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作者：Szabo, Botond; Vuursteen, Lasse; van Zanten, Harry
作者单位：Bocconi University; Delft University of Technology; Vrije Universiteit Amsterdam
摘要：We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central ma-chine is limited to b bits. We investigate both the d- and infinite-dimensional signal detection problem under Gaussian white noise. We also derive dis-tributed testing algorithms reaching the theoretical lower bounds. Our results show that distributed testing is subject to fundamentally dif-ferent phenomena that are not observed in distributed esti...
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作者：Barber, Rina Foygel; Candes, Emmanuel J.; Ramdas, Aaditya; Tibshirani, Ryan J.
作者单位：University of Chicago; Stanford University; Carnegie Mellon University
摘要：Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model fitting algorithm as a function of the data. However, exchangeability is often violated when predictive models are deployed in practice. For example, if the data distribution drifts over time, then the data points are no longer ex-changeable; moreover, in such se...
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作者：Bellec, Pierre C.; Zhang, Cun-Hui
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：New upper bounds are developed for the L2 distance between & xi;/ Var[& xi;]1/2 and linear and quadratic functions of z & SIM; N(0, In) for random vari-ables of the form & xi; = z ⠃f (z) - div f (z). The linear approximation yields a central limit theorem when the squared norm of f (z) dominates the squared Frobenius norm of backward difference f (z) in expectation.Applications of this normal approximation are given for the asymptotic normality of debiased estimators in linear regression with...
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作者：Panigrahi, Snigdha
作者单位：University of Michigan System; University of Michigan
摘要：Complex studies involve many steps. Selecting promising findings based on pilot data is a first step. As more observations are collected, the investigator must decide how to combine the new data with the pilot data to construct valid selective inference. Carving, introduced by Fithian, Sun and Taylor (2014), enables the reuse of pilot data during selective inference and accounts for overoptimism from the selection process. However, currently, carving is only justified for parametric models suc...
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作者：Zhang, Linfan; Amini, Arash a.
作者单位：University of California System; University of California Los Angeles
摘要：We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of n multinomial distributions with d(1), ... , d(n) observations. In the context of network models, the num-ber of multinomials, n, grows much faster than the number of observations, di, corresponding to the degree of node i, hence the setting deviates from classical asymptotics. We show that a simple adjustm...
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作者：Avella-medina, Marco; Bradshaw, Casey; Loh, Po-ling
作者单位：Columbia University; University of Cambridge
摘要：We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions. First, we show that robust statistics can be used in conjunction with noisy gradient descent or noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively. We establish local and global convergence guarantees, under both local strong convexity and self-co...
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作者：Bu, Zhiqi; Klusowski, Jason M.; Rush, Cynthia; Su, Weijie J.
作者单位：University of Pennsylvania; Princeton University; Columbia University; University of Pennsylvania
摘要：Sorted l(1) regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this paper, we study how this rel-atively new regularization technique improves variable selection by charac-terizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I error and power. Assuming a regime of linea...
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作者：Christgau, Alexander Mangulad; Petersen, Lasse; Hansen, Niels richard
作者单位：University of Copenhagen
摘要：Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolu-tion of one process is directly influenced by another process given the histo-ries of additional processes, and it is important for the description and learn-ing of causal relations among processes. We develop a model-free framework for testing the hypothesis that a counting process is conditionally locally in-dependent of another process. To this end...
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作者：Tang, Rong; Yang, Yun
作者单位：Hong Kong University of Science & Technology; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Statistical inference from high-dimensional data with low-dimensional structures has recently attracted a lot of attention. In machine learning, deep generative modelling approaches implicitly estimate distributions of complex objects by creating new samples from the underlying distribution, and have achieved great success in generating synthetic realistic-looking images and texts. A key step in these approaches is the extraction of latent features or representations (encoding) that can be use...
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作者：Berrett, Thomas B.; Samworth, Richard J.
作者单位：University of Warwick; University of Cambridge
摘要：We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a diver-gence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the con-struction of asymptotically valid confidenc...
