| Type: | Package |
| Title: | Covariance and Inverse Covariance Matrix Estimation Using Joint Penalty |
| Version: | 1.0 |
| Date: | 2015-08-20 |
| Author: | Ashwini Maurya |
| Maintainer: | Ashwini Maurya <mauryaas@msu.edu> |
| Description: | A Joint PENalty Estimation of Covariance and Inverse Covariance Matrices. |
| Depends: | mvtnorm(≥ 1.0-2), stats(≥ 2.15.0), |
| License: | GPL-2 |
| NeedsCompilation: | no |
| Packaged: | 2015-09-06 23:34:02 UTC; STT User |
| Repository: | CRAN |
| Date/Publication: | 2015-09-16 10:05:02 |
Covariance and Inverse Covariance Matrix Estimation Using Joint Penalty
Description
A Joint PENalty Estimation of Covariance and Inverse Covariance Matrices.
Details
The DESCRIPTION file:
| Package: | JPEN |
| Type: | Package |
| Title: | Covariance and Inverse Covariance Matrix Estimation Using Joint Penalty |
| Version: | 1.0 |
| Date: | 2015-08-20 |
| Author: | Ashwini Maurya |
| Maintainer: | Ashwini Maurya <mauryaas@msu.edu> |
| Description: | A Joint PENalty Estimation of Covariance and Inverse Covariance Matrices. |
| Depends: | mvtnorm(>= 1.0-2), stats(>= 2.15.0), |
| License: | GPL-2 |
Index of help topics:
JPEN-package Covariance and Inverse Covariance Matrix
Estimation Using Joint Penalty
f.K.fold Subset the data into K fold, training and test
data.
jpen JPEN Estimate of covariance matrix
jpen.inv JPEN estimate of inverse cov matrix
jpen.inv.tune Tuning parameter Selection for inverse
covariance matrix estimation based on
minimization of Gaussian log-likelihood.
jpen.tune Tuning parameter selection based on
minimization of 5 fold mean square error.
lamvec returns a vector of values of lambda for given
value of gamma
tr Trace of matrix
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu. Ashwini Maurya Maintainer: Ashwini Maurya <mauryaas@msu.edu>
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
See Also
jpen,jpen.inv
Subset the data into K fold, training and test data.
Description
K-fold subsetting.
Usage
f.K.fold(Nobs, K = 5)Arguments
Nobs |
n is number of observations |
K |
K is number of folds, typically 5 fold. |
Details
K-fold subset of observations into training and test data.
Value
Returns the index for K-fold training and test data subsets.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
Examples
n=100;K=5;cv=f.K.fold(n,K);
JPEN Estimate of covariance matrix
Description
Estimate of covariance Matrix using Joint Penalty Method
Usage
jpen(S, gam, lam=NULL)
Arguments
S |
Sample covariance matrix. |
gam |
Tuning parameter gamma. gam is non-negative. |
lam |
Tuning parameter lambda. lam is non-negative. |
Details
This function returns an estimate of covariance matrix using Joint Penalty method.
Value
Estimate of Covariance Matrix.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
See Also
jpen.tune, jpen.inv
Examples
p=10;n=100;
Sig=diag(p);
y=rmvnorm(n,mean=rep(0,p),sigma=Sig);
gam=1.0;S=var(y);
lam=2/p;
Sighat=jpen(S,gam,lam);
JPEN estimate of inverse cov matrix
Description
A well conditioned and sparse estimate of inverse covariance matrix using Joint Penalty
Usage
jpen.inv(S, gam, lam=NULL)
Arguments
S |
Sample cov matrix or a positive definite estimate based on covariance matrix. |
gam |
gam is tuning parameter for eigenvalues shrinkage. |
lam |
lam is tuning parameter for sparsity. |
Details
Estimates a well conditioned and sparse inverse covariance matrix using Joint Penalty. If input matrix is singular or nearly singular, a JPEN estimate of covariance matrix is used in place of S.
Value
Returns a well conditioned and positive inverse covariance matrix.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu.
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
See Also
jpen,jpen.tune,jpen.inv.tune
Examples
p=10;n=100;
Sig=diag(p);
y=rmvnorm(n,mean=rep(0,p),sigma=Sig);
S=var(y);
gam=1.0;
lam=2*max(abs(S[col(S)!=row(S)]))/p;
Omghat=jpen.inv(var(y),gam,lam);
Tuning parameter Selection for inverse covariance matrix estimation based on minimization of Gaussian log-likelihood.
Description
Returns optimal values of tuning parameters lambda and gamma
Usage
jpen.inv.tune(Ytr, gama, lambda=NULL)
Arguments
Ytr |
Ytr is matrix of observations. |
gama |
A vector of gamma values. |
lambda |
Optional vector of values of lambda. If optional, the algorithm automatically calculates 10 values of lambda for each gamma and finds the optimal values of (lambda,gamma) that minimizes the negative of Gaussian likelihood function using K-fold cross validation. |
Details
Returns the value of optimal tuning parameters. The function uses K-fold cross validation to select the best tuning parameter from among a set of of values of lambda and gamma.
Value
Returns the optimal values of lambda and gamma.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu.
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
See Also
jpen
Examples
p=10;n=100;
Sig=diag(p);
y=rmvnorm(n,mean=rep(0,p),sigma=Sig);
gama=c(0.5,1.0);
opt=jpen.inv.tune(var(y),gama);
Tuning parameter selection based on minimization of 5 fold mean square error.
Description
Returns optimal values of tuning parameters lambda and gamma which minimizes the K-fold crossvalidation error on
Usage
jpen.tune(Ytr, gama, lambda=NULL)
Arguments
Ytr |
Ytr is matrix of observations. |
gama |
gama is vector of gamma values. gamma is non-negative. |
lambda |
lambda is vector of lambda values. lambda is non-negative. |
Details
Returns the value of optimal tuning parameters. The function uses K-fold cross validation to select the best tuning parameter from among a set of of values of lambda and gamma.
Value
Returns the optimal values of lambda and gamma.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu.
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
See Also
jpen
Examples
p=10;n=100;
Sig=diag(p);
y=rmvnorm(n,mean=rep(0,p),sigma=Sig);
gama=c(0.5,1.0);
opt=jpen.tune(Ytr=y,gama);
returns a vector of values of lambda for given value of gamma
Description
returns 10 values of lambda for each gamma.
Usage
lamvec(c, gam, p)
Arguments
c |
c is absolute maximum of off-diagonal entries of sample covariance matrix. |
gam |
gamma is a non-negative constant. |
p |
p is number of rows/columns of matrix. |
Details
The lamvec function retuns a 10 values of lambda for each value of gamma. A larger value of lambda yields sparse estimate but need not be positive definite, however at least one combination of (lambda, gamma) will yield a positive definite solution. If two different combination of (lambda, gamma) yeilds same cross validation error, a larger values of lambda will be selected which results in more sparse solution.
Value
A vector of values of lambda for each combination of gama. By choosing c as the maximum of off-diagonal elements of sample covariance matrix, the largest value of lambda yields an estimate which diagonal matrix with elements proportional to the diagonal elements of sample covariance matrix.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
See Also
jpen, jpen.inv, jpen.tune, jpen.tune.inv
Examples
p=10;n=100;Sig=diag(p);
y=rmvnorm(n,mean=rep(0,p),sigma=Sig);
gam=c(0.5);
S=var(y);
c=max(abs(S[row(S)!=col(S)]));
lambda=lamvec(c,gam,p);
Trace of matrix
Description
Returns the trace of a matrix
Usage
tr(A)
Arguments
A |
A is the input matrix. |
Details
Returns the trace (sum of diagonal elements )of input matrix).
Value
Trace of input matrix.
Author(s)
Ashwini Maurya, Email: mauryaas@msu.edu
References
A Well Conditioned and Sparse Estimate of Covariance and Inverse Covariance Matrix Using Joint Penalty. Submitted. http://arxiv.org/pdf/1412.7907v2.pdf
Examples
p=10;n=100;Sig=diag(p);
y=rmvnorm(n,mean=rep(0,p),sigma=Sig);
S=var(y);
tr(S);