Package 'LINselect'

penalty

Description

Calculate the penalty function for estimators selection.

Usage

penalty(Delta, n, p, K)

Arguments

Delta	vector with Dmax+1 components : weights in the penalty function.
n	integer : number of observatons.
p	integer : number of variables.
K	scalar : constant in the penalty function.

Value

A vector with the same length as Delta: for each d=0, ..., Dmax, let N=n-d, D=d+1 and
pen(d) = x K N/(N-1) where x satisfies

$\phi$(x) = exp(-Delta(d)), when Delta(d)<50,
where $\phi$(x)=pf(q=x/(D+2),df1=D+2,df2=N-1,lower.tail=F)-(x/D)pf(q=(N+1)x/D(N-1),df1=D,df2=N+1,lower.tail=F)

$\psi$(x) = Delta(d), when Delta(d)$\ge$50,
where $\psi$(x)=lbeta(1+D/2,(N-1)/2)-log(2(2x+(N-1)D)/((N-1)(N+2)x))-(N-1)/2log((N-1)/(N-1+x))-(D/2)log(x/(N-1+x))

Note

The values of the penalty function greater than 1e+08 are set to 1e+08.

If for some Delta(d) the equation $\phi$(x) = exp(-Delta(d)/(d+1)) has no solution, then the execution is stopped.

Author(s)

Yannick Baraud, Christophe Giraud, Sylvie Huet

---

simulData

Description

Function to simulate data $Y = X \beta + \sigma N(0, 1)$

Usage

simulData(p = 100, n = 100, beta = NULL, C = NULL, r = 0.95, 
    rSN = 10)

Arguments

p	integer : number of variates. Should be >15 if beta=NULL
n	integer : number of observations
beta	vector with p components. See details.
C	matrix p x p. Covariance matrix of X. See details.
r	scalar for calculating the covariance of X when C=NULL.
rSN	scalar : ratio signal/noise

Details

When beta is NULL, then p should be greater than 15 and beta=c(rep(2.5,5),rep(1.5,5),rep(0.5,5),rep(0,p-15))

When C is NULL, then C is block diagonal with
C[a,b] = r**abs(a-b) for $1 \le a, b \le 15$
C[a,b] = r**abs(a-b) for $16 \le a, b \le p$

The lines of X are n i.i.d. gaussian variables with mean 0 and covariance matrix C.

The variance sigma**2 equals the squared euclidean norm of $X \beta$ divided by rSN*n.

Value

A list with components :

Y	vector n : $Y = X \beta + \sigma N(0, 1)$
X	matrix n x p : values of the covariates. See details.
C	matrix p x p. See details
sigma	scalar. See details.
beta	vector with p components. See details.

Note

Library mvtnorm is loaded.

Author(s)

Yannick Baraud, Christophe Giraud, Sylvie Huet

---

tuneLasso

Description

tune the lasso parameter in the regression model : $Y= X \beta + \sigma N(0,1)$ using the lasso or the gauss-lasso method

Usage

tuneLasso(Y, X, normalize = TRUE, method = c("lasso", "Glasso"), 
    dmax = NULL, Vfold = TRUE, V = 10, LINselect = TRUE, a = 0.5, 
    K = 1.1, verbose = TRUE, max.steps = NULL)

Arguments

Y	vector with n components : response variable.
X	matrix with n rows and p columns : covariates.
normalize	logical : corresponds to the input normalize of the functions enet and cv.enet. If TRUE the variates X are normalized.
method	vector of characters whose components are subset of (“lasso”, “Glasso”)
dmax	integer : maximum number of variables in the lasso estimator. dmax $\le$ D where D = min (3*p/4 , n-5) if p$\ge$n D= min(p,n-5) if p < n. Default : dmax = D.
Vfold	logical : if TRUE the tuning is done by Vfold-CV
V	integer. Gives the value of V in the Vfold-CV procedure
LINselect	logical : if TRUE the tuning is done by LINselect
a	scalar : value of the parameter $\alpha$ in the LINselect criteria
K	scalar : value of the parameter $K$ in the LINselect criteria
verbose	logical : if TRUE a trace of the current process is displayed in real time.
max.steps	integer : maximum number of steps in the lasso procedure. Corresponds to the input max.steps of the function enet. Default : max.steps = 2*min(p,n)

Value

A list with one or two components according to method.
lasso if method contains "lasso" is a list with one or two components according to Vfold and LINselect.

• Ls if LINselect=TRUE. A list with components

  • support: vector of integers. Estimated support of the parameter vector $\beta$.

  • coef: vector whose first component is the estimated intercept.
    The other components are the estimated non zero coefficients.

  • fitted: vector with length n. Fitted value of the response.

  • crit: vector containing the values of the criteria for each value of lambda.

  • lambda: vector containing the values of the tuning parameter of the lasso algorithm.

• CV if Vfold=TRUE. A list with components

  • support: vector of integers. Estimated support of the parameter vector $\beta$.

  • coef: vector whose first component is the estimated intercept.
    The other components are the estimated non zero coefficients.

  • fitted: vector with length n. Fitted value of the response.

  • crit: vector containing the values of the criteria for each value of lambda.

  • crit.err: vector containing the estimated standard-error of the criteria.

  • lambda: vector containing the values of the tuning parameter of the lasso algorithm.

Glasso if method contains "Glasso". The same as lasso.

Note

library elasticnet is loaded.

Author(s)

Yannick Baraud, Christophe Giraud, Sylvie Huet

References

See Baraud et al. 2010 http://hal.archives-ouvertes.fr/hal-00502156/fr/
Giraud et al., 2013, https://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1356098553

Examples

#source("charge.R")
library("LINselect")

# simulate data with
## Not run: ex <- simulData(p=100,n=100,r=0.8,rSN=5)

## Not run: ex1.tuneLasso <- tuneLasso(ex$Y,ex$X)

## Not run: data(diabetes)
## Not run: attach(diabetes)
## Not run: ex.diab <- tuneLasso(y,x2)
## Not run: detach(diabetes)

---

VARselect

Description

Estimation in the regression model : $Y= X \beta + \sigma N(0,1)$
Variable selection by choosing the best predictor among predictors emanating
from different methods as lasso, elastic-net, adaptive lasso, pls, randomForest.

Usage

VARselect(Y, X, dmax = NULL, normalize = TRUE, method = c("lasso", 
    "ridge", "pls", "en", "ALridge", "ALpls", "rF", "exhaustive"), 
    pen.crit = NULL, lasso.dmax = NULL, ridge.dmax = NULL, pls.dmax = NULL, 
    en.dmax = NULL, ALridge.dmax = NULL, ALpls.dmax = NULL, rF.dmax = NULL, 
    exhaustive.maxdim = 5e+05, exhaustive.dmax = NULL, en.lambda = c(0.01, 
        0.1, 0.5, 1, 2, 5), ridge.lambda = c(0.01, 0.1, 0.5, 
        1, 2, 5), rF.lmtry = 2, pls.ncomp = 5, ALridge.lambda = c(0.01, 
        0.1, 0.5, 1, 2, 5), ALpls.ncomp = 5, max.steps = NULL, 
    K = 1.1, verbose = TRUE, long.output = FALSE)

Arguments

Y	vector with n components : response variable.
X	matrix with n rows and p columns : covariates.
dmax	integer : maximum number of variables in the lasso estimator. dmax $\le$ D where D = min (3*p/4 , n-5) if p$\ge$n D= min(p,n-5) if p < n. Default : dmax = D.
normalize	logical : if TRUE the columns of X are scaled
method	vector of characters whose components are subset of “lasso”, “ridge”, “pls”, “en”, “ALridge”, “ALpls”, “rF”, “exhaustive”.
pen.crit	vector with dmax+1 components : for d=0, ..., dmax, penalty[d+1] gives the value of the penalty for the dimension d. Default : penalty = NULL. In that case, the penalty will be calculated by the function penalty.
lasso.dmax	integer lower than dmax, default = dmax.
ridge.dmax	integer lower than dmax, default = dmax.
pls.dmax	integer lower than dmax, default = dmax.
en.dmax	integer lower than dmax, default = dmax.
ALridge.dmax	integer lower than dmax, default = dmax.
ALpls.dmax	integer lower than dmax, default = dmax.
rF.dmax	integer lower than dmax, default = dmax.
exhaustive.maxdim	integer : maximum number of subsets of covariates considered in the exhaustive method. See details.
exhaustive.dmax	integer lower than dmax, default = dmax
en.lambda	vector : tuning parameter of the ridge. It is the input parameter lambda of function enet
ridge.lambda	vector : tuning parameter of the ridge. It is the input parameter lambda of function lm.ridge
rF.lmtry	vector : tuning paramer mtry of function randomForest, mtry =p/rF.lmtry.
pls.ncomp	integer : tuning parameter of the pls. It is the input parameter ncomp of the function plsr. See details.
ALridge.lambda	similar to ridge.lambda in the adaptive lasso procedure.
ALpls.ncomp	similar to pls.ncomp in the adaptive lasso procedure. See details.
max.steps	integer. Maximum number of steps in the lasso procedure. Corresponds to the input max.steps of the function enet. Default : max.steps = 2*min(p,n)
K	scalar : value of the parameter $K$ in the LINselect criteria.
verbose	logical : if TRUE a trace of the current process is displayed in real time.
long.output	logical : if FALSE only the component summary will be returned. See Value.

Details

When method is pls or ALpls, the LINselect procedure is carried out considering the number of components in the pls method as the tuning parameter.
This tuning parameter varies from 1 to pls.ncomp.

When method is exhaustive, the maximum number of variate d is calculated as follows.
Let q be the largest integer such that choose(p,q) < exhaustive.maxdim. Then d = min(q, exhaustive.dmax,dmax).

Value

A list with at least length(method) components.
For each procedure in method a list with components

• support: vector of integers. Estimated support of the parameters $\beta$ for the considered procedure.

• crit: scalar equals to the LINselect criteria calculated in the estimated support.

• fitted: vector with length n. Fitted value of the response calculated when the support of $\beta$ equals support.

• coef: vector whose first component is the estimated intercept.
  The other components are the estimated non zero coefficients when the support of $\beta$ equals support.

If length(method) > 1, the additional component summary is a list with three components:

• support: vector of integers. Estimated support of the parameters $\beta$ corresponding to the minimum of the criteria among all procedures.

• crit: scalar. Minimum value of the criteria among all procedures.

• method: vector of characters. Names of the procedures for which the minimum is reached

If pen.crit = NULL, the component pen.crit gives the values of the penalty calculated by the function penalty. If long.output is TRUE the component named chatty is a list with length(method) components.
For each procedure in method, a list with components

• support where support[[l]] is a vector of integers containing an estimator of the support of the parameters $\beta$.

• crit : vector where crit[l] contains the value of the LINselect criteria calculated in support[[l]].

Note

When method is lasso, library elasticnet is loaded.

When method is en, library elasticnet is loaded.

When method is ridge, library MASS is loaded.

When method is rF, library randomForest is loaded.

When method is pls, library pls is loaded.

When method is ALridge, libraries MASS and elasticnet are loaded.

When method is ALpls, libraries pls and elasticnet are loaded.

When method is exhaustive, library gtools is loaded.

Author(s)

Yannick Baraud, Christophe Giraud, Sylvie Huet

References

See Baraud et al. 2010 http://hal.archives-ouvertes.fr/hal-00502156/fr/
Giraud et al., 2013, https://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1356098553

Examples

#source("charge.R")
library("LINselect")

# simulate data with
# beta=c(rep(2.5,5),rep(1.5,5),rep(0.5,5),rep(0,p-15))
ex <- simulData(p=100,n=100,r=0.8,rSN=5)

## Not run: ex1.VARselect <- VARselect(ex$Y,ex$X,exhaustive.dmax=2)

## Not run: data(diabetes)
## Not run: attach(diabetes)
## Not run: ex.diab <- VARselect(y,x2,exhaustive.dmax=5)
## Not run: detach(diabetes)

---