# decoupdyad: Dyadic algorithm to order variables In mht: Multiple Hypothesis Testing for Variable Selection in High-Dimensional Linear Models

## Description

Dyadic algorithm using the Bolasso technique to order the variables

## Usage

 `1` ```dyadiqueordre(data,Y,m,maxordre,var_nonselect,showtest,showordre,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. `m` Number of bootstrap iteration of the Lasso. Default is `m`=100. `maxordre` Number of variables to order. Default is min(n/2-1,p/2-1). `var_nonselect` Number of variables that don't undergo feature selection. They have to be in the first columns of data. Default is 1, the selection is not performed on the intercept. `showtest` Logical value. If TRUE, show the number of regularization parameters tested to show the steps of the algorithm. Default is FALSE. `showordre` Logical value. If TRUE, shows the ordered variables at each step of the algorithm. Default is TRUE. `random` optionnal parameter. Matrix of size n*m, the m bootstrap samples are constructed from the m columns.

## Details

The algorithm starts from a large regularization parameter given by one run of Lasso. It proceeds by dyadic splitting until one variable is isolated; e.g one variable alone achieve a frequency of 1; it is the first ordered variable. And so on until `maxordre` variables are ordered.

## 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. `ordre` The order obtained on the variables. `mu` Vector of the positive regularization sequence that was used in the algorithm. `frequency` Matrix of p rows. Appearance frequency of each variable for the regularization parameter in `mu`.

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