A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

Details A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

2011-02-10

arxiv.org/abs/1102.2233v1

Statistics

Methodology

To appear in Journal of the American Statistical Association

Scientific paper

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In particular, it is shown that the rate of convergence between the estimator and the true $s$-sparse precision matrix under the spectral norm is $s\sqrt{\log p/n}$ when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise $L_{\infty}$ norm and Frobenius norm are also presented. In addition, graphical model selection is considered. The procedure is easily implementable by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset. The procedure performs favorably in comparison to existing methods.

Affiliated with

Also associated with

No associations

Rating

A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-631533