An R package, available on the CRAN. A Statistical Methodology to Select Covariates in High-Dimensional Data under Dependenc

Gégout-Petit, Anne

Muller-Gueudin, Aurélie

English

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HAL Id: hal-02363338
https://hal.archives-ouvertes.fr/hal-02363338
Submitted on 14 Nov 2019
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entific research documents, whether they are pub-
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publics ou privés.
Package ’armada’ : A Statistical Methodology to Select
Covariates in High-Dimensional Data under Dependence
Aurélie Muller-Gueudin, Anne Gégout-Petit
To cite this version:
Aurélie Muller-Gueudin, Anne Gégout-Petit. Package ’armada’ : A Statistical Methodology to Select
Covariates in High-Dimensional Data under Dependence. 2019. ￿hal-02363338￿
HAL Id: hal-02363338
https://hal.archives-ouvertes.fr/hal-02363338
Submitted on 14 Nov 2019
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Package ’armada’ : A Statistical Methodology to Select
Covariates in High-Dimensional Data under Dependence
Aurélie Muller-Gueudin, Anne Gégout-Petit
To cite this version:
Aurélie Muller-Gueudin, Anne Gégout-Petit. Package ’armada’ : A Statistical Methodology to Select
Covariates in High-Dimensional Data under Dependence. 2019. ￿hal-02363338￿
Package ‘armada’
April 4, 2019
Type Package
Title A Statistical Methodology to Select Covariates in High-Dimensional Data under Dependence
Version 0.1.0
Description Two steps variable selection procedure in a context of high-dimensional dependent data
but few observations. First step is dedicated to eliminate dependence between variables (clustering
of variables, followed by factor analysis inside each cluster).
Second step is a variable selection using by aggregation of adapted methods.
Bastien B., Chakir H., Gegout-Petit A., Muller-Gueudin A., Shi Y.
A statistical methodology to select covariates in high-dimensional data under dependence.
Application to the classification of genetic profiles associated with outcome of a non-small-cell
lung cancer treatment. 2018. <https://hal.archives-ouvertes.fr/hal-01939694>.
License GPL-3
LazyData true
RoxygenNote 6.1.1
Imports stats,
mvtnorm,
ClustOfVar,
FAMT,
graphics,
VSURF,
glmnet,
anapuce,
qvalue,
parallel,
doParallel,
impute,
ComplexHeatmap,
circlize
R topics documented:
ARMADA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
ARMADA.heatmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
ARMADA.select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
ARMADA.summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
covariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1
Auteurs : Aurélie Muller-Gueudin,  Anne Gégout-Petit
2 ARMADA
toys.data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
toys.data.multi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
toys.data.reg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
X_decor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Index 12
ARMADA Scores of all the covariates present in X, given the vector Y of the
response.
Description
Scores of all the covariates present in X, given the vector Y of the response.
Usage
ARMADA(X, Y, nclust = NULL, clusterType = c("PSOCK", "FORK"),
parallel = FALSE)
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates). X must have rownames, which are the names of the
n subjects (i.e. the user ID of the n subjects). X must have colnames, which are
the names of the p covariates.
Y the vector of the response, length n.
nclust the number of clusters in the covariates dataset X.
clusterType to precise the type of cluster of the machine. Possible choices: "PSOCK", or
"FORK" (for UNIX or MAC systems, but not for WINDOWS).
parallel = TRUE if the calculus are made in parallel (default choice is FALSE).
Value
a 3-list with: "tree" which is the dendrogram of the data X, "nclust" which is a proposition of the
number of clusters in the data X, "result" which is a data.frame with p rows and 2 columns, the first
column gives the names of the covariates, the second column is the scores of the covariates.
Examples
library(ClustOfVar)
library(impute)
library(FAMT)
library(VSURF)
library(glmnet)
library(anapuce)
library(qvalue)
set.seed(1)
p <- 40
n <- 30
indexRow <- paste0("patient",1:n)
ARMADA.heatmap 3
indexCol <- paste0("G",1:p)
X <- matrix(rnorm(p*n),ncol=p)
colnames(X) <- indexCol
rownames(X) <- indexRow
Y <- c(rep(-1,n/2), rep(1,n/2))
X[,1:4] <- X[,1:4] + matrix(rnorm(n*4, mean=2*Y, sd=1), ncol=4)
Y<-as.factor(Y)
resultat <- ARMADA(X,Y, nclust=1)
## Not run:
X<-toys.data$x
Y<-toys.data$Y
result<-ARMADA(X,Y, nclust=2)
## End(Not run)
ARMADA.heatmap Heatmap of the selected covariates.
Description
Heatmap of the selected covariates.
Usage
ARMADA.heatmap(X, Y, res.ARMADA.summary, threshold = 5)
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates). X must have rownames, which are the names of the
n subjects (i.e. the user ID of the n subjects). X must have colnames, which are
the names of the p covariates.
Y the vector of the response, length n.
res.ARMADA.summary
the result of the function ARMADA, or output of the function ARMADA.summary.
threshold an integer between 0 and 8: the selected covariates are those which have a score
greater or equal to "threshold."
Details
This function plots the heatmap of the covariates which have a score higher than some threshold
chosen by the user, with respect to the values of Y.
Value
the plot of the heatmap, and a data.frame of the selected covariables.
4 ARMADA.select
Examples
library(ClustOfVar)
library(impute)
library(FAMT)
library(VSURF)
library(glmnet)
library(anapuce)
library(qvalue)
library(ComplexHeatmap)
library(circlize)
set.seed(1)
p <- 40
n <- 30
indexRow <- paste0("patient",1:n)
indexCol <- paste0("G",1:p)
X <- matrix(rnorm(p*n),ncol=p)
colnames(X) <- indexCol
rownames(X) <- indexRow
Y <- c(rep(-1,n/2), rep(1,n/2))
X[,1:4] <- X[,1:4] + matrix(rnorm(n*4, mean=2*Y, sd=1), ncol=4)
Y<-as.factor(Y)
resultat <- ARMADA(X,Y, nclust=1)
tracer <- ARMADA.heatmap(X, Y, resultat[[3]], threshold=5)
## Not run:
X<-toys.data$x
Y<-toys.data$Y
result<-ARMADA(X,Y, nclust=2)
select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)
## End(Not run)
ARMADA.select Covariates selection via 8 selection methods
Description
Covariates selection via 8 selection methods
Usage
ARMADA.select(X, X.decorrele, Y, test, type.cor.test = NULL,
type.measure_glmnet = c("deviance", "class"),
family_glmnet = c("gaussian", "binomial", "multinomial"),
clusterType = c("PSOCK", "FORK"), parallel = c(FALSE, TRUE))
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates). X must have rownames and colnames.
X.decorrele the matrix of decorrelated covariates, dimension n*p (n is the sample size, p the
number of covariates). X.decorrele has been obtained by the function X_decor.
Y the vector of the response, length n.
ARMADA.summary 5
test the type of test to apply ("wilox.test" or "t.test" if Y is a binary variable; "kruskal.test"
or "anova" if Y is a factor with more than 2 levels; "cor.test" if Y is a continuous
variable).
type.cor.test if test="cor.test", precise the type of test (possible choices: "pearson","kendall",
"spearman"). Default value is NULL, which corresponds to "pearson".
type.measure_glmnet
argument for the lasso regression. The lasso regression is done with the function
cv.glmnet (package glmnet), and you can precise the type of data in cv.glmnet.
Possible choices for type.measure_glmnet: "deviance" (for gaussian models, lo-
gistic, regression and Cox), "class" (for binomial or multinomial regression).
family_glmnet argument for the lasso regression. The lasso regression is done with the function
glmnet. Possible choices for family_glmnet: "gaussian" (if Y is quantitative),
"binomial" (if Y is a factor with two levels), "multinomial" (if Y is a factor with
more than two levels).
clusterType to precise the type of cluster of the machine. Possible choices: "PSOCK" or
"FORK" (for UNIX or MAC systems, but not for WINDOWS).
parallel TRUE if the calculus are made in parallel.
Details
The function ARMADA.select applies 8 selection methods on the decorrelated covariates (named
X.decorrele), given the variable of interest Y. It resturns a list of 8 vectors of the selected covariates,
each vector correspond to one selection method. The methods are (in the order): Random forest
(threshold step), Random forest (interpretation step), Lasso, multiple testing with Bonferroni, mul-
tiple testing with Benjamini-Hochberg, multiple testing with qvalues, multiple testing with localfdr,
FAMT.
Value
a list with 8 vectors, called: genes_rf_thres, genes_rf_interp, genes_lasso, genes_bonferroni, genes_BH,
genes_qvalues, genes_localfdr, genes_FAMT. The 8 vectors are the selected covariates by the cor-
responding selection methods.
ARMADA.summary Scores of the covariates X
Description
Scores of the covariates X
Usage
ARMADA.summary(X, resultat.ARMADA.select)
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates). X must have colnames.
6 clustering
resultat.ARMADA.select
the output of the ARMADA.select function: a list with 8 vectors, called: genes_rf_thres,
genes_rf_interp, genes_lasso, genes_bonferroni, genes_BH, genes_qvalues, genes_localfdr,
genes_FAMT. The 8 vectors are the selected covariates by the corresponding se-
lection methods.
Details
The function ARMADA.summary gives the scores of all the covariates. The score of a variable is an
integer between 0 and 8, and represents the number of selections of this variable by the 8 selection
methods.
Value
gene_list: data.frame with p rows and 2 columns, the first column gives the names of the covariates,
the second column is the scores of the covariates.
clustering To obtain the dendrogram of the covariates contained in the
data.frame X, and a proposition for the number of clusters of covari-
ates in X.
Description
To obtain the dendrogram of the covariates contained in the data.frame X, and a proposition for the
number of clusters of covariates in X.
Usage
clustering(X, plot = TRUE)
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates).
plot if plot = TRUE" (default value): it gives the dendrogram and the plot of the
height versus the number of clusters, for the 30 first clusters.
Value
a 2-list composed by: "tree" (the dendrogram of X), and "nclust" which is a proposition of the
number of clusters. The proposed number of clusters is calculated as following: in the graph of
the decreasing height versus the number of clusters, we define variation_height = (height[1:29]-
height[2:30])/height[2:30], and our proposition is nclust=min(which(variation_height<0.05)). It is
preferable that the user chooses its own number of clusters. Warning: nclust must be not too
high. Indeed, if nclust is too high, the clusters contain a small number of covariates, and it is then
possible that all the covariates of one or several cluster(s) are included in H0. In that case, the
FAMT procedure will have a dysfunction.
covariables 7
Examples
toys.data
X<-toys.data$x
clustering(X)
covariables concatenation of the rownames of X and of the response vector Y.
Description
concatenation of the rownames of X and of the response vector Y.
Usage
covariables(X, Y)
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates). X must have rownames, which are the names of the
n subjects (i.e. the user ID of the n subjects).
Y the vector of the response, length n.
Details
internal function. Concatenation of the rownames of X (X is the matrix n*p of the covariates), and
of the response vector Y. X must have rownames, which are the names of the n subjects (i.e. the
user ID of the n subjects).
Value
a data.frame with dimension n*2: the first column gives the names of the subjects, and the second
column is Y.
Examples
X<-matrix(rnorm(50),nrow=10)
rownames(X)<-letters[1:10]
covariables(X, 1:10)
8 toys.data
toys.data Toys data
Description
toys.data is a simple simulated dataset of a binary classification problem, introduced by Weston
et.al..
Usage
toys.data
Format
An object of class list of length 2.
Details
• $Y: output variable: a factor with 2 levels "-1" and "1";
• $x A data-frame containing input variables: with 30 obs. of 50 variables.
The data-frame x is composed by 2 independant clusters, each cluster contains 25 correlated vari-
ables. It is an equiprobable two class problem, Y belongs to -1,1, with 12 true variables (6 true
variables in each cluster), the others being noise. The simulation model is defined through the con-
ditional distribution of the X^j for Y=y. In the first cluster, the X^j are simulated in the following
way:
• with probability 0.7, X^j ~N(y,2) for j=1,2,3, and X^j ~ N(0,2) for j=4,5,6 ;
• with probability 0.3, X^j ~ N(0,2) for j=1,2,3, and X^j ~ N(y(j-3),2) for j=4,5,6 ;
• the other variables are noise, X^j ~ N(0,1) for j=7,. . . ,25.
The second cluster of 25 variables is simulated in a similar way.
Source
Weston, J., Elisseff, A., Schoelkopf, B., Tipping, M. (2003), Use of the zero norm with linear
models and Kernel methods, J. Machine Learn. Res. 3, 1439-14611
Examples
library(ClustOfVar)
library(impute)
library(FAMT)
library(VSURF)
library(glmnet)
library(anapuce)
library(qvalue)
X<-toys.data$x
Y<-toys.data$Y
scoreX<-data.frame(c(rep(8,6),rep(0,19),rep(8,6),rep(0,19)))
rownames(scoreX)<-colnames(X)
select<-ARMADA.heatmap(X, Y, scoreX, threshold=1)
## Not run:
toys.data.multi 9
result<-ARMADA(X,Y, nclust=2)
select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)
## End(Not run)
toys.data.multi Toys data in multinomial case
Description
toys.data.multi is a simple simulated dataset of a multinomial classification problem.
Usage
toys.data.multi
Format
An object of class list of length 2.
Details
• $Y: output variable: a factor with 3 levels "-1", "0", and "2";
• $x A data-frame containing input variables: with 60 obs. of 50 variables.
The data-frame x is composed by 2 independant clusters, each cluster contains 25 correlated vari-
ables. It is an equiprobable three class problem, Y belongs to -1,0,1. There is only 6 true variables,
that are in the first cluster, the others being noise. The simulation model is defined through the con-
ditional distribution of the X^j for Y=y. In the first cluster, the X^j are simulated in the following
way:
• X^j ~ N(2*y,2) for j=1,2,3,4,5,6;
• the other variables are noise, X^j ~ N(0,1) for j=7,. . . ,25.
The second cluster of 25 variables contains only noise variables.
Examples
library(ClustOfVar)
library(impute)
library(FAMT)
library(VSURF)
library(glmnet)
library(anapuce)
library(qvalue)
X<-toys.data.multi$x
Y<-toys.data.multi$Y
scoreX<-data.frame(c(rep(8,6),rep(0,44)))
rownames(scoreX)<-colnames(X)
select<-ARMADA.heatmap(X, Y, scoreX, threshold=1)
## Not run:
result<-ARMADA(X,Y, nclust=2)
select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)
## End(Not run)
10 toys.data.reg
toys.data.reg Toys data in regression case
Description
toys.data.reg is a simple simulated dataset of a regression problem.
Usage
toys.data.reg
Format
An object of class list of length 2.
Details
• $Y: output variable;
• $x A data-frame containing input variables: with 30 obs. of 50 variables.
The data-frame x is composed by 2 independant clusters, each cluster contains 25 correlated vari-
ables. There is only 5 true variables, that are in the first cluster : Y =50*(x[,1]+x[,2]+x[,3]+x[,4]+x[,5]).
The other variables are noise.
Examples
library(ClustOfVar)
library(impute)
library(FAMT)
library(VSURF)
library(glmnet)
library(anapuce)
library(qvalue)
X<-toys.data.reg$x
Y<-toys.data.reg$Y
scoreX<-data.frame(c(rep(8,5),rep(0,45)))
rownames(scoreX)<-colnames(X)
select<-ARMADA.heatmap(X, Y, scoreX, threshold=1)
## Not run:
result<-ARMADA(X,Y, nclust=2)
select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)
## End(Not run)
X_decor 11
X_decor Decorrelation of a matrix X, given a response variable Y.
Description
Decorrelation of a matrix X, given a response variable Y.
Usage
X_decor(X, Y, tree = NULL, nclust = 1, maxnbfactors = 10)
Arguments
X the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, p
the number of covariates). X must have colnames and rownames.
Y the vector of the response, length n.
tree the dendrogram of the covariates (object obtained before by the function clus-
tering). By default, tree=NULL.
nclust integer, the number of clusters in the covariates (1 by default).
maxnbfactors integer, the maximum number of factors in the clusters. By default: maxnbfac-
tors=10.
Details
The function X_decor applies the factor analysis method FAMT in the different clusters of variables.
The clusters must have been defined before (with the function "clustering").
Value
a matrix X.decorrele, with the same dimension, same rownames and same colnames than X.
Examples
toys.data
X<-toys.data$x
Y<-toys.data$Y
Tree <- clustering(X,plot=FALSE)
nclust <- Tree[[2]]
tree <- Tree[[1]]
library(ClustOfVar)
library(FAMT)
X.deco<- X_decor(X, Y, tree, nclust, maxnbfactors=10)
Index
∗Topic datasets
toys.data, 8
toys.data.multi, 9
toys.data.reg, 10
ARMADA, 2
ARMADA.heatmap, 3
ARMADA.select, 4
ARMADA.summary, 5
clustering, 6
covariables, 7
toys.data, 8
toys.data.multi, 9
toys.data.reg, 10
X_decor, 11
12


Package 'armada' : A Statistical Methodology to Select Covariates in High-Dimensional Data under Dependence

INRIA a CCSD electronic archive server

HAL Id: hal-02363338https://hal.archives-ouvertes.fr/hal-02363338Submitted on 14 Nov 2019HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Package ’armada’ : A Statistical Methodology to SelectCovariates in High-Dimensional Data under DependenceAurélie Muller-Gueudin, Anne Gégout-PetitTo cite this version:Aurélie Muller-Gueudin, Anne Gégout-Petit. Package ’armada’ : A Statistical Methodology to SelectCovariates in High-Dimensional Data under Dependence. 2019. ￿hal-02363338￿HAL Id: hal-02363338https://hal.archives-ouvertes.fr/hal-02363338Submitted on 14 Nov 2019HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Package ’armada’ : A Statistical Methodology to SelectCovariates in High-Dimensional Data under DependenceAurélie Muller-Gueudin, Anne Gégout-PetitTo cite this version:Aurélie Muller-Gueudin, Anne Gégout-Petit. Package ’armada’ : A Statistical Methodology to SelectCovariates in High-Dimensional Data under Dependence. 2019. ￿hal-02363338￿Package ‘armada’April 4, 2019Type PackageTitle A Statistical Methodology to Select Covariates in High-Dimensional Data under DependenceVersion 0.1.0Description Two steps variable selection procedure in a context of high-dimensional dependent databut few observations. First step is dedicated to eliminate dependence between variables (clusteringof variables, followed by factor analysis inside each cluster).Second step is a variable selection using by aggregation of adapted methods.Bastien B., Chakir H., Gegout-Petit A., Muller-Gueudin A., Shi Y.A statistical methodology to select covariates in high-dimensional data under dependence.Application to the classification of genetic profiles associated with outcome of a non-small-celllung cancer treatment. 2018. <https://hal.archives-ouvertes.fr/hal-01939694>.License GPL-3LazyData trueRoxygenNote 6.1.1Imports stats,mvtnorm,ClustOfVar,FAMT,graphics,VSURF,glmnet,anapuce,qvalue,parallel,doParallel,impute,ComplexHeatmap,circlizeR topics documented:ARMADA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2ARMADA.heatmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3ARMADA.select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4ARMADA.summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6covariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Auteurs : Aurélie Muller-Gueudin,  Anne Gégout-Petit2 ARMADAtoys.data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8toys.data.multi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9toys.data.reg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10X_decor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Index 12ARMADA Scores of all the covariates present in X, given the vector Y of theresponse.DescriptionScores of all the covariates present in X, given the vector Y of the response.UsageARMADA(X, Y, nclust = NULL, clusterType = c("PSOCK", "FORK"),parallel = FALSE)ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates). X must have rownames, which are the names of then subjects (i.e. the user ID of the n subjects). X must have colnames, which arethe names of the p covariates.Y the vector of the response, length n.nclust the number of clusters in the covariates dataset X.clusterType to precise the type of cluster of the machine. Possible choices: "PSOCK", or"FORK" (for UNIX or MAC systems, but not for WINDOWS).parallel = TRUE if the calculus are made in parallel (default choice is FALSE).Valuea 3-list with: "tree" which is the dendrogram of the data X, "nclust" which is a proposition of thenumber of clusters in the data X, "result" which is a data.frame with p rows and 2 columns, the firstcolumn gives the names of the covariates, the second column is the scores of the covariates.Exampleslibrary(ClustOfVar)library(impute)library(FAMT)library(VSURF)library(glmnet)library(anapuce)library(qvalue)set.seed(1)p <- 40n <- 30indexRow <- paste0("patient",1:n)ARMADA.heatmap 3indexCol <- paste0("G",1:p)X <- matrix(rnorm(p*n),ncol=p)colnames(X) <- indexColrownames(X) <- indexRowY <- c(rep(-1,n/2), rep(1,n/2))X[,1:4] <- X[,1:4] + matrix(rnorm(n*4, mean=2*Y, sd=1), ncol=4)Y<-as.factor(Y)resultat <- ARMADA(X,Y, nclust=1)## Not run:X<-toys.data$xY<-toys.data$Yresult<-ARMADA(X,Y, nclust=2)## End(Not run)ARMADA.heatmap Heatmap of the selected covariates.DescriptionHeatmap of the selected covariates.UsageARMADA.heatmap(X, Y, res.ARMADA.summary, threshold = 5)ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates). X must have rownames, which are the names of then subjects (i.e. the user ID of the n subjects). X must have colnames, which arethe names of the p covariates.Y the vector of the response, length n.res.ARMADA.summarythe result of the function ARMADA, or output of the function ARMADA.summary.threshold an integer between 0 and 8: the selected covariates are those which have a scoregreater or equal to "threshold."DetailsThis function plots the heatmap of the covariates which have a score higher than some thresholdchosen by the user, with respect to the values of Y.Valuethe plot of the heatmap, and a data.frame of the selected covariables.4 ARMADA.selectExampleslibrary(ClustOfVar)library(impute)library(FAMT)library(VSURF)library(glmnet)library(anapuce)library(qvalue)library(ComplexHeatmap)library(circlize)set.seed(1)p <- 40n <- 30indexRow <- paste0("patient",1:n)indexCol <- paste0("G",1:p)X <- matrix(rnorm(p*n),ncol=p)colnames(X) <- indexColrownames(X) <- indexRowY <- c(rep(-1,n/2), rep(1,n/2))X[,1:4] <- X[,1:4] + matrix(rnorm(n*4, mean=2*Y, sd=1), ncol=4)Y<-as.factor(Y)resultat <- ARMADA(X,Y, nclust=1)tracer <- ARMADA.heatmap(X, Y, resultat[[3]], threshold=5)## Not run:X<-toys.data$xY<-toys.data$Yresult<-ARMADA(X,Y, nclust=2)select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)## End(Not run)ARMADA.select Covariates selection via 8 selection methodsDescriptionCovariates selection via 8 selection methodsUsageARMADA.select(X, X.decorrele, Y, test, type.cor.test = NULL,type.measure_glmnet = c("deviance", "class"),family_glmnet = c("gaussian", "binomial", "multinomial"),clusterType = c("PSOCK", "FORK"), parallel = c(FALSE, TRUE))ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates). X must have rownames and colnames.X.decorrele the matrix of decorrelated covariates, dimension n*p (n is the sample size, p thenumber of covariates). X.decorrele has been obtained by the function X_decor.Y the vector of the response, length n.ARMADA.summary 5test the type of test to apply ("wilox.test" or "t.test" if Y is a binary variable; "kruskal.test"or "anova" if Y is a factor with more than 2 levels; "cor.test" if Y is a continuousvariable).type.cor.test if test="cor.test", precise the type of test (possible choices: "pearson","kendall","spearman"). Default value is NULL, which corresponds to "pearson".type.measure_glmnetargument for the lasso regression. The lasso regression is done with the functioncv.glmnet (package glmnet), and you can precise the type of data in cv.glmnet.Possible choices for type.measure_glmnet: "deviance" (for gaussian models, lo-gistic, regression and Cox), "class" (for binomial or multinomial regression).family_glmnet argument for the lasso regression. The lasso regression is done with the functionglmnet. Possible choices for family_glmnet: "gaussian" (if Y is quantitative),"binomial" (if Y is a factor with two levels), "multinomial" (if Y is a factor withmore than two levels).clusterType to precise the type of cluster of the machine. Possible choices: "PSOCK" or"FORK" (for UNIX or MAC systems, but not for WINDOWS).parallel TRUE if the calculus are made in parallel.DetailsThe function ARMADA.select applies 8 selection methods on the decorrelated covariates (namedX.decorrele), given the variable of interest Y. It resturns a list of 8 vectors of the selected covariates,each vector correspond to one selection method. The methods are (in the order): Random forest(threshold step), Random forest (interpretation step), Lasso, multiple testing with Bonferroni, mul-tiple testing with Benjamini-Hochberg, multiple testing with qvalues, multiple testing with localfdr,FAMT.Valuea list with 8 vectors, called: genes_rf_thres, genes_rf_interp, genes_lasso, genes_bonferroni, genes_BH,genes_qvalues, genes_localfdr, genes_FAMT. The 8 vectors are the selected covariates by the cor-responding selection methods.ARMADA.summary Scores of the covariates XDescriptionScores of the covariates XUsageARMADA.summary(X, resultat.ARMADA.select)ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates). X must have colnames.6 clusteringresultat.ARMADA.selectthe output of the ARMADA.select function: a list with 8 vectors, called: genes_rf_thres,genes_rf_interp, genes_lasso, genes_bonferroni, genes_BH, genes_qvalues, genes_localfdr,genes_FAMT. The 8 vectors are the selected covariates by the corresponding se-lection methods.DetailsThe function ARMADA.summary gives the scores of all the covariates. The score of a variable is aninteger between 0 and 8, and represents the number of selections of this variable by the 8 selectionmethods.Valuegene_list: data.frame with p rows and 2 columns, the first column gives the names of the covariates,the second column is the scores of the covariates.clustering To obtain the dendrogram of the covariates contained in thedata.frame X, and a proposition for the number of clusters of covari-ates in X.DescriptionTo obtain the dendrogram of the covariates contained in the data.frame X, and a proposition for thenumber of clusters of covariates in X.Usageclustering(X, plot = TRUE)ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates).plot if plot = TRUE" (default value): it gives the dendrogram and the plot of theheight versus the number of clusters, for the 30 first clusters.Valuea 2-list composed by: "tree" (the dendrogram of X), and "nclust" which is a proposition of thenumber of clusters. The proposed number of clusters is calculated as following: in the graph ofthe decreasing height versus the number of clusters, we define variation_height = (height[1:29]-height[2:30])/height[2:30], and our proposition is nclust=min(which(variation_height<0.05)). It ispreferable that the user chooses its own number of clusters. Warning: nclust must be not toohigh. Indeed, if nclust is too high, the clusters contain a small number of covariates, and it is thenpossible that all the covariates of one or several cluster(s) are included in H0. In that case, theFAMT procedure will have a dysfunction.covariables 7Examplestoys.dataX<-toys.data$xclustering(X)covariables concatenation of the rownames of X and of the response vector Y.Descriptionconcatenation of the rownames of X and of the response vector Y.Usagecovariables(X, Y)ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates). X must have rownames, which are the names of then subjects (i.e. the user ID of the n subjects).Y the vector of the response, length n.Detailsinternal function. Concatenation of the rownames of X (X is the matrix n*p of the covariates), andof the response vector Y. X must have rownames, which are the names of the n subjects (i.e. theuser ID of the n subjects).Valuea data.frame with dimension n*2: the first column gives the names of the subjects, and the secondcolumn is Y.ExamplesX<-matrix(rnorm(50),nrow=10)rownames(X)<-letters[1:10]covariables(X, 1:10)8 toys.datatoys.data Toys dataDescriptiontoys.data is a simple simulated dataset of a binary classification problem, introduced by Westonet.al..Usagetoys.dataFormatAn object of class list of length 2.Details• $Y: output variable: a factor with 2 levels "-1" and "1";• $x A data-frame containing input variables: with 30 obs. of 50 variables.The data-frame x is composed by 2 independant clusters, each cluster contains 25 correlated vari-ables. It is an equiprobable two class problem, Y belongs to -1,1, with 12 true variables (6 truevariables in each cluster), the others being noise. The simulation model is defined through the con-ditional distribution of the X^j for Y=y. In the first cluster, the X^j are simulated in the followingway:• with probability 0.7, X^j ~N(y,2) for j=1,2,3, and X^j ~ N(0,2) for j=4,5,6 ;• with probability 0.3, X^j ~ N(0,2) for j=1,2,3, and X^j ~ N(y(j-3),2) for j=4,5,6 ;• the other variables are noise, X^j ~ N(0,1) for j=7,. . . ,25.The second cluster of 25 variables is simulated in a similar way.SourceWeston, J., Elisseff, A., Schoelkopf, B., Tipping, M. (2003), Use of the zero norm with linearmodels and Kernel methods, J. Machine Learn. Res. 3, 1439-14611Exampleslibrary(ClustOfVar)library(impute)library(FAMT)library(VSURF)library(glmnet)library(anapuce)library(qvalue)X<-toys.data$xY<-toys.data$YscoreX<-data.frame(c(rep(8,6),rep(0,19),rep(8,6),rep(0,19)))rownames(scoreX)<-colnames(X)select<-ARMADA.heatmap(X, Y, scoreX, threshold=1)## Not run:toys.data.multi 9result<-ARMADA(X,Y, nclust=2)select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)## End(Not run)toys.data.multi Toys data in multinomial caseDescriptiontoys.data.multi is a simple simulated dataset of a multinomial classification problem.Usagetoys.data.multiFormatAn object of class list of length 2.Details• $Y: output variable: a factor with 3 levels "-1", "0", and "2";• $x A data-frame containing input variables: with 60 obs. of 50 variables.The data-frame x is composed by 2 independant clusters, each cluster contains 25 correlated vari-ables. It is an equiprobable three class problem, Y belongs to -1,0,1. There is only 6 true variables,that are in the first cluster, the others being noise. The simulation model is defined through the con-ditional distribution of the X^j for Y=y. In the first cluster, the X^j are simulated in the followingway:• X^j ~ N(2*y,2) for j=1,2,3,4,5,6;• the other variables are noise, X^j ~ N(0,1) for j=7,. . . ,25.The second cluster of 25 variables contains only noise variables.Exampleslibrary(ClustOfVar)library(impute)library(FAMT)library(VSURF)library(glmnet)library(anapuce)library(qvalue)X<-toys.data.multi$xY<-toys.data.multi$YscoreX<-data.frame(c(rep(8,6),rep(0,44)))rownames(scoreX)<-colnames(X)select<-ARMADA.heatmap(X, Y, scoreX, threshold=1)## Not run:result<-ARMADA(X,Y, nclust=2)select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)## End(Not run)10 toys.data.regtoys.data.reg Toys data in regression caseDescriptiontoys.data.reg is a simple simulated dataset of a regression problem.Usagetoys.data.regFormatAn object of class list of length 2.Details• $Y: output variable;• $x A data-frame containing input variables: with 30 obs. of 50 variables.The data-frame x is composed by 2 independant clusters, each cluster contains 25 correlated vari-ables. There is only 5 true variables, that are in the first cluster : Y =50*(x[,1]+x[,2]+x[,3]+x[,4]+x[,5]).The other variables are noise.Exampleslibrary(ClustOfVar)library(impute)library(FAMT)library(VSURF)library(glmnet)library(anapuce)library(qvalue)X<-toys.data.reg$xY<-toys.data.reg$YscoreX<-data.frame(c(rep(8,5),rep(0,45)))rownames(scoreX)<-colnames(X)select<-ARMADA.heatmap(X, Y, scoreX, threshold=1)## Not run:result<-ARMADA(X,Y, nclust=2)select<-ARMADA.heatmap(X, Y, result[[3]], threshold=5)## End(Not run)X_decor 11X_decor Decorrelation of a matrix X, given a response variable Y.DescriptionDecorrelation of a matrix X, given a response variable Y.UsageX_decor(X, Y, tree = NULL, nclust = 1, maxnbfactors = 10)ArgumentsX the matrix (or data.frame) of covariates, dimension n*p (n is the sample size, pthe number of covariates). X must have colnames and rownames.Y the vector of the response, length n.tree the dendrogram of the covariates (object obtained before by the function clus-tering). By default, tree=NULL.nclust integer, the number of clusters in the covariates (1 by default).maxnbfactors integer, the maximum number of factors in the clusters. By default: maxnbfac-tors=10.DetailsThe function X_decor applies the factor analysis method FAMT in the different clusters of variables.The clusters must have been defined before (with the function "clustering").Valuea matrix X.decorrele, with the same dimension, same rownames and same colnames than X.Examplestoys.dataX<-toys.data$xY<-toys.data$YTree <- clustering(X,plot=FALSE)nclust <- Tree[[2]]tree <- Tree[[1]]library(ClustOfVar)library(FAMT)X.deco<- X_decor(X, Y, tree, nclust, maxnbfactors=10)Index∗Topic datasetstoys.data, 8toys.data.multi, 9toys.data.reg, 10ARMADA, 2ARMADA.heatmap, 3ARMADA.select, 4ARMADA.summary, 5clustering, 6covariables, 7toys.data, 8toys.data.multi, 9toys.data.reg, 10X_decor, 1112

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Package 'armada' : A Statistical Methodology to Select Covariates in High-Dimensional Data under Dependence

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