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Sparse Inverse Covariance Estimation with Calibration
Tuo Zhao · Han Liu

Sun Dec 08 02:00 PM -- 06:00 PM (PST) @ Harrah's Special Events Center, 2nd Floor #None
We propose a semiparametric procedure for estimating high dimensional sparse inverse covariance matrix. Our method, named ALICE, is applicable to the elliptical family. Computationally, we develop an efficient dual inexact iterative projection (${\rm D_2}$P) algorithm based on the alternating direction method of multipliers (ADMM). Theoretically, we prove that the ALICE estimator achieves the parametric rate of convergence in both parameter estimation and model selection. Moreover, ALICE calibrates regularizations when estimating each column of the inverse covariance matrix. So it not only is asymptotically tuning free, but also achieves an improved finite sample performance. We present numerical simulations to support our theory, and a real data example to illustrate the effectiveness of the proposed estimator.

Author Information

Tuo Zhao (Johns Hopkins University Princeton University)
Han Liu (Tencent AI Lab)

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