-
作者：Igollet, Philippe; Tromme, Austin j.
作者单位：Massachusetts Institute of Technology (MIT); Institut Polytechnique de Paris; ENSAE Paris
摘要：We study the sample complexity of entropic optimal transport in high diadvance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function, which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport and establish parametric rates of convergence for nonparametric regression and classification.
-
作者：Zhan, Haoran; Zhang, Mingke; Xia, Yingcun
作者单位：National University of Singapore; University of Electronic Science & Technology of China
摘要：Projection pursuit regression (PPR) and artificial neural networks (ANNs), both introduced around the same time, share a similar approach to approximating complex structures in data. However, PPR has received far less attention than ANNs and other popular statistical learning methods such as random forests (RF) and support vector machines (SVM). In this paper, we revisit the estimation of PPR and propose an optimal greedy algorithm and an ensemble approach via feature bagging, hereafter referr...
-
作者：Ando, Tomohiro; Li, Ker-chau
作者单位：University of Melbourne; University of California System; University of California Los Angeles
摘要：Noncrossing quantile regression with an emphasis on model misspecification is investigated. While many sophisticated methods for noncrossing quantile have been developed under the assumption of correct model specification, model misspecification and extrapolation are two issues rarely considered in the literature. In this paper, a monotonicity representation for quantile regression models is obtained under simplex embedding, which leads to the simplex quantile regression (SQR) method. SQR mode...
-
作者：Zhou, Yuchen; Chen, Yuxin
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Pennsylvania
摘要：This paper is concerned with estimating the column subspace of a low- rank matrix X star E Rn1xn2 from contaminated data. How to obtain optimal statistical accuracy while accommodating the widest range of signalto-noise ratios (SNRs) becomes particularly challenging in the presence of heteroskedastic noise and unbalanced dimensionality (i.e., n2 >> n1). While the state-of-the-art algorithm HeteroPCA emerges as a powerful solution for solving this problem, it suffers from the curse of ill-condi...
-
作者：Hen, Fan; Mei, Song; Bai, Yu
作者单位：Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; Salesforce
摘要：Modern Reinforcement Learning (RL) is more than just learning the optimal policy; alternative learning goals such as exploring the environment, estimating the underlying model and learning from preference feedback are all of practical importance. While provably sample-efficient algorithms for each specific goal have been proposed, these algorithms often depend strongly on the particular learning goal, and thus admit different structures correspondingly. It is an urging open question whether th...
-
作者：Einmahl, John h. j.; Krajina, Andrea; Cai, Juan juan
作者单位：Tilburg University; University of Gottingen; Vrije Universiteit Amsterdam
摘要：Multivariate regular variation is a common assumption in the statistics literature and needs to be verified in real-data applications. We develop a novel hypothesis test for multivariate regular variation, employing localized empirical likelihood. We establish the weak convergence of the test statistic to a nonstandard, distribution-free limit and hence can provide universal critical values for the test. We show the very good finite-sample behavior of the procedure through simulations and appl...
-
作者：Luo, Wei
作者单位：Zhejiang University
摘要：Efficient dimension reduction regarding the interaction between two response variables, which facilitates statistical analysis in multiple important application scenarios, was initially discussed by Luo (J. R. Stat. Soc. Ser. B. spaces were introduced, and, under mild conditions on the predictor, they were equated with the family of dual inverse regression subspaces. Besides the general framework, however, limited theory has been proposed to uncover the mystery of these spaces. In this paper, ...
