2016

最新文章

• NONPARAMETRIC STOCHASTIC APPROXIMATION WITH LARGE STEP-SIZES AI翻译
  作者：Dieuleveut, Aymeric; Bach, Francis
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function within an RKHS H, even if the optimal predictor (i.e., the conditional expectation) is not in H. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized least-mean-square algorith...
• OPTIMAL ESTIMATION FOR THE FUNCTIONAL COX MODEL AI翻译
  作者：Qu, Simeng; Wang, Jane-Ling; Wang, Xiao
  作者单位：Purdue University System; Purdue University; University of California System; University of California Davis
  摘要：Functional covariates are common in many medical, biodemographic and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coe...
• GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES AI翻译
  作者：Doss, Charles R.; Wellner, Jon A.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle
  摘要：We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on R. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n(-2/5) when -1 < s < infinity where s = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of s-concave densities with s < -1.
• FUNCTIONAL LINEAR REGRESSION WITH POINTS OF IMPACT AI翻译
  作者：Kneip, Alois; Poss, Dominik; Sarda, Pascal
  作者单位：University of Bonn; University of Bonn; University of Bonn; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
  摘要：The paper considers functional linear regression, where scalar responses Y1,..., Yn are modeled in dependence of i.i.d. random functions X1,..., Xn. We study a generalization of the classical functional linear regression model. It is assumed that there exists an unknown number of points of impact, that is, discrete observation times where the corresponding functional values possess significant influences on the response variable. In addition to estimating a functional slope parameter, the prob...
• ESTIMATION IN EXPONENTIAL FAMILIES ON PERMUTATIONS AI翻译
  作者：Mukherjee, Sumit
  作者单位：Columbia University
  摘要：Asymptotics of the normalizing constant are computed for a class of one parameter exponential families on permutations which include Mallows models with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE and a computable approximation of the MLE are shown to be consistent. The pseudo-likelihood estimator of Besag is shown to be root n-consistent. An iterative algorithm (IPFP) is proved to converge to the limiting normalizing constant. The Mallows model with Kendall's tau i...
• ON THE COMPUTATIONAL COMPLEXITY OF HIGH-DIMENSIONAL BAYESIAN VARIABLE SELECTION AI翻译
  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 ...
• APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RENYI DIVERGENCES AI翻译
  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...
• PARTIALLY LINEAR ADDITIVE QUANTILE REGRESSION IN ULTRA-HIGH DIMENSION AI翻译
  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...
• RATE EXACT BAYESIAN ADAPTATION WITH MODIFIED BLOCK PRIORS AI翻译
  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.
• A NEW PRIOR FOR DISCRETE DAG MODELS WITH A RESTRICTED SET OF DIRECTIONS AI翻译
  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...