Title（标题）：Estimation of high dimensional inverse covariance matrix

Speaker（汇报人）：Dr. Liu Weidong, from University of Pennsylvania, USA

Time（功夫）：2010年12月15日（周三）下午3:00-4:00

Place（地址）：北京大学理科一号楼1418教室

Abstract（提要）：In this presentation, I will talk about the estimation of sparse inverse covariance matrices. A constrained l₁minimization method is proposed for estimating a sparse inverse covariance matrix. 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 trues-sparse precision matrix under the spectral norm iss(log(p/n))^1/2when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise l_∞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.