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作者：Yang, Yun; Wainwright, Martin J.; Jordan, Michael I.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that the statistical criterion of posterior concentration need not imply the computational desideratum of rapid mixing of the MCMC algorithm. By introducing a truncated sparsity prior ...
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作者：Han, Qiyang; Wellner, Jon A.
作者单位：University of Washington; University of Washington Seattle
摘要：In this paper, we study the approximation and estimation of s-concave densities via Renyi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist. 38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q: if Q(n) -> Q in the Wasserstein metric, then the projec...
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作者：Sherwood, Ben; Wang, Lan
作者单位：Johns Hopkins University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates nonlinearity and circum...
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作者：Gao, Chao; Zhou, Harrison H.
作者单位：Yale University
摘要：A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rate-optimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequence model, Gaussian regression and spectral density estimation.
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作者：Massam, Helene; Wesolowski, Jacek
作者单位：York University - Canada; Warsaw University of Technology
摘要：In this paper, we first develop a new family of conjugate prior distributions for the cell probability parameters of discrete graphical models Markov with respect to a set P of moral directed acyclic graphs with skeleton a given decomposable graph G. This family, which we call the P-Dirichlet, is a generalization of the hyper Dirichlet given in [Ann. Statist. 21 (1993) 12721317]: it keeps the directed strong hyper Markov property for every DAG in P but increases the flexibility in the choice o...
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作者：Chang, Jinyuan; Tang, Cheng Yong; Wu, Yichao
作者单位：Southwestern University of Finance & Economics - China; University of Melbourne; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; North Carolina State University
摘要：We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal non...
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作者：Jin, Jiashun; Wang, Wanjie
作者单位：Carnegie Mellon University; National University of Singapore
摘要：We consider a clustering problem where we observe feature vectors X-i is an element of R-P, i = 1, 2,..., n, from K possible classes. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the modern regime of p >> n, where classical clustering methods face challenges. We propose Influential Features PCA (IF-PCA) as a new clustering procedure. In IF-PCA, we select a small fraction of features with the largest Kolmogorov Smirnov (KS) scores, obtai...
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作者：Stepanova, Natalia A.; Tsybakov, Alexandre B.
作者单位：Carleton University; Institut Polytechnique de Paris; ENSAE Paris
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作者：Karwa, Vishesh; Slavkovic, Aleksandra
作者单位：Carnegie Mellon University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：The beta-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the beta-model, and show that the MLE never exists for the degree partition beta-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of beta-model, a...
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作者：Devroye, Luc; Lerasle, Matthieu; Lugosi, Gabor; Olivetra, Roberto I.
作者单位：McGill University; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Pompeu Fabra University
摘要：We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a nonasymptotic point of view. In particular, we define estimators with a sub-Gaussian behavior even for certain heavy-tailed distributions. We also prove various impossibility results for mean estimators.
