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具有差异化收缩的图模型贝叶斯正则化AI 解读

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…

Skinny Gibbs：一致且可扩展的模型选择 Gibbs 采样器AI 解读

Naveen N. Narisettya, Juan Shenb* & Xuming Heca Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, ILb Department of Statistics, Fudan University, Shanghai, Chinac Department of Statistics, University of Michigan, Ann Arbor, MICONTACT Juan Shen shenjuan@fudan.edu.cn Department of Statistics, Fudan University, Shanghai, ChinaColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary…

函数型数据的极端深度及其应用AI 解读

We propose a new notion called “extremal depth” (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme “outlyingness.” ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous…