Class

Class "QuadrupenFit"

Details

Class of object returned by any fitting function of the quadrupen package (elastic.net or bounded.reg).

This class comes with the usual predict(), fitted(), coef(), residuals(), show(), print() and deviance() S3 methods.

Specific R6 methods are available for model extraction QuadrupenFit$get_model(), cross validation QuadrupenFit$cross_validate(), stability selection QuadrupenFit$stability_path(), criteria derivation QuadrupenFit$criteria() and plotting QuadrupenFit$plot(). They come with equivalent S3 methods : cross_validate(), stability() and plot().

The "path"plot is available as soon as a fit has been performed. For the others, the appropriate post-treatments must have been made via the methods QuadrupenFit$criteria(), QuadrupenFit$cross_validate() or QuadrupenFit$stability()

All plots functions are given with the default arguments, except for labels and log_scale. If you need more control, please use the dedicated methods: QuadrupenFit$plot_path(), InformationCriteria$plot(), CrossValidation$plot(), StabilityPath$plot() or the corresponding S3 methods.

Plot method for regularization path

Active bindings

nvar: number of coefficient (without intercept)
nobs: sample size
dataModel: an object with class DataModel storing the data
major_tuning: vector of "leading" tuning parameters (either l1, linf or l2)
minor_tuning: vector of "minor" tuning parameters (either l1 or l2)
optim_monitoring: list monitoring the optimization
optim_config: list with low level options used for optimization.
fitted: Matrix of fitted values, each column corresponding to a value of lambda1.
coefficients: Matrix (class "dgCMatrix") of coefficients with respect to the original input. The number of rows corresponds the length of lambda1.
intercept: A vector containing the successive values of the (unpenalized) intercept. Equals to zero if intercept has been set to FALSE.
debias: logical, should we rely on the debias coefficient of the regularizer (if available) or not
residuals: Matrix of residuals, each column corresponding to a value of lambda1.
deviance: the model deviance
degrees_freedom: Estimated degree of freedoms for the successive lambda1.
r_squared: vector giving the coefficient of determination as a function of lambda1.
information_criteria: object with class InformationCriteria storing various information criteria (AIC, BIC, GCV, etc) for the current fit.
cross_validation: object with class CrossValidation storing output of CV job. Only available once method cross_validate has been called.
stability_path: object with class StabilityPath storing output of stability selection. Only available once method $stability has been called.

Methods

Method `new()`

Initialize a QuadrupenFit model

Usage

QuadrupenFit$new(data, intercept, regParam)

Arguments

data: a DataModel object
intercept: a logical; should an intercept be included in the mode?
regParam: a list with two elements, a vector and a scalar, for the regularization

Method `show()`

User friendly print method

Usage

QuadrupenFit$show()

Method `print()`

User friendly print method

Usage

QuadrupenFit$print()

Method `fit()`

function performing the optimization

Usage

QuadrupenFit$fit(control)

Arguments

control: list controlling the optimization process

Method `get_model()`

Model extraction

Usage

QuadrupenFit$get_model(selection, type = c("coefficients", "penalty", "index"))

Arguments

selection: either a character (model selection criteria) of a scalar (lambda value)
type: character for the desired output

Returns

either a vector of coefficients, a scalar or the model index

Method `predict()`

Predict response for new sample based on the current model

Usage

QuadrupenFit$predict(newx = NULL, selection = NULL)

Arguments

newx: matrix of new values for the regressor with which to predict. If omitted, the fitted values are used.
selection: either a character (model selection criteria) of a scalar (lambda value)

Returns

a vector of predicted value Cross-validation for Quadrupen object

Method `cross_validate()`

Function that computes K-fold cross-validated error of a quadrupen fit, possibly on a grid of lambda1, lambda2.

Usage

QuadrupenFit$cross_validate(
  K = 10,
  folds = split(sample(1:self$nobs), rep(1:K, length = self$nobs)),
  lambda2 = self$minor_tuning,
  verbose = TRUE,
  cores = max(K, detectCores() - 2)
)

Arguments

K: integer indicating the number of folds. Default is 10.
folds: list of K vectors that describes the folds to use for the cross-validation. By default, the folds are randomly sampled with the specified K. The same folds are used for each values of lambda2.
lambda2: tunes the $\ell_2$-penalty (ridge-like) of the fit. If none is provided, a vector of values is generated and a CV is performed on a grid of lambda2 and lambda1, using the same folds for each lambda2.
verbose: logical; indicates if the progression (the current lambda2 should be displayed. Default is TRUE.
cores: the number of cores to use. The default uses all the cores available.

Returns

an object with class CrossValidation is sent back and stored as a field of the original QuadrupenFit object.

Method `stability()`

Compute the stability path of a (possibly randomized) fitting procedure as introduced by Meinshausen and Buhlmann (2010).

Usage

QuadrupenFit$stability(
  n_subsamples = 50,
  subsample_size = floor(self$nobs/2),
  subsamples = replicate(n_subsamples, sample(1:self$nobs, subsample_size), simplify =
    FALSE),
  weakness = 1,
  verbose = TRUE,
  cores = detectCores() - 2
)

Arguments

n_subsamples: integer indicating the number of subsamplings used to estimate the selection probabilities. Default is 100.
subsample_size: integer indicating the size of each subsamples. Default is floor(n/2).
subsamples: list with subsamples entries with vectors describing the folds to use for the stability procedure. By default, the folds are randomly sampled with the specified n_subsamples and subsample_size argument.
weakness: Coefficient used for randomizing the weights of each features. Default is 1` for no randomization. See details below.
verbose: logical; indicates if the progression should be displayed. Default is TRUE.
cores: the number of cores to use. The default uses all the cores available.

Returns

an object with class StabilityPath is sent back and stored as a field of the original QuadrupenFit object.

Method `criteria()`

Produce a plot or send back the values of some penalized criteria accompanied with the vector(s) of parameters selected accordingly. The default behavior plots the BIC and the AIC (with respective factor $\log(n)$ and $2$) yet the user can specify any penalty.

Usage

QuadrupenFit$criteria(
  penalty = setNames(c(2, log(self$nobs), log(self$nvar), log(self$nobs) + 2 *
    log(self$nvar)), c("AIC", "BIC", "mBIC", "eBIC")),
  sigma = NULL
)

Arguments

penalty: a vector with as many penalties a desired. The default contains the penalty corresponding to the AIC and the BIC ($2$ and $\log(n)$). Setting the "names" attribute, as done in the default definition, leads to outputs which are easier to read.
sigma: scalar: an estimate of the residual variance. When available, it is plugged-in the criteria, which may be more relevant. If NULL (the default), it is estimated as usual (see details).

Returns

an object with class InformationCriteria is sent back and stored as a field of the original QuadrupenFit object.

Method `plot()`

Plot method for QuadrupenFit

Usage

QuadrupenFit$plot(
  type = c("path", "criteria", "crossval", "stability"),
  log_scale = TRUE,
  labels = NULL
)

Arguments

type: the type of plot, either "path" for regularization path; "criteria" for BIC-like information criteria ; "crossval" for cross-validation plot ; and "stability" for stability path.
log_scale: logical; indicates if a log-scale should be used when xvar="lambda". Default is TRUE.
labels: vector indicating the names associated to the plotted variables. When specified, a legend is drawn in order to identify each variable. Only relevant when the number of predictor is small. Remind that the intercept does not count. Default is NULL.

Method `plot_path()`

Produce a plot of the solution path of a QuadrupenFit object.

Usage

QuadrupenFit$plot_path(
  xvar = c("lambda", "fraction", "df"),
  log_scale = TRUE,
  title = paste(self$penalty, " path", sep = ""),
  standardize = TRUE,
  labels = NULL
)

Arguments

xvar: variable to plot on the X-axis: either "lambda" ($\ell_1$ penalty level, or $\ell_2$ for ridge and $\ell_\infty$) or "fraction" ($\ell_1$-norm of the coefficients) or df for estimated degrees of freedom. Default is set to "lambda".
log_scale: logical; indicates if a log-scale should be used when xvar="lambda". Default is TRUE.
title: the title. Default is set to the model name followed by what is on the Y-axis.
standardize: logical; standardize the coefficients before plotting (with the norm of the predictor). Default is TRUE.
labels: vector indicating the names associated to the plotted variables. When specified, a legend is drawn in order to identify each variable. Only relevant when the number of predictor is small. Remind that the intercept does not count. Default is NULL.

Returns

a ggplot2 object .

Examples

\dontrun{
## 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))
cor <- 0.75
Soo <- toeplitz(cor^(0:(25-1))) ## Toeplitz correlation for irrelevant variables
Sww  <- matrix(cor,10,10) ## bloc correlation between active variables
Sigma <- bdiag(Soo,Sww,Soo,Sww,Soo)
diag(Sigma) <- 1
n <- 50
x <- as.matrix(matrix(rnorm(95*n),n,95) %*% chol(Sigma))
y <- 10 + x %*% beta + rnorm(n,0,10)

## Plot the Lasso path
plot(lasso(x,y), title="Lasso solution path")
## Plot the Elastic-net path
plot(elastic.net(x,y), title = "Elastic-net solution path")
## Plot the Elastic-net path (fraction on X-axis, unstandardized coefficient)
plot(elastic.net(x,y, lambda2=10), standardize=FALSE, xvar="fraction")
## Plot the Bounded regression path (fraction on X-axis)
plot(bounded.reg(x,y, lambda2=10), xvar="fraction")
}

Method `clone()`

The objects of this class are cloneable with this method.

Usage

QuadrupenFit$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples


## ------------------------------------------------
## Method `QuadrupenFit$plot_path`
## ------------------------------------------------

if (FALSE) { # \dontrun{
## 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))
cor <- 0.75
Soo <- toeplitz(cor^(0:(25-1))) ## Toeplitz correlation for irrelevant variables
Sww  <- matrix(cor,10,10) ## bloc correlation between active variables
Sigma <- bdiag(Soo,Sww,Soo,Sww,Soo)
diag(Sigma) <- 1
n <- 50
x <- as.matrix(matrix(rnorm(95*n),n,95) %*% chol(Sigma))
y <- 10 + x %*% beta + rnorm(n,0,10)

## Plot the Lasso path
plot(lasso(x,y), title="Lasso solution path")
## Plot the Elastic-net path
plot(elastic.net(x,y), title = "Elastic-net solution path")
## Plot the Elastic-net path (fraction on X-axis, unstandardized coefficient)
plot(elastic.net(x,y, lambda2=10), standardize=FALSE, xvar="fraction")
## Plot the Bounded regression path (fraction on X-axis)
plot(bounded.reg(x,y, lambda2=10), xvar="fraction")
} # }

Class "QuadrupenFit"

Details

See also

Active bindings

Methods

Public methods

Method new()

Usage

Arguments

Method show()

Usage

Method print()

Usage

Method fit()

Usage

Arguments

Method get_model()

Usage

Arguments

Returns

Method predict()

Usage

Arguments

Returns

Method cross_validate()

Usage

Arguments

Returns

Method stability()

Usage

Arguments

Returns

Method criteria()

Usage

Arguments

Returns

Method plot()

Usage

Arguments

Method plot_path()

Usage

Arguments

Returns

Examples

Method clone()

Usage

Arguments

Examples

Method `new()`

Method `show()`

Method `print()`

Method `fit()`

Method `get_model()`

Method `predict()`

Method `cross_validate()`

Method `stability()`

Method `criteria()`

Method `plot()`

Method `plot_path()`

Method `clone()`