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作者：Argiento, Raffaele; De Iorio, Maria
作者单位：University of Bergamo; National University of Singapore
摘要：Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce a new class of priors: the Normalized Independent Point Process. We investigate the probabilistic properties of this new class and present many special cases. In particular, we provide an explicit formula for the distribution of the implied partition, as well as the posterior characterization of the new process in t...
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作者：Spector, Asher; Janson, Lucas
作者单位：Harvard University
摘要：Model-X knockoffs (J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 (2018) 551-577) allows analysts to perform feature selection using almost any machine learning algorithm while provably controlling the expected proportion of false discoveries. This procedure involves constructing synthetic variables, called knockoffs, which effectively act as controls during feature selection. The gold standard for constructing knockoffs has been to minimize the mean absolute correlation (MAC) between features an...
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作者：LI, Cheng
作者单位：National University of Singapore
摘要：Gaussian process models typically contain finite-dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging model with an isotropic Matern covariance function, which has many applications in spatial statistics. We show that when the dimen-sion of domain is less than or equal to three, the joint posterior distribution of the microergodic parameter and the range par...
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作者：Efromovich, Sam
作者单位：University of Texas System; University of Texas Dallas
摘要：It is well known that estimation of a bivariate cumulative distribution function of a pair of right censored lifetimes presents challenges unparalleled to the univariate case where a product-limit Kaplan-Meyer's methodology typically yields optimal estimation, and the literature on optimal estimation of the joint probability density is next to none. The paper, for the first time in the survival analysis literature, develops the theory and methodology of sharp minimax and adaptive nonparametric...
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作者：Giordano, Matteo; Ray, Kolyan
作者单位：University of Cambridge; Imperial College London
摘要：We study nonparametric Bayesian models for reversible multidimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure. The general theorem is applied to Gaussian priors and p-exponential priors, which are shown to converge to the truth at the optimal nonparametric rate over...
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作者：Goodman, Jesse
作者单位：University of Auckland
摘要：The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of n unobserved i.i.d. terms, the basic classical result is that the relative error in the density is of order 1/ n. If instead the approximation is interpreted as a likelihood and maximised as a function of model parameters, the result is an approximation to the maximum likelihood estimate (MLE) that can be m...
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作者：Javanmard, Adel; Soltanolkotabi, Mahdi
作者单位：University of Southern California; University of Southern California
摘要：Despite the wide empirical success of modern machine learning algorithms and models in a multitude of applications, they are known to be highly susceptible to seemingly small indiscernible perturbations to the input data known as adversarial attacks. A variety of recent adversarial training procedures have been proposed to remedy this issue. Despite the success of such procedures at increasing accuracy on adversarially perturbed inputs or robust accuracy, these techniques often reduce accuracy...
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作者：Bing, Xin; Ning, Yang; Xu, Yaosheng
作者单位：Cornell University
摘要：A prominent concern of scientific investigators is the presence of unobserved hidden variables in association analysis. Ignoring hidden variables often yields biased statistical results and misleading scientific conclusions. Motivated by this practical issue, this paper studies the multivariate response regression with hidden variables, Y = (psi*)(T) X + (B*)(T) Z + E, where Y is an element of R-m is the response vector, X is an element of R-p is the observable feature, Z is an element of R-K ...
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作者：Luo, Yuetian; Zhang, Anru R.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Duke University
摘要：This paper studies the statistical and computational limits of high-order clustering with planted structures. We focus on two clustering models, constant high-order clustering (CHC) and rank-one higher-order clustering (ROHC), and study the methods and theory for testing whether a cluster exists (detection) and identifying the support of cluster (recovery). Specifically, we identify the sharp boundaries of signal-to-noise ratio for which CHC and ROHC detection/recovery are statistically possib...
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作者：Mukherjee, Gourab; Johnstone, Iain M.
作者单位：University of Southern California; Stanford University; Stanford University
摘要：We study predictive density estimation under Kullback-Leibler loss in l(0)-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. Fundamental for this is a new risk decomposition for sparse, or spike-and-slab priors. A surprise is the existence of a phase transition in the future-to-past variance ratio r. For r < r(0) = (root 5 - 1)/4, the natural discrete prior ceases to be asymptotically optimal. Instead, fo...
