The paper introduces a method for estimating the inverse covariance matrix in high-dimensional settings, focusing on sparse estimators. The method, called SPICE (Sparse Permutation Invariant Covariance Estimator), uses a penalized normal likelihood approach with a lasso-type penalty to enforce sparsity. The authors establish a rate of convergence in the Frobenius norm as both the data dimension \( p \) and sample size \( n \) grow, showing that the rate depends on the sparsity of the true concentration matrix. They also show that a correlation-based version of the method exhibits better rates in the operator norm. A fast iterative algorithm based on the Cholesky decomposition is derived, which remains permutation invariant. The method is compared to other estimators on simulated data and a real data example of tumor tissue classification using gene expression data. The results demonstrate the effectiveness of SPICE in high-dimensional settings, particularly for sparse concentration matrices.The paper introduces a method for estimating the inverse covariance matrix in high-dimensional settings, focusing on sparse estimators. The method, called SPICE (Sparse Permutation Invariant Covariance Estimator), uses a penalized normal likelihood approach with a lasso-type penalty to enforce sparsity. The authors establish a rate of convergence in the Frobenius norm as both the data dimension \( p \) and sample size \( n \) grow, showing that the rate depends on the sparsity of the true concentration matrix. They also show that a correlation-based version of the method exhibits better rates in the operator norm. A fast iterative algorithm based on the Cholesky decomposition is derived, which remains permutation invariant. The method is compared to other estimators on simulated data and a real data example of tumor tissue classification using gene expression data. The results demonstrate the effectiveness of SPICE in high-dimensional settings, particularly for sparse concentration matrices.