4期

最新文章

• ONLINE CHANGE-POINT DETECTION FOR MATRIX-VALUED TIME SERIES WITH LATENT TWO-WAY FACTOR STRUCTURE AI翻译
  作者：He, Yong; Kong, Xinbing; Trapani, Lorenzo; Yu, Long
  作者单位：Shandong University; Nanjing Audit University; University of Pavia; Shanghai University of Finance & Economics
  摘要：This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases (e.g., in the presence of a change in the loadings, or if a new factor emerges). Based on this, we propose two families of procedures-one based on the fluctuations of partial sums, and one based o...
• HEAVY-TAILED BAYESIAN NONPARAMETRIC ADAPTATION AI翻译
  作者：Agapiou, Sergios; Castillo, Ismael
  作者单位：University of Cyprus; Sorbonne Universite; Universite Paris Cite
  摘要：We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy-tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior distributions achieve adaptive rates of contraction in the minimax sense (up to logarithmic factors) without the need to sample hyperparameters. Unlike many existing procedures, where a form of direct model (or estimator) selection is performed, the method can be se...
• 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 ...
• 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...
• HIGHER-ORDER COVERAGE ERRORS OF BATCHING METHODS VIA EDGEWORTH EXPANSIONS ON t-STATISTICS AI翻译
  作者：He, Shengyi; Lam, Henry
  作者单位：Columbia University
  摘要：While batching methods have been widely used in simulation and statistics, their higher-order coverage behaviors and relative advantages in this regard remain open. We develop techniques to obtain higher-order coverage errors for batching methods by building Edgeworth-type expansions on t-statistics. The coefficients in these expansions are intricate analytically, but we provide algorithms to estimate the coefficients of the n(-1) error terms via Monte Carlo simulation. We provide insights on ...
• MAJORITY VOTE FOR DISTRIBUTED DIFFERENTIALLY PRIVATE SIGN SELECTION AI翻译
  作者：Liu, Weidong; Tu, Jiyuan; Mao, Xiaojun; Chen, Xi
  作者单位：Shanghai Jiao Tong University; Shanghai University of Finance & Economics; New York University
  摘要：Privacy-preserving data analysis has become more prevalent in recent years. In this study, we propose a distributed group differentially private Majority Vote mechanism, for the sign selection problem in a distributed setup. To achieve this, we apply the iterative peeling to the stability function and use the exponential mechanism to recover the signs. For enhanced applicability, we study the private sign selection for mean estimation and linear regression problems, in distributed systems. Our...
• SHARP MULTIPLE TESTING BOUNDARY FOR SPARSE SEQUENCES AI翻译
  作者：Abraham, Kweku; Castillo, Ismael; Roquain, Etienne
  作者单位：University of Cambridge; Universite Paris Cite; Sorbonne Universite
  摘要：This work investigates multiple testing by considering minimax separation rates in the sparse sequence model, when the testing risk is measured as the sum FDR+FNR + FNR (False Discovery Rate plus False Negative Rate). First, using the popular beta-min separation condition, with all nonzero signals separated from 0 by at least some amount, we determine the sharp minimax testing risk asymptotically and thereby explicitly describe the transition from achievable multiple testing with vanishing ris...
• STATISTICAL INFERENCE FOR ROUGH VOLATILITY: MINIMAX THEORY AI翻译
  作者：Chong, Carsten H.; Hoffmann, Marc; Liu, Yanghui; Rosenbaum, Mathieu; Szymansky, Gregoire
  作者单位：Hong Kong University of Science & Technology; Universite PSL; Universite Paris-Dauphine; City University of New York (CUNY) System; Baruch College (CUNY); Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：In recent years, rough volatility models have gained considerable attention in quantitative finance. In this paradigm, the stochastic volatility of the price of an asset has quantitative properties similar to that of a fractional Brownian motion with small Hurst index H < 1/2. In this work, we provide the first rigorous statistical analysis of the problem of estimating H from historical observations of the underlying asset. We establish minimax lower bounds and design optimal procedures based ...
• HOW DO NOISE TAILS IMPACT ON DEEP RELU NETWORKS? AI翻译
  作者：Fan, Jianqian; Gu, Yihong; Zhou, Wen-Xin
  作者单位：Princeton University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
  摘要：This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite pth moment. We unveil how the optimal rate of convergence depends on p, the degree of smoothness and the intrinsic dimension in a class of nonparametric regression functions with hierarchical composition structure when both the adaptive Huber loss and deep ReLU neural networks are used. This optimal rate of convergence cannot be obtained by the o...