sparseCov: Sparse covariance matrix estimator with error control
In sparseMatEst: Sparse Matrix Estimation and Inference

Description Usage Arguments Details Value Author(s) References Examples

Given a data matrix, sparseCov estimates the covariance matrix for the data under the assumption that the true covariance matrix is sparse, i.e. that most of the off-diagonal entries are equal to zero.

1	sparseCov(dat, alf = 0.5, iter = 10, pnrm = Inf, THRSH = "hard")

`dat`	nxk data matrix, n observations, k dimensions
`alf`	false positive rate in [0,1], Default is 0.5
`iter`	number of iterates, Default is 10
`pnrm`	norm to use, Default = Inf
`THRSH`	Type of thresholding used; Takes values: hard, soft, adpt, scad.

The algorithm begins with the empirical covariance estimator as computed by cov. It then iteratively computes covariance estimators with false positive rates of alf, alf^2, and so on until iter estimators have been constructed.

The norm chosen determines the topology on the space of matrices. pnorm defaults to Inf being the operator norm or maximal eigenvalue. This is theoretically justified to work in the references. Other norms could be considered, but their performance is not a strong.

Four thresholding methods are implemented. THRSH defaults to hard thresholding where small matrix entries are set to zero while large entries are not affected. The soft and adpt thresholds shrink all entries towards zero. The scad threshold interpolates between hard and soft thresholding. More details can be found in the references.

a list of arrays containing iter+1 sparse covariance matrices corresponding to false positive rates of 1, alf, alf^2,..., alf^iter. Each list corresponds to one type of thresholding chosen by THRSH.

Adam B Kashlak kashlak@ualberta.ca

Kashlak, Adam B., and Linglong Kong. "A concentration inequality based methodology for sparse covariance estimation." arXiv preprint arXiv:1705.02679 (2017).

# Generate four sparse covariance matrix estimators
# with false positive rates of 0.5, 0.25, 0.125,
# and 0.0625
n = 30
k = 50
dat = matrix(rnorm(n*k),n,k)
out = sparseCov( dat, alf=0.5, iter=4, THRSH=c("hard","soft") )
  par(mfcol=c(2,2))
  lab = c(1,0.5,0.5^2,0.5^3,0.5^4);
  for( i in 2:5 )
    image( out$hard[,,i]!=0, main=lab[i] )
  for( i in 2:5 )
    image( log(abs(out$hard[,,i] - out$soft[,,i])), main=lab[i] )