4期

最新文章

• UNIVERSALITY OF REGULARIZED REGRESSION ESTIMATORS IN HIGH DIMENSIONS AI翻译
  作者：Han, Qiyang; Shen, Yandi
  作者单位：Rutgers University System; Rutgers University New Brunswick; University of Chicago
  摘要：The Convex Gaussian Min-Max Theorem (CGMT) has emerged as a prominent theoretical tool for analyzing the precise stochastic behavior of various statistical estimators in the so-called high-dimensional proportional regime, where the sample size and the signal dimension are of the same order. However, a well-recognized limitation of the existing CGMT machinery rests in its stringent requirement on the exact Gaussianity of the design matrix, therefore rendering the obtained precise high-dimension...
• RELAXING THE IID ASSUMPTION: ADAPTIVELY MINIMAX OPTIMAL REGRET VIA ROOT-ENTROPIC REGULARIZATION AI翻译
  作者：Bilodeau, Blair; Negrea, Jeffrey; Roy, Daniel M.
  作者单位：University of Toronto; University of Waterloo
  摘要：We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semiadversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm-long known to be minimax (rate) optimal in the adversarial regime-was recently shown to ...
• A CROSS-VALIDATION FRAMEWORK FOR SIGNAL DENOISING WITH APPLICATIONS TO TREND FILTERING, DYADIC CART AND BEYOND AI翻译
  作者：Chaudhuri, Anamitra; Chatterjee, Sabyasachi
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：This paper formulates a general cross-validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as trend filtering and dyadic CART. The resulting crossvalidated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross-validated versions of trend filtering or dyadic CART. To illustrate the generality of the f...
• LEARNING LOW-DIMENSIONAL NONLINEAR STRUCTURES FROM HIGH-DIMENSIONAL NOISY DATA: AN INTEGRAL OPERATOR APPROACH AI翻译
  作者：Ding, Xiucai; Ma, Rong
  作者单位：University of California System; University of California Davis; Stanford University
  摘要：We propose a kernel-spectral embedding algorithm for learning lowdimensional nonlinear structures from noisy and high-dimensional observations, where the data sets are assumed to be sampled from a nonlinear manifold model and corrupted by high-dimensional noise. The algorithm employs an adaptive bandwidth selection procedure which does not rely on prior knowledge of the underlying manifold. The obtained low-dimensional embeddings can be further utilized for downstream purposes such as data vis...
• BOOTSTRAPPING PERSISTENT BETTI NUMBERS AND OTHER STABILIZING STATISTICS AI翻译
  作者：Roycraft, Benjamin; Krebs, Johannes; Polonik, Wolfgang
  作者单位：University of California System; University of California Davis
  摘要：We investigate multivariate bootstrap procedures for general stabilizing statistics, with specific application to topological data analysis. The work relates to other general results in the area of stabilizing statistics, including central limit theorems for geometric and topological functionals of Poisson and binomial processes in the critical regime, where limit theorems prove difficult to use in practice, motivating the use of a bootstrap approach. A smoothed bootstrap procedure is shown to...