-
作者：Liang, Tengyuan; Rakhlin, Alexander
作者单位：University of Chicago; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：In the absence of explicit regularization, Kernel Ridgeless Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable geometric properties of ...
-
作者：Yang, Yun; Pati, Debdeep; Bhattacharya, Anirban
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Texas A&M University System; Texas A&M University College Station
摘要：We provide statistical guarantees for a family of variational approximations to Bayesian posterior distributions, called alpha-VB, which has close connections with variational approximations of tempered posteriors in the literature. The standard variational approximation is a special case of alpha-VB with alpha = 1. When alpha is an element of (0, 1], a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the objective function...
-
作者：Goes, John; Lerman, Gilad; Nadler, Boaz
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Weizmann Institute of Science
摘要：Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental task in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Toward bridging this gap, in this work we consider estimating a sparse shape matrix from n samples following a possibly heavy-tailed elliptical distribution. We propose estimators based on thresholding either Tyler's M-estimator or its regularized variant. We prove that in the joi...
-
作者：Belitser, Eduard; Ghosal, Subhashis
作者单位：Vrije Universiteit Amsterdam; North Carolina State University
摘要：We propose an empirical Bayes method for high-dimensional linear regression models. Following an oracle approach that quantifies the error locally for each possible value of the parameter, we show that an empirical Bayes posterior contracts at the optimal rate at all parameters and leads to uniform size-optimal credible balls with guaranteed coverage under an excessive bias restriction condition. This condition gives rise to a new slicing of the entire space that is suitable for ensuring unifo...
-
作者：Javanmard, Adel; Mondelli, Marco; Montanari, Andrea
作者单位：University of Southern California; Institute of Science & Technology - Austria; Stanford University; Stanford University
摘要：Fitting a function by using linear combinations of a large number N of simple components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to kernel regression, to boosting. In general, the resulting risk minimization problem is nonconvex and is solved by gradient descent or its variants. Unfortunately, little is known about global convergence properties of these approaches. Here, we consider the proble...
-
作者：Rohde, Angelika; Steinberger, Lukas
作者单位：University of Freiburg; University of Vienna
摘要：We study the problem of estimating a functional theta(P) of an unknown probability distribution P is an element of P in which the original iid sample X-1,..., X-n is kept private even from the statistician via an alpha-local differential privacy constraint. Let omega TV denote the modulus of continuity of the functional theta over P with respect to total variation distance. For a large class of loss functions l and a fixed privacy level alpha, we prove that the privatized minimax risk is equiv...
-
作者：Gu, Yuqi; Xu, Gongjun
作者单位：University of Michigan System; University of Michigan
摘要：Latent class models have wide applications in social and biological sciences. In many applications, prespecified restrictions are imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners' assumptions about how the observed responses depend on subjects' latent traits. Though widely used in various fields, such restricted latent class models suffer from nonidentifiability due to their discreteness nature and complex structure of restrictions. This ...
-
作者：Szabo, Botond; van Zanten, Harry
作者单位：Leiden University; Leiden University - Excl LUMC; Vrije Universiteit Amsterdam
摘要：We study estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.
-
作者：Shen, Jinqi; Hsing, Tailen
作者单位：University of Michigan System; University of Michigan
摘要：This paper considers a wide range of issues concerning the estimation of the Hurst function of a multifractional Brownian motion when the process is observed on a regular grid. A theoretical lower bound for the minimax risk of this inference problem is established for a wide class of smooth Hurst functions. We also propose a new nonparametric estimator and show that it is rate optimal. Implementation issues of the estimator including how to overcome the presence of a nuisance parameter and cho...
-
作者：Li, Xinran; Ding, Peng; Rubin, Donald B.
作者单位：University of Pennsylvania; University of California System; University of California Berkeley; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the treatment factors to satisfy certain covariate balance criteria, possibly conforming to the tiers of factorial effects and covariates based on their relative importances. This is rerandomization in factorial experiments. We study the asymptotic properties of...
