TITLE: High dimensional inverse covariance matrix estimation

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.