A Constrained ℓ 1 Minimization Approach to Sparse Precision Matrix Estimation

This article proposes a constrained ℓ1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is when the population distribution has either exponential-type tails or polynomial-type tails. We present convergence rates under the elementwise ℓ∞ norm and Frobenius norm. In addition, we consider graphical model selection. The procedure is easily implemented by linear programming. Numerical performance of the estimator is investigated using both…

• NS
  National Science Foundation

  Awards: DMS-0854973, 0854973