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作者：Reiss, Markus; Wahl, Martin
作者单位：Humboldt University of Berlin
摘要：We analyse the reconstruction error of principal component analysis (PCA) and prove nonasymptotic upper bounds for the corresponding excess risk. These bounds unify and improve existing upper bounds from the literature. In particular, they give oracle inequalities under mild eigenvalue conditions. The bounds reveal that the excess risk differs significantly from usually considered subspace distances based on canonical angles. Our approach relies on the analysis of empirical spectral projectors...
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作者：Chan, Hock Peng
作者单位：National University of Singapore
摘要：Lai and Robbins (Adv. in Appl. Math. 6 (1985) 4-22) and Lai (Ann. Statist. 15 (1987) 1091-1114) provided efficient parametric solutions to the multi-armed bandit problem, showing that arm allocation via upper confidence bounds (UCB) achieves minimum regret. These bounds are constructed from the Kullback-Leibler information of the reward distributions, estimated from specified parametric families. In recent years, there has been renewed interest in the multi-armed bandit problem due to new appl...
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作者：Lee, Stephen M. S.; Yang, Puyudi
作者单位：University of Hong Kong; University of California System; University of California Davis
摘要：Suppose that a confidence region is desired for a subvector theta of a multidimensional parameter xi = (theta, psi), based on an M-estimator (xi) over cap (n) = ((theta) over cap (n )= (psi) over cap (n)) calculated from a random sample of size n. Under nonstandard conditions (xi) over cap (n) often converges at a nonregular rate (xi) over cap (n), in which case consistent estimation of the distribution of r(n) ((theta) over cap (n) - theta), a pivot commonly chosen for confidence region const...
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作者：Zou, Changliang; Wang, Guanghui; Li, Runze
作者单位：Nankai University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalizat...
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作者：Han, Yuefeng; Wu, Wei Biao
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Chicago
摘要：The paper introduces a new test for testing structures of covariances for high dimensional vectors and the data dimension can be much larger than the sample size. Under proper normalization, central and noncentral limit theorems are established. The asymptotic theory is attained without imposing any explicit restriction between data dimension and sample size. To facilitate the related statistical inference, we propose the balanced Rademacher weighted differencing scheme, which is also the dele...
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作者：Li, Zeng; Han, Fang; Yao, Jianfeng
作者单位：Southern University of Science & Technology; University of Washington; University of Washington Seattle; University of Hong Kong
摘要：This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow proportionally. The form of the joint limiting distribution is applied to conduct Johnson-Graybill-type tests, a family of approaches testing for signals in a statistical model. For this, higher order correction is further made, helping alleviate the impact of finit...
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作者：Huang, Hanwen
作者单位：University System of Georgia; University of Georgia
摘要：Mean square error (MSE) of the estimator can be used to evaluate the performance of a regression model. In this paper, we derive the asymptotic MSE of l(1)-penalized robust estimators in the limit of both sample size n and dimension p going to infinity with fixed ratio n/p -> delta. We focus on the l(1)-penalized least absolute deviation and l(1)-penalized Huber's regressions. Our analytic study shows the appearance of a sharp phase transition in the two-dimensional sparsity-undersampling phas...
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作者：Li, Haoran; Aue, Alexander; Paul, Debashis; Peng, Jie; Wang, Pei
作者单位：University of California System; University of California Davis; Icahn School of Medicine at Mount Sinai
摘要：We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling's T-2. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the ridge-regularized Hotelli...
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作者：Bresler, Guy; Karzand, Mina
作者单位：Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison
摘要：We study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables given values of some other subset of variables. Virtually all previous work on graphical model learning has focused on recovering the true underlying graph. We define a distance (small set TV or ssTV) between distributions P and Q by taking the maximum, over all...
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作者：El Alaoui, Ahmed; Krzakala, Florent; Jordan, Michael
作者单位：Stanford University; Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; University of California System; University of California Berkeley
摘要：We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the nonspiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a spectral nature, and that it is degenerate above. This establishes the maximal region of contiguity between the planted an...
