# bolasso: Bolasso: Bootstrapped Lasso In mht: Multiple Hypothesis Testing for Variable Selection in High-Dimensional Linear Models

## Description

Perform a bootstrapped Lasso on some random subsamplings of the input data

## Usage

 `1` ```bolasso(data,Y,mu,m,probaseuil,penalty.factor,random) ```

## Arguments

 `data` Input matrix of dimension n * p; each of the n rows is an observation vector of p variables. The intercept should be included in the first column as (1,...,1). If not, it is added. `Y` Response variable of length n. `mu` Positive regularization sequence to be used for the Lasso. `m` Number of bootstrap iteration of the Lasso. Default is m=100. `probaseuil` A frequency threshold for selecting the most stable variables over the `m` boostrap iteration of the Lasso. Default is 1. `penalty.factor` Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is 1 for all variables except the intercept. `random` optionnal parameter, matrix of size n*m. If `random` is provided, the `m` bootstrap samples are constructed from its m columns.

## Details

The Lasso from the `glmnet` package is performed with the regularization parameter mu over m bootstrap samples. An appearance frequency is obtained which shows the predictive power of each variable. It is calculated as the number of times a variables has been selected by the Lasso over the `m` bootstrap iteration.

## Value

A 'bolasso' object is returned for which the method `plot` is available.

 `data` A list containing: X - The scaled matrix used in the algorithm, the first column being (1,...,1). Y - the input response vector means.X - Vector of means of the input data matrix. sigma.X - Vector of variances of the input data matrix. `ind` Set of selected variables for the regularization `mu` and the threshold `probaseuil`. `frequency` Appearance frequency of each variable; number of times each variables is selected over the m bootstrap iterations.

## References

Model-consistent sparse estimation through the bootstrap; F. Bach 2009

`plot.bolasso`, `dyadiqueordre`
 ```1 2 3 4 5 6 7 8 9``` ```## Not run: x=matrix(rnorm(100*20),100,20) beta=c(rep(1,5),rep(0,15)) y=x%*%beta+rnorm(100) mod=bolasso(x,y,mu=seq(1.5,0.1,-0.1)) mod ## End(Not run) ```