Title: Screen and clean variable selection procedures

Version: 1.0.1

Date: 2012年10月30日

Author: Pengsheng Ji, Jiashun Jin, Qi Zhang

Maintainer: Qi Zhang <karlmzhang@gmail.com>

Description: Routines for a collection of screen-and-clean type variable selection procedures, including UPS and GS.

Imports: MASS, Matrix, quadprog

License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Packaged: 2012年10月30日 14:23:17 UTC; Zhang-Qi

Repository: CRAN

Date/Publication: 2012年10月30日 17:34:49

NeedsCompilation: no

Package: ScreenClean

Type: Package

Version: 1.0.1

Date: 2012年10月30日

License: GPL (>= 2)

CleaningStep(survivor, y.tilde, gram, lambda, uu)

survivor

the result of the screening step, a logical vector.

y.tilde

X'y, where X and y are the predictor matrix and the reponse vector.

gram

the thresholded sparse gram matrix

lambda

the tuning parameters of the cleaning step, whose optimal choice is tied to the sparse level.

uu

the tuning parameter of the cleaning step; its optimal choice has the intuition of the detected minimal signal strength.

beta.gs

the estimated regression coefficient of the graphlet screening, a numeric vector

##See the demoGs.r

FindAllCG(adjacency.matrix, lc)

adjacency.matrix

p by p adjacency matrix of an undirected graph; it must be symmetric.

lc

the maximal size of the connected subgraphs to be listed

cg.all

A list, whose kth component is a matrix with k columns that lists all the connected subgraphs with k nodes.

require(MASS)
require(Matrix)
p <- 10
Omega <- sparseMatrix(c(1:(p-1),2:p),c(2:p,1:(p-1)),x=1)
cg.all <- FindAllCG(Omega,3)

FindCG(adjacency.matrix, cg.initial)

adjacency.matrix

p by p adjacency matrix of an undirected graph. It must be symmetric.

cg.initial

It could be 1:p or a matrix, whose elements are positive integers from 1 to p. If it is a length p vector, FindCG converts it into a matrix with one column. For a matrix with k columns, FindCG reads its rows as th indices of a collection of connected subgraphs with k nodes.

cg.new

If the input is a matrix with k columns and stores the indices of all the size k connected subgraphs, the output is a matrix with k+1 columns storing the indices of all the connected subgraphs with k+1 nodes.

require(MASS)
require(Matrix)
p <- 10
Omega <- sparseMatrix(c(1:(p-1),2:p),c(2:p,1:(p-1)),x=1)
cg.2 <- FindCG(Omega,c(1:p))
cg.3 <- FindCG(Omega,cg.2)

IterGS(y.tilde, gram, gram.bias, cg.all, sp, tau, nm, q0=0.1, scale = 1, max.iter = 3, 
std.thresh = 1.05, beta.initial = NULL)

y.tilde

X'y where X and y are the predictor matrix and the response vector, respectively.

gram

the threholded gram matrix

gram.bias

the bias of the threholded gram matrix

cg.all

all the connected cg.alls of gram with size no more than nm.

sp

the expected sparse level

tau

the minimal signal strength to be detected

nm

the maximal size of the connected subgaphs considered in the screening step.

q0

the minimal screening parameter

scale

optional numerical parameter of the screening step. The default is 1

max.iter

the maximal number of iterations. The default is 3.

std.thresh

the threshold of the std change that stop the loop. The default is 1.05.

beta.initial

the initial estimate of beta in reducing the bias. The default is uu*sign(y.tilde)*(abs(y.tilde)>uu).

estimate

The iterative GS estimate of beta

n.iter

The number of iterations it takes

##See demoIterGs.r

PMLE(gram, y, lambda, uu)

gram

the sub gram matrix of the small scale quadratic problem.

y

the sub-vector of y.tilde

lambda

the tuning parameter of the cleaning step, tied to the sparse level.

uu

the tuning parameters of the cleaning step. It has the intuitive interpretation of the minimal signal strength to be detected.

b

the estimate of the subvector of beta

ScreeningStep(y.tilde, gram, cg.all, nm, v, r, q0 = 0.1, scale = 1)

y.tilde

X'y, where X and y are the predictor matrix and the reponse vector.

gram

the regularized gram matrix

cg.all

a list whose kth element is a matrix of k columns. Its rows contain all the connected subgraph with k nodes.

nm

the maximal subgraph invesgated in the screening step

v

an essential tuning parameter of graphlet screening, tied to the sparse level

r

an essential tuning parameter of graphlet screening, tied to the signal strength

q0

the minimal screening parameter

scale

q(D,F)=q^{max}(D,F)*scale, default is scale=1

survivor

A logical vector, where TRUE means retained as a protential signal.

##See the demoGS.r

ThresholdGram(gram.full, delta = 1/log(dim(gram.full)[1]))

gram.full

the gram matrix before the elementwise thresholding, a p by p symmetric matrix

delta

the threshold, the default is 1/log(p)

gram.sd

the threhsolded gram matrix, a sparse matrix

gram.bias

the difference of the orginal matrix and the threholded matrix

p <-10
off.diag<-matrix(runif(p^2),p,p)
omega <- (off.diag+t(off.diag))*0.3
diag(omega) <- 1
omega.omega<-ThresholdGram(omega,0.3)
omega.omega$gram
omega.omega$gram.bias

VectorizeBase(i, base, length)

i

the non-negative number to be converted

base

the base to be converted on

length

the length of the converted vector

vector

A vector with the given length, whose elements can be read as the number i with the given base.