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作者：Mukherjee, Gourab; Johnstone, Iain M.
作者单位：University of Southern California; Stanford University
摘要：We consider estimating the predictive density under Kullback-Leibler loss in an l(0) sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Suboptimal performance of the class of plug-in density estimates reflects t...
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作者：Fan, Yingying; Kong, Yinfei; Li, Daoji; Zheng, Zemin
作者单位：University of Southern California; University of Southern California; University of Southern California
摘要：This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (ITS) approach based on transforming the original p-dimensional feature vector is proposed, and in the second step a sparse quadratic discriminant analysis (SQDA) is proposed for further selecting important interactions and main effects and simultaneously conducting cl...
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作者：Sarkar, Purnamrita; Bickel, Peter J.
作者单位：University of Texas System; University of Texas Austin; University of California System; University of California Berkeley
摘要：Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comp...
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作者：Maathuis, Marloes H.; Colombo, Diego
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We generalize Pearl's back-door criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs and/or allow for arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back-door criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explic...
