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作者：Bhattacharya, Sohom; Fan, Jianqing; Mukherjee, Debarghya
作者单位：State University System of Florida; University of Florida; Princeton University; Boston University
摘要：Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the literature. However, most of the studies require the input dimension to be fixed, and consequently, they ignore the effect of dimension on the rate of convergence and hamper their applications to modern big data with high dimensionality. In this paper, we bridge t...
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作者：Durante, Daniele; Pozza, Francesco; Szabo, Botond
作者单位：Bocconi University; Bocconi University
摘要：Gaussian deterministic approximations are routinely employed in Bayesian statistics to ease inference when the target posterior is intractable. While these approximations are justified, in asymptotic regimes, by Bernstein-von Mises type results, in practice the expected Gaussian behavior might poorly represent the actual shape of the target posterior, thus affecting approximation accuracy. Motivated by these considerations, we derive an improved class of closed-form and valid deterministic app...
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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...
