Type: Package
Title: Multi-Layer Group-Lasso
Version: 1.0.0
Date: 2023-03-15
Copyright: Inria
Description: It implements a new procedure of variable selection in the context of redundancy between explanatory variables, which holds true with high dimensional data (Grimonprez et al. (2023) <doi:10.18637/jss.v106.i03>).
BugReports: https://github.com/modal-inria/MLGL/issues
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Imports: gglasso, MASS, Matrix, fastcluster, FactoMineR, parallelDist
RoxygenNote: 7.2.3
Encoding: UTF-8
NeedsCompilation: no
Packaged: 2023-03-15 10:09:58 UTC; quentin
Author: Quentin Grimonprez [aut, cre], Samuel Blanck [ctb], Alain Celisse [ths], Guillemette Marot [ths], Yi Yang [ctb], Hui Zou [ctb]
Maintainer: Quentin Grimonprez <quentingrim@yahoo.fr>
Repository: CRAN
Date/Publication: 2023-03-15 12:50:05 UTC

MLGL

Description

This package presents a method combining Hierarchical Clustering and Group-lasso. Usually, a single partition of the covariates is used in the group-lasso. Here, we provide several partitions from the hierarchical tree.

A post-treatment method based on statistical test (with FWER and FDR control) for selecting the regularization parameter and the optimal group for this value is provided. This method can be applied for the classical group-lasso and our method.

Details

The MLGL function performs the hierarchical clustering and the group-lasso. The post-treatment method can be performed with hierarchicalFWER and selFWER functions. The whole process can be run with the fullProcess function.

Author(s)

Quentin Grimonprez

References

Grimonprez Q, Blanck S, Celisse A, Marot G (2023). "MLGL: An R Package Implementing Correlated Variable Selection by Hierarchical Clustering and Group-Lasso." Journal of Statistical Software, 106(3), 1-33. doi:10.18637/jss.v106.i03.

See Also

MLGL, cv.MLGL, fullProcess, hierarchicalFWER

Examples

# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)

F-test

Description

Perform a F-test

Usage

Ftest(X, y, varToTest)

Arguments

X

design matrix of size n*p

y

response vector of length n

varToTest

vector containing the index of the column of X to test

Details

y = X * beta + epsilon

null hypothesis: beta[varToTest] = 0 alternative hypothesis: it exists an index k in varToTest such that beta[k] != 0

The test statistic is based on a full and a reduced model. full: y = X * beta[varToTest] + epsilon reduced: the null model

Value

a vector of the same length as varToTest containing the p-values of the test.

See Also

partialFtest

Hierarchical Multiple Testing procedure

Description

Apply Hierarchical Multiple Testing procedure on a MLGL object

Usage

HMT(
  res,
  X,
  y,
  control = c("FWER", "FDR"),
  alpha = 0.05,
  test = partialFtest,
  addRoot = FALSE,
  Shaffer = FALSE,
  ...
)

Arguments

res

MLGL object

X

matrix of size n*p

y

vector of size n.

control

either "FDR" or "FWER"

alpha

control level for testing procedure

test

test used in the testing procedure. Default is partialFtest

addRoot

If TRUE, add a common root containing all the groups

Shaffer

If TRUE, a Shaffer correction is performed (only if control = "FWER")

...

extra parameters for selFDR

Value

a list containing:

lambdaOpt

lambda values maximizing the number of rejects

var

A vector containing the index of selected variables for the first lambdaOpt value

group

A vector containing the values index of selected groups for the first lambdaOpt value

selectedGroups

Selected groups for the first lambdaOpt value

indLambdaOpt

indices associated with optimal lambdas

reject

Selected groups for all lambda values

alpha

Control level

test

Test used in the testing procedure

control

"FDR" or "FWER"

time

Elapsed time

hierTest

list containing the output of the testing function for each lambda. Each element can be used with the selFWER or selFDR functions.

lambda

lambda path

nGroup

Number of groups before testing

nSelectedGroup

Numer of groups after testing

See Also

hierarchicalFWER hierarchicalFDR selFWER selFDR

Examples

set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
res <- MLGL(X, y)

# perform hierarchical testing with FWER control
out <- HMT(res, X, y, alpha = 0.05)

# test a new value of alpha for a specific lambda
selFWER(out$hierTest[[60]], alpha = 0.1)

Multi-Layer Group-Lasso

Description

Run hierarchical clustering following by a group-lasso on all the different partitions.

Usage

MLGL(X, ...)

## Default S3 method:
MLGL(
  X,
  y,
  hc = NULL,
  lambda = NULL,
  weightLevel = NULL,
  weightSizeGroup = NULL,
  intercept = TRUE,
  loss = c("ls", "logit"),
  sizeMaxGroup = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'formula'
MLGL(
  formula,
  data,
  hc = NULL,
  lambda = NULL,
  weightLevel = NULL,
  weightSizeGroup = NULL,
  intercept = TRUE,
  loss = c("ls", "logit"),
  verbose = FALSE,
  ...
)

Arguments

X

matrix of size n*p

...

Others parameters for gglasso function

y

vector of size n. If loss = "logit", elements of y must be in -1,1

hc

output of hclust function. If not provided, hclust is run with ward.D2 method. User can also provide the desired method: "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid", "median".

lambda

lambda values for group lasso. If not provided, the function generates its own values of lambda

weightLevel

a vector of size p for each level of the hierarchy. A zero indicates that the level will be ignored. If not provided, use 1/(height between 2 successive levels). Only if hc is provided

weightSizeGroup

a vector of size 2*p-1 containing the weight for each group. Default is the square root of the size of each group. Only if hc is provided

intercept

should an intercept be included in the model ?

loss

a character string specifying the loss function to use, valid options are: "ls" least squares loss (regression) and "logit" logistic loss (classification)

sizeMaxGroup

maximum size of selected groups. If NULL, no restriction

verbose

print some information

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

an optional data.frame, list or environment (or object coercible by as.data.frame to a data.frame) containing the variables in the model. If not found in data, the variables are taken from environment (formula)

Value

a MLGL object containing:

lambda

lambda values

b0

intercept values for lambda

beta

A list containing the values of estimated coefficients for each values of lambda

var

A list containing the index of selected variables for each values of lambda

group

A list containing the values index of selected groups for each values of lambda

nVar

A vector containing the number of non zero coefficients for each values of lambda

nGroup

A vector containing the number of non zero groups for each values of lambda

structure

A list containing 3 vectors. var: all variables used. group: associated groups. weight: weight associated with the different groups. level: for each group, the corresponding level of the hierarchy where it appears and disappears. 3 indicates the level with a partition of 3 groups.

time

computation time

dim

dimension of X

hc

Output of hierarchical clustering

call

Code executed by user

Author(s)

Quentin Grimonprez

See Also

cv.MLGL, stability.MLGL, listToMatrix, predict.MLGL, coef.MLGL, plot.cv.MLGL

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)

Hierarchical Clustering with distance matrix computed using bootstrap replicates

Description

Hierarchical Clustering with distance matrix computed using bootstrap replicates

Usage

bootstrapHclust(X, frac = 1, B = 50, method = "ward.D2", nCore = NULL)

Arguments

X

data

frac

fraction of sample used at each replicate

B

number of replicates

method

desired method: "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid", "median".

nCore

number of cores

Value

An object of class hclust

Examples

hc <- bootstrapHclust(USArrests, nCore = 1)

Get coefficients from a MLGL object

Description

Get coefficients from a MLGL object

Usage

## S3 method for class 'MLGL'
coef(object, s = NULL, ...)

Arguments

object

MLGL object

s

values of lambda. If NULL, use values from object

...

Not used. Other arguments to predict.

Value

A matrix with estimated coefficients for given values of s.

Author(s)

Quentin Grimonprez

See Also

MLGL, predict.MLGL

Get coefficients from a cv.MLGL object

Description

Get coefficients from a cv.MLGL object

Usage

## S3 method for class 'cv.MLGL'
coef(object, s = c("lambda.1se", "lambda.min"), ...)

Arguments

object

cv.MLGL object

s

Either "lambda.1se" or "lambda.min"

...

Not used. Other arguments to predict.

Value

A matrix with estimated coefficients for given values of s.

Author(s)

Quentin Grimonprez

See Also

cv.MLGL, predict.cv.MLGL

Compute the group size weight vector with an authorized maximal size

Description

Compute the group size weight vector with an authorized maximal size

Usage

computeGroupSizeWeight(hc, sizeMax = NULL)

Arguments

hc

output of hclust

sizeMax

maximum size of cluster to consider

Value

the weight vector

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# use 20 as the maximal number of group
hc <- hclust(dist(t(X)))
w <- computeGroupSizeWeight(hc, sizeMax = 20)
# Apply MLGL method
res <- MLGL(X, y, hc = hc, weightSizeGroup = w)

Multi-Layer Group-Lasso with cross V-fold validation

Description

V-fold cross validation for MLGL function

Usage

cv.MLGL(
  X,
  y,
  nfolds = 5,
  lambda = NULL,
  hc = NULL,
  weightLevel = NULL,
  weightSizeGroup = NULL,
  loss = c("ls", "logit"),
  intercept = TRUE,
  sizeMaxGroup = NULL,
  verbose = FALSE,
  ...
)

Arguments

X

matrix of size n*p

y

vector of size n. If loss = "logit", elements of y must be in -1,1

nfolds

number of folds

lambda

lambda values for group lasso. If not provided, the function generates its own values of lambda

hc

output of hclust function. If not provided, hclust is run with ward.D2 method

weightLevel

a vector of size p for each level of the hierarchy. A zero indicates that the level will be ignored. If not provided, use 1/(height between 2 successive levels)

weightSizeGroup

a vector

loss

a character string specifying the loss function to use, valid options are: "ls" least squares loss (regression) and "logit" logistic loss (classification)

intercept

should an intercept be included in the model ?

sizeMaxGroup

maximum size of selected groups. If NULL, no restriction

verbose

print some informations

...

Others parameters for cv.gglasso function

Details

Hierarchical clustering is performed with all the variables. Then, the partitions from the different levels of the hierarchy are used in the different run of MLGL for cross validation.

Value

a cv.MLGL object containing:

lambda

values of lambda.

cvm

the mean cross-validated error.

cvsd

estimate of standard error of cvm

cvupper

upper curve = cvm+cvsd

cvlower

lower curve = cvm-cvsd

lambda.min

The optimal value of lambda that gives minimum cross validation error cvm.

lambda.1se

The largest value of lambda such that error is within 1 standard error of the minimum.

time

computation time

Author(s)

Quentin Grimonprez

See Also

MLGL, stability.MLGL, predict.cv.gglasso, coef.cv.MLGL, plot.cv.MLGL

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply cv.MLGL method
res <- cv.MLGL(X, y)

Full process of MLGL

Description

Run hierarchical clustering following by a group-lasso on all the different partition and a hierarchical testing procedure. Only for linear regression problem.

Usage

fullProcess(X, ...)

## Default S3 method:
fullProcess(
  X,
  y,
  control = c("FWER", "FDR"),
  alpha = 0.05,
  test = partialFtest,
  hc = NULL,
  fractionSampleMLGL = 1/2,
  BHclust = 50,
  nCore = NULL,
  addRoot = FALSE,
  Shaffer = FALSE,
  ...
)

## S3 method for class 'formula'
fullProcess(
  formula,
  data,
  control = c("FWER", "FDR"),
  alpha = 0.05,
  test = partialFtest,
  hc = NULL,
  fractionSampleMLGL = 1/2,
  BHclust = 50,
  nCore = NULL,
  addRoot = FALSE,
  Shaffer = FALSE,
  ...
)

Arguments

X

matrix of size n*p

...

Others parameters for MLGL

y

vector of size n.

control

either "FDR" or "FWER"

alpha

control level for testing procedure

test

test used in the testing procedure. Default is partialFtest

hc

output of hclust function. If not provided, hclust is run with ward.D2 method. User can also provide the desired method: "single", "complete", "average", "mcquitty", "ward.D", "ward.D2", "centroid", "median".

fractionSampleMLGL

a real between 0 and 1: the fraction of individuals to use in the sample for MLGL (see Details).

BHclust

number of replicates for computing the distance matrix for the hierarchical clustering tree

nCore

number of cores used for distance computation. Use all cores by default.

addRoot

If TRUE, add a common root containing all the groups

Shaffer

If TRUE, a Shaffer correction is performed (only if control = "FWER")

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment (formula)

Details

Divide the n individuals in two samples. Then the three following steps are done: 1) Bootstrap Hierarchical Clustering of the variables of X 2) MLGL on the second sample of individuals 3) Hierarchical testing procedure on the first sample of individuals.

Value

a list containing:

res

output of MLGL function

lambdaOpt

lambda values maximizing the number of rejects

var

A vector containing the index of selected variables for the first lambdaOpt value

group

A vector containing the values index of selected groups for the first lambdaOpt value

selectedGroups

Selected groups for the first lambdaOpt value

reject

Selected groups for all lambda values

alpha

Control level

test

Test used in the testing procedure

control

"FDR" or "FWER"

time

Elapsed time

Author(s)

Quentin Grimonprez

See Also

MLGL, hierarchicalFDR, hierarchicalFWER, selFDR, selFWER

Examples

# least square loss
set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
res <- fullProcess(X, y)

Hierarchical testing with FDR control

Description

Apply hierarchical test for each hierarchy, and test external variables for FDR control at level alpha

Usage

hierarchicalFDR(X, y, group, var, test = partialFtest, addRoot = FALSE)

Arguments

X

original data

y

associated response

group

vector with index of groups. group[i] contains the index of the group of the variable var[i].

var

vector with the variables contained in each group. group[i] contains the index of the group of the variable var[i].

test

function for testing the nullity of a group of coefficients in linear regression. The function has 3 arguments: X, the design matrix, y, response, and varToTest, a vector containing the indices of the variables to test. The function returns a p-value

addRoot

If TRUE, add a common root containing all the groups

Details

Version of the hierarchical testing procedure of Yekutieli for MLGL output. You can use th selFDR function to select groups at a desired level alpha.

Value

a list containing:

pvalues

pvalues of the different test (without correction)

adjPvalues

adjusted pvalues

groupId

Index of the group

hierMatrix

Matrix describing the hierarchical tree.

References

Yekutieli, Daniel. "Hierarchical False Discovery Rate-Controlling Methodology." Journal of the American Statistical Association 103.481 (2008): 309-16.

See Also

selFDR, hierarchicalFWER

Examples

set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
res <- MLGL(X, y)
test <- hierarchicalFDR(X, y, res$group[[20]], res$var[[20]])

Hierarchical testing with FWER control

Description

Apply hierarchical test for each hierarchy, and test external variables for FWER control at level alpha

Usage

hierarchicalFWER(
  X,
  y,
  group,
  var,
  test = partialFtest,
  Shaffer = FALSE,
  addRoot = FALSE
)

Arguments

X

original data

y

associated response

group

vector with index of groups. group[i] contains the index of the group of the variable var[i].

var

vector with the variables contained in each group. group[i] contains the index of the group of the variable var[i].

test

function for testing the nullity of a group of coefficients in linear regression. The function has 3 arguments: X, the design matrix, y, response, and varToTest, a vector containing the indices of the variables to test. The function returns a p-value

Shaffer

boolean, if TRUE, a Shaffer correction is performed

addRoot

If TRUE, add a common root containing all the groups

Details

Version of the hierarchical testing procedure of Meinshausen for MLGL output. You can use th selFWER function to select groups at a desired level alpha

Value

a list containing:

pvalues

pvalues of the different test (without correction)

adjPvalues

adjusted pvalues

groupId

Index of the group

hierMatrix

Matrix describing the hierarchical tree.

References

Meinshausen, Nicolai. "Hierarchical Testing of Variable Importance." Biometrika 95.2 (2008): 265-78.

See Also

selFWER, hierarchicalFDR

Examples

set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
res <- MLGL(X, y)
test <- hierarchicalFWER(X, y, res$group[[20]], res$var[[20]])

Obtain a sparse matrix of the coefficients of the path

Description

Obtain a sparse matrix of the coefficients of the path

Usage

listToMatrix(x, row = c("covariates", "lambda"))

Arguments

x

MLGL object

row

"lambda" or "covariates". If row="covariates", each row of the output matrix represents a covariate else if row="lambda", it represents a value of lambda.

Details

This function can be used with a MLGL object to obtain a matrix with all estimated coefficients for the p original variables. In case of overlapping groups, coefficients from repeated variables are summed.

Value

a sparse matrix containing the estimated coefficients for different lambdas

See Also

MLGL, overlapgglasso

Examples

# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)
# Convert output in sparse matrix format
beta <- listToMatrix(res)

Group-lasso with overlapping groups

Description

Group-lasso with overlapping groups

Usage

overlapgglasso(
  X,
  y,
  var,
  group,
  lambda = NULL,
  weight = NULL,
  loss = c("ls", "logit"),
  intercept = TRUE,
  ...
)

Arguments

X

matrix of size n*p

y

vector of size n. If loss = "logit", elements of y must be in -1,1

var

vector containing the variable to use

group

vector containing the associated groups

lambda

lambda values for group lasso. If not provided, the function generates its own values of lambda

weight

a vector the weight for each group. Default is the square root of the size of each group

loss

a character string specifying the loss function to use, valid options are: "ls" least squares loss (regression) and "logit" logistic loss (classification)

intercept

should an intercept be included in the model ?

...

Others parameters for gglasso function

Details

Use a group-lasso algorithm (see gglasso) to solve a group-lasso with overlapping groups. Each variable j of the original matrix X is paste k(j) times in a new dataset with k(j) the number of different groups containing the variable j. The new dataset is used to solve the group-lasso with overlapping groups running a group-lasso algorithm.

Value

a MLGL object containing:

lambda

lambda values

b0

intercept values for lambda

beta

A list containing the values of estimated coefficients for each values of lambda

var

A list containing the index of selected variables for each values of lambda

group

A list containing the values index of selected groups for each values of lambda

nVar

A vector containing the number of non zero coefficients for each values of lambda

nGroup

A vector containing the number of non zero groups for each values of lambda

structure

A list containing 3 vectors. var: all variables used. group: associated groups. weight: weight associated with the different groups.

time

computation time

dim

dimension of X

Source

Laurent Jacob, Guillaume Obozinski, and Jean-Philippe Vert. 2009. Group lasso with overlap and graph lasso. In Proceedings of the 26th Annual International Conference on Machine Learning (ICML '09).

See Also

listToMatrix

Examples

# Least square loss
set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
var <- c(1:60, 1:8, 7:15)
group <- c(rep(1:12, each = 5), rep(13, 8), rep(14, 9))
res <- overlapgglasso(X, y, var, group)

# Logistic loss
y <- 2 * (rowSums(X[, 1:4]) > 0) - 1
var <- c(1:60, 1:8, 7:15)
group <- c(rep(1:12, each = 5), rep(13, 8), rep(14, 9))
res <- overlapgglasso(X, y, var, group, loss = "logit")

Partial F-test

Description

Perform a partial F-test

Usage

partialFtest(X, y, varToTest)

Arguments

X

design matrix of size n*p

y

response vector of length n

varToTest

vector containing the index of the column of X to test

Details

y = X * beta + epsilon

null hypothesis: beta[varToTest] = 0 alternative hypothesis: it exists an index k in varToTest such that beta[k] != 0

The test statistic is based on a full and a reduced model. full: y = X * beta + epsilon reduced: y = X * beta[-varToTest] + epsilon

Value

a vector of the same length as varToTest containing the p-values of the test.

See Also

Ftest

Plot the path obtained from HMT function

Description

Plot the path obtained from HMT function

Usage

## S3 method for class 'HMT'
plot(
  x,
  log.lambda = FALSE,
  lambda.lines = FALSE,
  lambda.opt = c("min", "max", "both"),
  ...
)

Arguments

x

fullProcess object

log.lambda

If TRUE, use log(lambda) instead of lambda in abscissa

lambda.lines

If TRUE, add vertical lines at lambda values

lambda.opt

If there is several optimal lambdas, which one to print "min", "max" or "both"

...

Other parameters for plot function

See Also

HMT

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)

out <- HMT(res, X, y)
plot(out)

Plot the path obtained from MLGL function

Description

Plot the path obtained from MLGL function

Usage

## S3 method for class 'MLGL'
plot(x, log.lambda = FALSE, lambda.lines = FALSE, ...)

Arguments

x

MLGL object

log.lambda

If TRUE, use log(lambda) instead of lambda in abscissa

lambda.lines

if TRUE, add vertical lines at lambda values

...

Other parameters for plot function

See Also

MLGL

Examples

# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)
# Plot the solution path
plot(res)

Plot the cross-validation obtained from cv.MLGL function

Description

Plot the cross-validation obtained from cv.MLGL function

Usage

## S3 method for class 'cv.MLGL'
plot(x, log.lambda = FALSE, ...)

Arguments

x

cv.MLGL object

log.lambda

If TRUE, use log(lambda) instead of lambda in abscissa

...

Other parameters for plot function

See Also

cv.MLGL

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply cv.MLGL method
res <- cv.MLGL(X, y)
# Plot the cv error curve
plot(res)

Plot the path obtained from fullProcess function

Description

Plot the path obtained from fullProcess function

Usage

## S3 method for class 'fullProcess'
plot(
  x,
  log.lambda = FALSE,
  lambda.lines = FALSE,
  lambda.opt = c("min", "max", "both"),
  ...
)

Arguments

x

fullProcess object

log.lambda

If TRUE, use log(lambda) instead of lambda in abscissa

lambda.lines

If TRUE, add vertical lines at lambda values

lambda.opt

If there is several optimal lambdas, which one to print "min", "max" or "both"

...

Other parameters for plot function

See Also

fullProcess

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- fullProcess(X, y)
# Plot the solution path
plot(res)

Plot the stability path obtained from stability.MLGL function

Description

Plot the stability path obtained from stability.MLGL function

Usage

## S3 method for class 'stability.MLGL'
plot(x, log.lambda = FALSE, threshold = 0.75, ...)

Arguments

x

stability.MLGL object

log.lambda

If TRUE, use log(lambda) instead of lambda in abscissa

threshold

Threshold for selection frequency

...

Other parameters for plot function

Value

A list containing:

var

Index of selected variables for the given threshold.

group

Index of the associated group.

threshold

Value of threshold

See Also

stability.MLGL

Examples


set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)

# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)

# Apply stability.MLGL method
res <- stability.MLGL(X, y)
selected <- plot(res)
print(selected)

Predict fitted values from a MLGL object

Description

Predict fitted values from a MLGL object

Usage

## S3 method for class 'MLGL'
predict(object, newx = NULL, s = NULL, type = c("fit", "coefficients"), ...)

Arguments

object

MLGL object

newx

matrix with new individuals for prediction. If type="coefficients", the parameter has to be NULL

s

values of lambda. If NULL, use values from object

type

if "fit", return the fitted values for each values of s, if "coefficients", return the estimated coefficients for each s

...

Not used. Other arguments to predict.

Value

A matrix with fitted values or estimated coefficients for given values of s.

Author(s)

original code from gglasso package Author: Yi Yang <yiyang@umn.edu>, Hui Zou <hzou@stat.umn.edu>

function inspired from predict function from gglasso package by Yi Yang and Hui Zou.

See Also

MLGL

Examples

X <- simuBlockGaussian(n = 50, nBlock = 12, sizeBlock = 5, rho = 0.7)
y <- drop(X[, c(2, 7, 12)] %*% c(2, 2, -1)) + rnorm(50, 0, 0.5)

m1 <- MLGL(X, y, loss = "ls")
predict(m1, newx = X)
predict(m1, s=3, newx = X)
predict(m1, s=1:3, newx = X)

Predict fitted values from a cv.MLGL object

Description

Predict fitted values from a cv.MLGL object

Usage

## S3 method for class 'cv.MLGL'
predict(
  object,
  newx = NULL,
  s = c("lambda.1se", "lambda.min"),
  type = c("fit", "coefficients"),
  ...
)

Arguments

object

cv.MLGL object

newx

matrix with new individuals for prediction. If type="coefficients", the parameter has to be NULL

s

Either "lambda.1se" or "lambda.min"

type

if "fit", return the fitted values for each values of s, if "coefficients", return the estimated coefficients for each s

...

Not used. Other arguments to predict.

Value

A matrix with fitted values or estimated coefficients for given values of s.

Author(s)

Quentin Grimonprez

See Also

cv.MLGL

Print Values

Description

Print a HMT object

Usage

## S3 method for class 'HMT'
print(x, ...)

Arguments

x

HMT object

...

Not used.

See Also

HMT summary.HMT

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)
out <- HMT(res, X, y)
print(out)

Print Values

Description

Print a MLGL object

Usage

## S3 method for class 'MLGL'
print(x, ...)

Arguments

x

MLGL object

...

Not used.

See Also

MLGL summary.MLGL

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)
print(res)

Print Values

Description

Print a fullProcess object

Usage

## S3 method for class 'fullProcess'
print(x, ...)

Arguments

x

fullProcess object

...

Not used.

See Also

fullProcess summary.fullProcess

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- fullProcess(X, y)
print(res)

Selection from hierarchical testing with FDR control

Description

Select groups from hierarchical testing procedure with FDR control (hierarchicalFDR)

Usage

selFDR(out, alpha = 0.05, global = TRUE, outer = TRUE)

Arguments

out

output of hierarchicalFDR function

alpha

control level for test

global

if FALSE the provided alpha is the desired level control for each family.

outer

if TRUE, the FDR is controlled only on outer node (rejected groups without rejected children). If FALSE, it is controlled on the full tree.

Details

See the reference for mode details about the method.

If each family is controlled at a level alpha, we have the following control: FDR control of full tree: alpha * delta * 2 (delta = 1.44) FDR control of outer node: alpha * L * delta * 2 (delta = 1.44)

Value

a list containing:

toSel

vector of boolean. TRUE if the group is selected

groupId

Names of groups

local.alpha

control level for each family of hypothesis

global.alpha

control level for the tree (full tree or outer node)

References

Yekutieli, Daniel. "Hierarchical False Discovery Rate-Controlling Methodology." Journal of the American Statistical Association 103.481 (2008): 309-16.

See Also

hierarchicalFDR

Examples

set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
res <- MLGL(X, y)
test <- hierarchicalFDR(X, y, res$group[[20]], res$var[[20]])
sel <- selFDR(test, alpha = 0.05)

Selection from hierarchical testing with FWER control

Description

Select groups from hierarchical testing procedure with FWER control (hierarchicalFWER)

Usage

selFWER(out, alpha = 0.05)

Arguments

out

output of hierarchicalFWER function

alpha

control level for test

Details

Only outer nodes (rejected groups without rejected children) are returned as TRUE.

Value

a list containing:

toSel

vector of boolean. TRUE if the group is selected

groupId

Names of groups

References

Meinshausen, Nicolai. "Hierarchical Testing of Variable Importance." Biometrika 95.2 (2008): 265-78.

See Also

hierarchicalFWER

Examples

set.seed(42)
X <- simuBlockGaussian(50, 12, 5, 0.7)
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
res <- MLGL(X, y)
test <- hierarchicalFWER(X, y, res$group[[20]], res$var[[20]])
sel <- selFWER(test, alpha = 0.05)

Simulate multivariate Gaussian samples with block diagonal variance matrix

Description

Simulate n samples from a gaussian multivariate law with 0 vector mean and block diagonal variance matrix with diagonal 1 and block of rho.

Usage

simuBlockGaussian(n, nBlock, sizeBlock, rho)

Arguments

n

number of samples to simulate

nBlock

number of blocks

sizeBlock

size of blocks

rho

correlation within each block

Value

a matrix of size n * (nBlock * sizeBlock) containing the samples

Author(s)

Quentin Grimonprez

Examples

X <- simuBlockGaussian(50, 12, 5, 0.7)

Stability Selection for Multi-Layer Group-lasso

Description

Stability selection for MLGL

Usage

stability.MLGL(
  X,
  y,
  B = 50,
  fraction = 0.5,
  hc = NULL,
  lambda = NULL,
  weightLevel = NULL,
  weightSizeGroup = NULL,
  loss = c("ls", "logit"),
  intercept = TRUE,
  verbose = FALSE,
  ...
)

Arguments

X

matrix of size n*p

y

vector of size n. If loss = "logit", elements of y must be in -1,1

B

number of bootstrap sample

fraction

Fraction of data used at each of the B sub-samples

hc

output of hclust function. If not provided, hclust is run with ward.D2 method

lambda

lambda values for group lasso. If not provided, the function generates its own values of lambda

weightLevel

a vector of size p for each level of the hierarchy. A zero indicates that the level will be ignored. If not provided, use 1/(height between 2 successive levels)

weightSizeGroup

a vector

loss

a character string specifying the loss function to use, valid options are: "ls" least squares loss (regression) and "logit" logistic loss (classification)

intercept

should an intercept be included in the model ?

verbose

print some informations

...

Others parameters for gglasso function

Details

Hierarchical clustering is performed with all the variables. Then, the partitions from the different levels of the hierarchy are used in the different runs of MLGL for estimating the probability of selection of each group.

Value

a stability.MLGL object containing:

lambda

sequence of lambda.

B

Number of bootstrap samples.

stability

A matrix of size length(lambda)*number of groups containing the probability of selection of each group

var

vector containing the index of covariates

group

vector containing the index of associated groups of covariates

time

computation time

Author(s)

Quentin Grimonprez

References

Meinshausen and Buhlmann (2010). Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72.4, p. 417-473.

See Also

cv.MLGL, MLGL

Examples


set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)

# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)

# Apply stability.MLGL method
res <- stability.MLGL(X, y)

Object Summaries

Description

Summary of a HMT object

Usage

## S3 method for class 'HMT'
summary(object, ...)

Arguments

object

HMT object

...

Not used.

See Also

HMT print.HMT

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)
out <- HMT(res, X, y)
summary(out)

Object Summaries

Description

Summary of a MLGL object

Usage

## S3 method for class 'MLGL'
summary(object, ...)

Arguments

object

MLGL object

...

Not used.

See Also

MLGL print.MLGL

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- MLGL(X, y)
summary(res)

Object Summaries

Description

Summary of a fullProcess object

Usage

## S3 method for class 'fullProcess'
summary(object, ...)

Arguments

object

fullProcess object

...

Not used.

See Also

fullProcess print.fullProcess

Examples

set.seed(42)
# Simulate gaussian data with block-diagonal variance matrix containing 12 blocks of size 5
X <- simuBlockGaussian(50, 12, 5, 0.7)
# Generate a response variable
y <- X[, c(2, 7, 12)] %*% c(2, 2, -2) + rnorm(50, 0, 0.5)
# Apply MLGL method
res <- fullProcess(X, y)
summary(res)

Find all unique groups in hclust results

Description

Find all unique groups in hclust results

Usage

uniqueGroupHclust(hc)

Arguments

hc

output of hclust function

Value

A list containing:

indexGroup

Vector containing the index of variables.

varGroup

Vector containing the index of the group of each variable.

Author(s)

Quentin Grimonprez

Examples

hc <- hclust(dist(USArrests), "average")
res <- uniqueGroupHclust(hc)