A Study on Bias Effect on Model Selection Criteria in Graphical Lasso

초록

Graphical lasso is one of the most popular methods to estimate a sparse precision matrix, which is an inverse of a covariance matrix. The objective function of graphical lasso imposes an 1 A study on Bias Effect on Model Selection Criteria in Graphical Lasso Young-Geun Choi1, Seyoung Jeong2, Donghyeon Yu2* 1SK Telecom, Seoul 04539, Korea 2Department of Statistics, Inha University, Incheon 22212, Korea (Received Oct 8, 2018; Revised Nov 4, 2018; Accepted Nov 12, 2018) Abstract Graphical lasso is one of the most popular methods to estimate a sparse precision matrix, which is an inverse of a covariance matrix. The objective function of graphical lasso imposes an ℓ-penalty on the (vectorized) precision matrix, where a tuning parameter controls the strength of the penalization. The selection of the tuning parameter is practically and theoretically important since the performance of the estimation depends on an appropriate choice of tuning parameter. While information criteria (e.g. AIC, BIC, or extended BIC) have been widely used, they require an asymptotically unbiased estimator to select optimal tuning parameter. Thus, the biasedness of the ℓ- regularized estimate in the graphical lasso may lead to a suboptimal tuning. In this paper, we propose a two-staged bias-correction procedure for the graphical lasso, where the first stage runs the usual graphical lasso and the second stage reruns the procedure with an additional constraint that zero estimates at the first stage remain zero

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