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作者：Weng, Haolei; Maleki, Arian; Zheng, Le
作者单位：Columbia University; Columbia University
摘要：We study the problem of estimating a sparse vector beta is an element of R-p from the response variables y = X beta + omega, where omega similar to N(0, sigma(2)(omega) I-nxn), under the following high-dimensional asymptotic regime: given a fixed number delta, p -> infinity, while n/p -> delta. We consider the popular class of l(q)-regularized least squares (LQLS), a.k.a. bridge estimators, given by the optimization problem (beta) over cap(lambda, q) is an element of arg min(beta) 1/2 parallel...
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作者：Jiang, Bai; Wu, Tung-Yu; Jin, Yifan; Wong, Wing H.
作者单位：Stanford University; Stanford University
摘要：The Contrastive Divergence ( CD) algorithm has achieved notable success in training energy-based models including Restricted Boltzmann Machines and played a key role in the emergence of deep learning. The idea of this algorithm is to approximate the intractable term in the exact gradient of the log-likelihood function by using short Markov chain Monte Carlo (MCMC) runs. The approximate gradient is computationally-cheap but biased. Whether and why the CD algorithm provides an asymptotically con...
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作者：Gu, Mengyang; Wang, Xiaojing; Berger, James O.
作者单位：Johns Hopkins University; University of Connecticut; Duke University
摘要：We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through various generalized maximum likelihood methods, mostly involving finding posterior modes; this is because full Bayesian analysis in computer model emulation is typically prohibitively expensive. The posterior modes that are studied arise from...
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作者：Heinrich, Philippe; Kahn, Jonas
作者单位：Universite de Lille; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study the rates of estimation of finite mixing distributions, that is, the parameters of the mixture. We prove that under some regularity and strong identifiability conditions, around a given mixing distribution with m(0) components, the optimal local minimax rate of estimation of a mixing distribution with m components is n(-1/(4(m-m0)+2)). This corrects a previous paper by Chen [Ann. Statist. 23 (1995) 221-233]. By contrast, it turns out that there are estimators with a (nonuniform) point...
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作者：Javanmard, Adel; Montanari, Andrea
作者单位：University of Southern California; Stanford University; Stanford University
摘要：Performing statistical inference in high-dimensional models is challenging because of the lack of precise information on the distribution of high-dimensional regularized estimators. Here, we consider linear regression in the high-dimensional regime p >> n and the Lasso estimator: we would like to perform inference on the parameter vector theta*is an element of R-p. Important progress has been achieved in computing confidence intervals and p-values for single coordinates. theta(i)*, i is an ele...
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作者：Escobar-Bach, Mikael; Goegebeur, Yuri; Guillou, Armelle
作者单位：University of Southern Denmark; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We consider the robust estimation of the Pickands dependence function in the random covariate framework. Our estimator is based on local estimation with the minimum density power divergence criterion. We provide the main asymptotic properties, in particular the convergence of the stochastic process, correctly normalized, towards a tight centered Gaussian process. The finite sample performance of our estimator is evaluated with a simulation study involving both uncontaminated and contaminated s...
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作者：Mak, Simon; Joseph, V. Roshan
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：This paper introduces a new way to compact a continuous probability distribution F into a set of representative points called support points. These points are obtained by minimizing the energy distance, a statistical potential measure initially proposed by Szekely and Rizzo [InterStat 5 (2004) 1-6] for testing goodness-of-fit. The energy distance has two appealing features. First, its distance-based structure allows us to exploit the duality between powers of the Euclidean distance and its Fou...
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作者：Evans, Robin J.
作者单位：University of Oxford
摘要：Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper, we provide a complete algebraic characterization of these models when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular, these two models h...
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作者：Collier, Olivier; Comminges, Laetitia; Tsybakov, Alexandre B.; Verzelen, Nicolas
作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Ecole Polytechnique; INRAE
摘要：We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta is an element of R-d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a nonasymptotic rate of convergence that differs from the minimax rate at most by a logarithmic factor. We also show that this optimal adaptive rate cannot be improved when s is unknown. Furthermore, we address the issue of simultaneous adaptation to s and...
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作者：Godolphin, Janet
作者单位：University of Surrey
摘要：Designs with blocks of size two have numerous applications. In experimental situations where observation loss is common, it is important for a design to be robust against breakdown. For designs with one treatment factor and a single blocking factor, with blocks of size two, conditions for connectivity and robustness are obtained using combinatorial arguments and results from graph theory. Lower bounds are given for the breakdown number in terms of design parameters. For designs with equal or n...
