| Type: | Package |
| Title: | Variable Selection via Tilted Correlation Screening Algorithm |
| Version: | 1.1.1 |
| Date: | 2016-12-22 |
| Author: | Haeran Cho [aut, cre], Piotr Fryzlewicz [aut] |
| Maintainer: | Haeran Cho <haeran.cho@bristol.ac.uk> |
| Description: | Implements an algorithm for variable selection in high-dimensional linear regression using the "tilted correlation", a new way of measuring the contribution of each variable to the response which takes into account high correlations among the variables in a data-driven way. |
| Depends: | R (≥ 2.14.0), mvtnorm |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| LazyLoad: | yes |
| NeedsCompilation: | no |
| Packaged: | 2016-12-26 10:05:59 UTC; h |
| Repository: | CRAN |
| Date/Publication: | 2016-12-26 12:25:13 |
Variable Selection via Tilted Correlation Screening Algorithm
Description
Implements an algorithm for variable selection in high-dimensional linear regression using the "tilted correlation", a way of measuring the contribution of each variable to the response which takes into account high correlations among the variables in a data-driven way.
Details
| Package: | tilting |
| Type: | Package |
| Version: | 1.1.1 |
| Date: | 2016-12-22 |
| License: | GPL (>= 2) |
| LazyLoad: | yes |
The main function of the package is tilting.
Author(s)
Haeran Cho, Piotr Fryzlewicz
Maintainer: Haeran Cho <haeran.cho@bristol.ac.ukk>
References
H. Cho and P. Fryzlewicz (2012) High-dimensional variable selection via tilting, Journal of the Royal Statistical Society Series B, 74: 593-622.
Examples
X <- matrix(rnorm(100*100), 100, 100) # 100-by-100 design matrix
y <- apply(X[,1:5], 1, sum)+rnorm(100) # first five variables are significant
tilt <- tilting(X, y, op=2)
tilt$active.hat # returns the finally selected variables
Compute the L2 norm of each column
Description
The function returns a vector containing the L2 norm of each column for a given matrix.
Usage
col.norm(X)
Arguments
X |
a matrix for which the column norms are computed. |
Value
A vector containing the L2 norm of the columns of X is returned.
Author(s)
Haeran Cho
Select a threshold for sample correlation matrix
Description
The function selects a threshold for sample correlation matrix.
Usage
get.thr(C, n, p, max.num = 1, alpha = NULL, step = NULL)
Arguments
C |
sample correlation matrix of a design matrix. |
n |
the number of observations of the design matrix. |
p |
the number of variables of the design matrix. |
max.num |
the number of times for which the threshold selection procedure is repeated. Usually max.num==1 is used. |
alpha |
The level at which the false discovery rate is controlled. When alpha==NULL, it is set to be 1/sqrt(p). |
step |
the size of a step taken when screening the p(p-1)/2 off-diagonal elements of C. |
Value
thr |
selected threshold. |
thr.seq |
when max.num>1, the sequence of thresholds selected at each iteration. |
Author(s)
Haeran Cho
References
H. Cho and P. Fryzlewicz (2012) High-dimensional variable selection via tilting, Journal of the Royal Statistical Society Series B, 74: 593-622.
Compute the least squares estimate on a given index set
Description
The function returns an estimate of the coefficient vector for a linear regression problem by setting the coefficients corresponding to a given index set to be the least squares estimate and the rest to be equal to zero.
Usage
lse.beta(X, y, active = NULL)
Arguments
X |
design matrix. |
y |
response vector. |
active |
the index set on which the least squares estimate is computed. |
Value
An estimate of the coefficient vector is returned as above. If active==NULL, a vector of zeros is returned.
Author(s)
Haeran Cho
Compute the projection matrix onto a given set of variables
Description
The function computes the projection matrix onto a set of columns of a given matrix.
Usage
projection(X, active = NULL)
Arguments
X |
a matrix containing the columns onto which the projection matrix is computed. |
active |
an index set of the columns of X. |
Value
Returns the projection matrix onto the columns of "X" whose indices are included in "active". When active==NULL, a null matrix is returned.
Author(s)
Haeran Cho
Select the final model
Description
The function returns the final model as a subset of the active set chosen by Tilted Correlation Screening algorithm, for which the extended BIC is minimised.
Usage
select.model(bic.seq, active)
Arguments
bic.seq |
the sequence of extended BIC at each iteration. |
active |
the index set of selected variables by Tilted Correlation Screening algorithm. |
Value
The index set of finally selected variables is returned.
Author(s)
Haeran Cho
Hard-threshold a matrix
Description
For a given matrix and a threshold, the function performs element-wise hard-thresholding based on the absolute value of each element.
Usage
thresh(C, alph, eps = 1e-10)
Arguments
C |
a matrix on which the hard-thresholding is performed. |
alph |
threshold. |
eps |
effective zero. |
Value
Returns the matrix C after hard-thresholding.
Author(s)
Haeran Cho
Variable selection via Tilted Correlation Screening algorithm
Description
Given a design matrix and a response vector, the function selects a threshold for the sample correlation matrix, computes an adaptive measure for the contribution of each variable to the response variable based on the thus-thresholded sample correlation matrix, and chooses a variable at each iteration. Once variables are selected in the "active" set, the extended BIC is used for the final model selection.
Usage
tilting(X, y, thr.step = NULL, thr.rep = 1, max.size = NULL, max.count = NULL,
op = 2, bic.gamma = 1, eps = 1e-10)
Arguments
X |
design matrix. |
y |
response vector. |
thr.step |
a step size used for threshold selection. When thr.step==NULL, it is chosen automatically. |
thr.rep |
the number of times for which the threshold selection procedure is repeated. |
max.size |
the maximum number of the variables conditional on which the contribution of each variable to the response is measured (when max.size==NULL, it is set to be half the number of observations). |
max.count |
the maximum number of iterations. |
op |
when op==1, rescaling 1 is used to compute the tilted correlation. If op==2, rescaling 2 is used. |
bic.gamma |
a parameter used to compute the extended BIC. |
eps |
an effective zero. |
Value
active |
active set containing the variables selected over the iterations. |
thr.seq |
a sequence of thresholds selected over the iterations. |
bic.seq |
extended BIC computed over the iterations. |
active.hat |
finally chosen variables using the extended BIC. |
Author(s)
Haeran Cho
References
H. Cho and P. Fryzlewicz (2012) High-dimensional variable selection via tilting, Journal of the Royal Statistical Society Series B, 74: 593-622.
Examples
X<-matrix(rnorm(100*100), 100, 100) # 100-by-100 design matrix
y<-apply(X[,1:5], 1, sum)+rnorm(100) # first five variables are significant
tilt<-tilting(X, y, op=2)
tilt$active.hat # returns the finally selected variables