Bayesian Regularization for Graphical Models With Unequal Shrinkage
Bayesian Regularization for Graphical Models With Unequal Shrinkage
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DOI：
10.1080/01621459.2018.1482755
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发表时间：
2019-07-03
影响因子：
3.7
通讯作者：
Liang, Feng
中科院分区：
文献类型：
--
作者：
Gan, Lingrui;Narisetty, Naveen N.;Liang, Feng
我们考虑一个用于估计高维稀疏精度矩阵的贝叶斯框架，其中自适应收缩和稀疏性由拉普拉斯先验的混合引起。除了从贝叶斯的角度讨论我们的配方，我们调查的MAP（最大后验概率）估计从惩罚似然的角度，产生了一个新的非凸惩罚近似的l（0）惩罚。最佳误差率估计一致性的各种矩阵规范沿着与选择一致性稀疏结构恢复的唯一MAP估计在温和的条件下。为了快速和有效的计算，EM算法被提出来计算精度矩阵的MAP估计和（近似）底层稀疏结构的边缘上的后验概率。通过大量的模拟研究和一个真实的应用到一个呼叫中心的数据，我们已经证明了我们的方法与现有的替代品相比，优良的性能。本文的补充材料可在网上查阅。
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 l(0) 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.