TY - JOUR
T1 - Bayesian Regularization for Graphical Models With Unequal Shrinkage
AU - Gan, Lingrui
AU - Narisetty, Naveen N.
AU - Liang, Feng
N1 - Funding Information:
The research is partially supported by the NSF Award DMS - 1811768.
Publisher Copyright:
© 2018, © 2018 American Statistical Association.
PY - 2019/7/3
Y1 - 2019/7/3
N2 - We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new nonconvex penalty approximating the ℓ0 penalty. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator under mild conditions. For fast and efficient computation, an EM algorithm is proposed to compute the MAP estimator of the precision matrix and (approximate) posterior probabilities on the edges of the underlying sparse structure. Through extensive simulation studies and a real application to a call center data, we have demonstrated the fine performance of our method compared with existing alternatives. Supplementary materials for this article are available online.
AB - We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian standpoint, we investigate the MAP (maximum a posteriori) estimator from a penalized likelihood perspective that gives rise to a new nonconvex penalty approximating the ℓ0 penalty. Optimal error rates for estimation consistency in terms of various matrix norms along with selection consistency for sparse structure recovery are shown for the unique MAP estimator under mild conditions. For fast and efficient computation, an EM algorithm is proposed to compute the MAP estimator of the precision matrix and (approximate) posterior probabilities on the edges of the underlying sparse structure. Through extensive simulation studies and a real application to a call center data, we have demonstrated the fine performance of our method compared with existing alternatives. Supplementary materials for this article are available online.
KW - Bayesian regularization
KW - Precision matrix estimation
KW - Sparse Gaussian graphical model
KW - Spike-and-slab priors
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U2 - 10.1080/01621459.2018.1482755
DO - 10.1080/01621459.2018.1482755
M3 - Article
AN - SCOPUS:85052106100
SN - 0162-1459
VL - 114
SP - 1218
EP - 1231
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 527
ER -