**SPEAKER:** Ming Yuan

**ABSTRACT:**

More and more often in practice, one needs to estimate a high dimensional covariance matrix. In this talk, we discuss how this task is often related to the sparsity of the inverse covariance matrix. In particular, we consider estimating a (inverse) covariance matrix that can be well approximated by ``sparse'' matrices. Taking advantage of the connection between multivariate linear regression and entries of the inverse covariance matrix, we introduce an estimating procedure that can effectively exploit such ``sparsity''. The proposed method can be computed using linear programming and therefore has the potential to be used in very high dimensional problems. Oracle inequalities are established for the estimation error in terms of several operator norms, showing that the method is adaptive to different types of sparsity of the problem.

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