The Annals of Statistics

最新文章

• STATISTICAL INFERENCE FOR FOUR-REGIME SEGMENTED REGRESSION MODELS AI翻译
  作者：Yan, Han; Chen, Song Xi
  作者单位：Peking University; Tsinghua University
  摘要：Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model for temporally dependent data with segmenting boundaries depending on multivariate covariates with nondiminishing boundary effects. A mixed integer quadratic programming algorithm is formulated to facilitate the least square estimation of the regression and ...
• ASYMPTOTIC NORMALITY AND OPTIMALITY IN NONSMOOTH STOCHASTIC APPROXIMATION AI翻译
  作者：Davis, Damek; Drusvyatskiy, Dmitriy; Jiang, Liwei
  作者单位：Cornell University; University of Washington; University of Washington Seattle
  摘要：In their seminal work, Polyak and Juditsky showed that stochastic approximation algorithms for solving smooth equations enjoy a central limit theorem. Moreover, it has since been argued that the asymptotic covariance of the method is best possible among any estimation procedure in a local minimax sense of H & aacute;jek and Le Cam. A long-standing open question in this line of work is whether similar guarantees hold for important nonsmooth problems, such as stochastic nonlinear programming or ...
• THE RIGHT COMPLEXITY MEASURE IN LOCALLY PRIVATE ESTIMATION: IT IS NOT THE FISHER INFORMATION AI翻译
  作者：Duchi, John C.; Ruan, Feng
  作者单位：Stanford University; Northwestern University
  摘要：We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning problems by developing the local minimax risk. In contrast to approaches based on worst-case (minimax) error, which are conservative, this allows us to evaluate the difficulty of individual problem instances and delineate the possibilities for adaptation in private...
• STATISTICAL-COMPUTATIONAL TRADE-OFFS IN TENSOR PCA AND RELATED PROBLEMS VIA COMMUNICATION COMPLEXITY AI翻译
  作者：Dudeja, Rishabh; Hsu, Daniel
  作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University
  摘要：Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA exhibits a statistical-computational gap, that is, a sample size regime where the problem is information-theoretically solvable but conjectured to be computationally hard. This paper derives computational lower bounds on the run -time of memory bounded algor...
• TENSOR-ON-TENSOR REGRESSION: RIEMANNIAN OPTIMIZATION, OVER-PARAMETERIZATION, STATISTICAL-COMPUTATIONAL GAP AND THEIR INTERPLAY AI翻译
  作者：Luo, Yuetian; Zhang, Anru r.
  作者单位：University of Chicago; Duke University; Duke University
  摘要：We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without prior knowledge of its intrinsic rank. We propose the Riemethods and cope with the challenge of unknown rank by studying the effect of rank over-parameterization. We provide the first convergence guarantee for the general tensor-on-tensor regression by showing that RGD and RGN respectively converge linearly and quadratically to a st...
• INCREASING DIMENSION ASYMPTOTICS FOR TWO-WAY CROSSED MIXED EFFECT MODELS AI翻译
  作者：Lyu, Ziyang; Sisson, S. A.; Welsh, A. H.
  作者单位：University of New South Wales Sydney; University of New South Wales Sydney; Australian National University
  摘要：This paper presents asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model, when the number of rows, columns, and the number of observations per cell tend to infinity. The relative growth rate for the number of rows, columns, and cells is unrestricted, whether considered pairwise or collectively. Under very mild conditions (which include moment conditions instead of requiring normality for either the random ...
• FUNDAMENTAL LIMITS OF LOW-RANK MATRIX ESTIMATION WITH DIVERGING ASPECT RATIOS AI翻译
  作者：Montanari, Andrea; Wu, Yuchen
  作者单位：Stanford University; Stanford University; University of Pennsylvania
  摘要：We consider the problem of estimating the factors of a low-rank n x d matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. Here, we characterize the asymptotics of the minimum estimation error under the assumption that the distribution of the en...
• E-STATISTICS, GROUP INVARIANCE AND ANYTIME-VALID TESTING AI翻译
  作者：Perez-Ortiz, Muriel Felipe; Lardy, Tyron; Heide, Rianne; Gruenwald, Peter D.
  作者单位：Eindhoven University of Technology; Leiden University - Excl LUMC; Leiden University; Vrije Universiteit Amsterdam
  摘要：We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant statistic. We show that among all e-statistics, invariant or not, the likelihood ratio of the maximally invariant statistic is GROW, both in the absolute and in the relative sense, and that an anytime-valid test can be based on it. The GROW e-statistic is equal...
• DIMENSION-FREE MIXING TIMES OF GIBBS SAMPLERS FOR BAYESIAN HIERARCHICAL MODELS AI翻译
  作者：Ascolani, Filippo; Zanella, Giacomo
  作者单位：Duke University; Bocconi University
  摘要：Gibbs samplers are popular algorithms to approximate posterior distributions arising from Bayesian hierarchical models. Despite their popularity and good empirical performance, however, there are still relatively few quantitative results on their convergence properties, for example, much less than for gradient-based sampling methods. In this work, we analyse the behaviour of total variation mixing times of Gibbs samplers targeting hierarchical models using tools from Bayesian asymptotics. We o...
• TRANSFER LEARNING FOR CONTEXTUAL MULTI-ARMED BANDITS AI翻译
  作者：Cai, Changxiao; Cai, T. Tony; Li, Hongzhe
  作者单位：University of Michigan System; University of Michigan; University of Pennsylvania; University of Pennsylvania
  摘要：Motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected from source bandits before the start of the target bandit learning. The minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. The results quantify the contribution of the data from the source d...