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头脑伟易博
学术钻研会

商务统计与经济计量系讲座

2010-12-10

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

Speaker(报告人):Dr. Liu Weidong, from University of Pennsylvania, USA

Time(时间):2010年12月15日(周三)下昼3:00-4:00

Abstract(摘要):

In this presentation, I will talk about the estimation of sparse inverse covariance matrices. A constrained l1 minimization 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 true s-sparse precision matrix under the spectral norm is s(log( p/n))1/2 when 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.

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