
labels <- factor(labels, ordered=TRUE, levels=c("relevant","irrelevant"))

enet <- elastic_net(x, y, lambda2 = 10, struct = solve(Sigma), minratio = 1e-2)
stab <- stability(enet, n_subsamples = 200)

## Build the plot an recover the selected variable
plot(stab, labels=labels)

cat("\nFalse positives for the randomized Elastic-net with stability selection: ",
     sum(labels[stab$selection()] != "relevant"))
cat("\nDONE.\n")

## End(Not run)

quadrupen documentation built on Sept. 18, 2026, 1:06 a.m.