-
作者：Bickel, Peter J.; Chen, Aiyou; Zhao, Yunpeng; Levina, Elizaveta; Zhu, Ji
作者单位：University of California System; University of California Berkeley; Alphabet Inc.; Google Incorporated; George Mason University; University of Michigan System; University of Michigan
摘要：This note corrects an error in two related proofs of consistency of community detection: under stochastic block models by Bickel and Chen [Proc. Natl. Acad. ScL USA 106 (2009) 21068-21073] and under degree-corrected stochastic block model by Zhao, Levina and Zhu [Ann. Statist. 40 (2012) 2266-2292].
-
作者：Lei, Jing; Vu, Vincent Q.
作者单位：Carnegie Mellon University; University System of Ohio; Ohio State University
摘要：The presence of a sparse truth has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? What can be said about the results of sparse PCA without assuming a sparse and unique truth? We ans...
-
作者：Hu, Linwei; Yang, Min; Stufken, John
作者单位：University System of Georgia; University of Georgia; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Arizona State University; Arizona State University-Tempe
摘要：We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stuficen [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and...
-
作者：Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong
作者单位：Stanford University; Harvard University; Harvard University
摘要：In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a functio...
-
作者：Bruna, Joan; Mallat, Stephane; Bacry, Emmanuel; Muzy, Jean-Francois
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes, fractional Brownian motions,...
-
作者：Chen, Hao; Zhang, Nancy
作者单位：University of California System; University of California Davis; University of Pennsylvania
摘要：We consider the testing and estimation of change-points-locations where the distribution abruptly changes-in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations, is proposed. The graph-based approach is nonparametric, and can be applied to any data set as long as an informative similarity measure on the sample space can be defined. Accurate analytic approximations to the significance of graph-based scan statistics for both...
-
作者：Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd
作者单位：Aalto University; University of California System; University of California Berkeley
摘要：Mixtures of r independent distributions for two discrete random variables can be represented by matrices of nonnegative rank r. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the set of fixed points of the Expectation-Maximization algorithm, and we study the boundary of the space of matrices with nonnegative rank at most 3. Both of these sets correspond to algebraic varietie...
-
作者：Amonenk, Inga S.; Robinson, John
作者单位：University of Sydney
摘要：We introduce a nonparametric test statistic for the permutation test in complete block designs. We find the region in which the statistic exists and consider particularly its properties on the boundary of the region. Further, we prove that saddlepoint approximations for tail probabilities can be obtained inside the interior of this region. Finally, numerical examples are given showing that both accuracy and power of the new statistic improves on these properties of the classical F-statistic un...
-
作者：Sherlock, Chris; Thiery, Alexandre H.; Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：Lancaster University; National University of Singapore; University of Warwick; University of Toronto
摘要：We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on the target distribution, we obtain limiting formulae for the acceptance rate and for the expected squared jump distance, as the dimension of the target approaches infinity, under the assumption that the noise in the estimate of the log-target is additive an...
-
作者：Cai, T. Tony; Zhang, Anru
作者单位：University of Pennsylvania
摘要：Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed est...
