2023

最新文章

• STATISTICAL INFERENCE ON A CHANGING EXTREME VALUE DEPENDENCE STRUCTURE AI翻译
  作者：Drees, Holger
  作者单位：University of Hamburg
  摘要：We analyze the extreme value dependence of independent, not necesMore specifically, we propose estimators of the spectral measure locally at some time point and of the spectral measures integrated over time. The uniform asymptotic normality of these estimators is proved under suitable nonparametric smoothness and regularity assumptions. We then use the process convergence of the integrated spectral measure to devise consistent tests for the null hypothesis that the spectral measure does not ch...
• NOISY LINEAR INVERSE PROBLEMS UNDER CONVEX CONSTRAINTS: EXACT RISK ASYMPTOTICS IN HIGH DIMENSIONS AI翻译
  作者：Han, Qiyang
  作者单位：Rutgers University System; Rutgers University New Brunswick
  摘要：In the standard Gaussian linear measurement model Y = X mu 0 + xi is an element of Rm with a fixed noise level sigma > 0, we consider the problem of estimating the unknown signal mu 0 under a convex constraint mu 0 is an element of K , where K is a closed convex set in Rn. We show that the risk of the natural convex constrained least squares estimator (LSE) mu?(sigma) can be characterized exactly in high dimensional limits, by that of the convex constrained LSE mu ?seQ K in the corresponding G...
• UNIVERSAL REGRESSION WITH ADVERSARIAL RESPONSES AI翻译
  作者：Blanchard, Moise; Jaillet, Patrick
  作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
  摘要：We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in this regression context. We consider universal consistency, which asks for strong consistency of a learner without restrictions on the value responses. Our analysis shows that such an objective is achievable for a significantly larger class of instance sequen...
• ON HIGH-DIMENSIONAL POISSON MODELS WITH MEASUREMENT ERROR: HYPOTHESIS TESTING FOR NONLINEAR NONCONVEX OPTIMIZATION AI翻译
  作者：Jiang, Fei; Zhou, Yeqing; Liu, Jianxuan; Ma, Yanyuan
  作者单位：University of California System; University of California San Francisco; Tongji University; Syracuse University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
  摘要：We study estimation and testing in the Poisson regression model with noisy high-dimensional covariates, which has wide applications in analyz-ing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a nonconvex target function to minimize. Treating the high -dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive th...
• THE LASSO WITH GENERAL GAUSSIAN DESIGNS WITH APPLICATIONS TO HYPOTHESIS TESTING AI翻译
  作者：Celentano, Michael; Montanari, Andrea; Wei, Yuting
  作者单位：University of California System; University of California Berkeley; Stanford University; University of Pennsylvania
  摘要：The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates p is of the same order or larger than the number of observations n. Classical asymptotic normality theory does not apply to this model due to two fundamental reasons: (1) The regularized risk is nonsmooth; (2) The distance between the estimator 0 ⠂and the true parameters vector 0* cannot be neglected. As a consequence, standard perturbative arguments that are the traditional basis f...
• MINIMAX RATES FOR CONDITIONAL DENSITY ESTIMATION VIA EMPIRICAL ENTROPY AI翻译
  作者：Bilodeau, Blair; Foster, Dylan J.; Roy, Daniel M.
  作者单位：University of Toronto; Microsoft
  摘要：We consider the task of estimating a conditional density using i.i.d. sam-ples from a joint distribution, which is a fundamental problem with applica-tions in both classification and uncertainty quantification for regression. For joint density estimation, minimax rates have been characterized for general density classes in terms of uniform (metric) entropy, a well-studied notion of statistical capacity. When applying these results to conditional density es-timation, the use of uniform entropy-...
• UNIFORM CONSISTENCY IN NONPARAMETRIC MIXTURE MODELS AI翻译
  作者：Aragam, Bryon; Yang, Ruiyi
  作者单位：University of Chicago; Princeton University
  摘要：We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing point -wise consistency results to uniform results. The ...
• POST-SELECTION INFERENCE VIA ALGORITHMIC STABILITY AI翻译
  作者：Zrnic, Tijana; Jordan, Michael I.
  作者单位：University of California System; University of California Berkeley
  摘要：When the target of statistical inference is chosen in a data-driven manner, the guarantees provided by classical theories vanish. We propose a solution to the problem of inference after selection by building on the framework of algorithmic stability, in particular its branch with origins in the field of differential privacy. Stability is achieved via randomization of selection and it serves as a quantitative measure that is sufficient to obtain nontrivial post-selection corrections for classic...
• GAUSSIAN PROCESS REGRESSION IN THE FLAT LIMIT AI翻译
  作者：Barthelme, Simon; Amblard, Pierre-Oliviera; Remblay, Nicolas; Usevich, Konstantin
  作者单位：Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
  摘要：Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused on a large-n asymptotics, characterising the behaviour of GP regression as the amount of data increases. Fixed-sample analysis is much more difficult outside of simple cases, such as locations on a regular grid.In this work, we perform a fixed-sample analys...
• TESTING FOR OUTLIERS WITH CONFORMAL P-VALUES AI翻译
  作者：Bates, Stephen; Candes, Emmanuel; Lei, Lihua; Romano, Yaniv; Sesia, Matteo
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Stanford University; Stanford University; Stanford University; Technion Israel Institute of Technology; Technion Israel Institute of Technology; University of Southern California
  摘要：This paper studies the construction of p-values for nonparametric out-lier detection, from a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a general framework yielding p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively de-pendent and enable exact false discovery r...