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作者：Steinberger, Lukas
作者单位：University of Vienna
摘要：We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter estimation is a classical and well-studied problem in mathematical statistics, it leads to several nontrivial obstacles that need to be tackled when dealing with the LDP case. Starting from a regular parametric model P = (P theta)theta E Theta, Theta C Rp, for the i.i.d. unobserved sensitive data X 1 , ...,Xn, we est...
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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 ...
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作者：Nickl, Richard
作者单位：University of Cambridge
摘要：Let (X-t) be a reflected diffusion process in a bounded convex domain in R-d, solving the stochastic differential equation dX(t) = del f(X-t)dt+root 2f(X-t)dW(t), t >= 0, with W-t a d-dimensional Brownian motion. The data X-0, X-D, ..., X-ND consist of discrete measurements and the time interval D between consecutive observations is fixed so that one cannot 'zoom' into the observed path of the process. The goal is to infer the diffusivity f and the associated transition operator P-t,P-f. We pr...
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作者：Fan, Zhou; Lederman, Roy R.; Sun, Yi; Wang, Tianhao; Xu, Sheng
作者单位：Yale University; University of Chicago
摘要：Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the function domain. We describe a stratification of the Fisher information eigenvalues according to transcendence degrees of graded pieces of the algebra of group invariants, and we relate critical points of the loglikelihood landscape to a sequence of moment ...
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作者：Lei, Jing; Zhang, Anru R.; Zhu, Zihan
作者单位：Carnegie Mellon University; Duke University; University of Pennsylvania
摘要：We study the problem of community recovery and detection in multi- layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two- block model, we reveal a computational barrier for such multilayer stochastic block models that does not exist for its single-layer counterpart: When there are no computational constraints, the density threshold depends linearly on the number of layers. However, when restricte...
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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...
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作者：Mao, Cheng; Wu, Yihong; Xu, Jiaming; Yu, Sophie h
作者单位：University System of Georgia; Georgia Institute of Technology; Yale University; Duke University; University of Pennsylvania
摘要：We propose a new procedure for testing whether two networks are edgecorrelated through some latent vertex correspondence. The test statistic is based on counting the cooccurrences of signed trees for a family of nonisomorphic trees. When the two networks are Erdos-R & eacute;nyi random graphs G(n, q) that are either independent or correlated with correlation coefficient rho, our test runs in n(2+o(1)) time and succeeds with high probability as n -> infinity, provided that n min{q, 1 - q} >= n(...
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作者：Zhang, Anderson Ye
作者单位：University of Pennsylvania
摘要：We study the performance of the spectral method for the phase synchronization problem with additive Gaussian noises and incomplete data. The spectral method utilizes the leading eigenvector of the data matrix followed by a normalization step. We prove that it achieves the minimax lower bound of the problem with a matching leading constant under a squared 2 pound loss. This shows that the spectral method has the same performance as more sophisticated procedures including maximum likelihood esti...
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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...
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作者：Chaudhuri, Anamitra; Fellouris, Georgios
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：The problem of joint sequential detection and isolation is considered in the context of multiple, not necessarily independent, data streams. A multiple testing framework is proposed, where each hypothesis corresponds to a different subset of data streams, the sample size is a stopping time of the observations, and the probabilities of four kinds of error are controlled below distinct, user-specified levels. Two of these errors reflect the detection component of the formulation, whereas the oth...
