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作者：Jiang, Tiefeng; Pham, Tuan
作者单位：The Chinese University of Hong Kong, Shenzhen; University of Texas System; University of Texas Austin
摘要：Given a random sample from a multivariate normal distribution whose covariance matrix is a Toeplitz matrix, we study the largest off-diagonal entry of the sample correlation matrix. Assuming the multivariate normal distribution has the covariance structure of an autoregressive sequence, we establish a phase transition in the limiting distribution of the largest off-diagonal entry. We show that the limiting distributions are of Gumbel-type (with different parameters), depending on how large or ...
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作者：Chen, Hongrui; Long, Jihao; Wu, Lei
作者单位：Stanford University; Peking University
摘要：We consider the problem of learning functions within the Fp,pi and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks as well as kernel methods. Leveraging tools from information-based complexity (IBC), we establish a dual equivalence between approximation and estimation and then apply it to study the learning of the preceding function spaces. The duality allows us to focus on the more tractable problem between approximation and est...
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作者：Li, Mengbing; Shi, Chengchun; Wu, Zhenke; Fryzlewicz, Piotr
作者单位：University of Michigan System; University of Michigan; University of London; London School Economics & Political Science
摘要：We consider reinforcement learning (RL) in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the state transition and reward functions to be constant over time. However, this assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a model-free test to assess the stationarity of the opti...
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作者：Zhou, Hang; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：We develop an inferential tool kit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end, we introduce conditional profile average transport costs, where we compare distance profiles that correspond to one-dimensional distributions of probability mass falling into balls of increasing radius through the optimal transport cost when moving from one distance profile to another....
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作者：Bhattacharya, Anirban; Pati, Debdeep; Yang, Yun
作者单位：Texas A&M University System; Texas A&M University College Station; University of Wisconsin System; University of Wisconsin Madison; University System of Maryland; University of Maryland College Park
摘要：As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable efficacy and superior efficiency. Several recent works provide theoretical justifications of VI by proving its statistical optimality for parameter estimation under various settings; meanwhile, formal analysis on the algorithmic convergence aspects of VI is s...
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作者：Leanthous, G.; Eorgiadis, A. G.; Epski, O. V.
作者单位：Maynooth University; Trinity College Dublin; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：This is the second part of the research project initiated in Cleanthous, Georgiadis and Lepski (2024a). We deal with the problem of the adaptive estimation of the L-2-norm of a probability density on & Ropf;(d), d >= 1, from independent observations. The unknown density is assumed to be uniformly bounded by unknown constant and to belong to the union of balls in the isotropic/anisotropic Nikolskii's spaces. In Cleanthous, Georgiadis and Lepski (2024a), we have proved that the optimally adaptiv...
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作者：Qiu, Jingkun; Chen, Song Xi; Shao, Qi-Man
作者单位：Peking University; Tsinghua University; Southern University of Science & Technology
摘要：Berry-Esseen type bounds for Gaussian approximation of standardized sums have been extensively studied under exponential type moment conditions. In this paper, a Cramer type moderate deviation theorem is established for self-normalized Gaussian approximation under finite moment conditions. More specifically, let X-1, X-2, ...,X-n be i.i.d. R-p-valued random vectors with zero means. Let Sn,j =Sigma(n)(i=1) Xij and V-2 (n,j) = Sigma(n)(i=1) X-2 (ij) . We show that if the correlation matrix of X-...
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作者：Amorino, Chiara; Gloter, Arnaud
作者单位：University of Luxembourg; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：Our research analyses the balance between maintaining privacy and preserving statistical accuracy when dealing with multivariate data that is subject to componentwise local differential privacy (CLDP). With CLDP, each component of the private data is made public through a separate privacy channel. This allows for varying levels of privacy protection for different components or for the privatization of each component by different entities, each with their own distinct privacy policies. It also ...
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作者：Leanthous, C.; Eorgiadis, A. G.; Epski, O., V
作者单位：Maynooth University; Trinity College Dublin; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We deal with the problem of the adaptive estimation of the L-2-norm of a probability density on R-d, d >= 1, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the union of balls in the isotropic/anisotropic Nikolskii's spaces. We will show that the optimally adaptive estimators over the collection of considered functional classes do no exist. Also, in the framework of an abstract density model we present several generic lower bounds related ...
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作者：Lin, Licong; Khamaru, Koulik; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; Rutgers University System; Rutgers University New Brunswick; Massachusetts Institute of Technology (MIT)
摘要：Many standard estimators, when applied to adaptively collected data, fail to be asymptotically normal, thereby complicating the construction of confidence intervals. We address this challenge in a semiparametric context: estimating the parameter vector of a generalized linear regression model contaminated by a nonparametric nuisance component. We construct suitably weighted estimating equations that account for adaptivity in data collection and provide conditions under which the associated est...
