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作者：Kwon, Caleb; Mbakop, Eric
作者单位：Harvard University; University of Calgary
摘要：We propose a novel estimator for the number of mixture components (denoted by M) in a nonparametric finite mixture model. The setting that we consider is one where the analyst has repeated observations of K >= 2 variables that are conditionally independent given a finitely supported latent variable withM support points. Under a mild assumption on the joint distribution of the observed and latent variables, we show that an integral operator T that is identified from the data has rank equal to M...
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作者：Di Benedetto, Giuseppe; Caron, Francois; Teh, Yee Whye
作者单位：University of Oxford
摘要：Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in various fields. While the exchangeability assumption is sensible in many cases, it implies that the size of the clusters necessarily grows linearly with the sample size, and such feature may be undesirable for some applications. We present here a flexible class of nonexchangeable random partition ...
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作者：Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Ganguly, Shirshendu
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：We study graphons as a nonparametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. In contrast to previous work, we relax the usual boundedness assumption for the generating graphon and instead assume only integrability, so that we can handle networks that have long tails in their degree distributions. We also relax the usual assumption that the graphon is defined on the unit interval, to allow latent p...
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作者：Eaton, Morris L.; George, Edward, I
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Pennsylvania
摘要：When statistical decision theory was emerging as a promising new paradigm, Charles Stein was to play a major role in the development of minimax theory for invariant statistical problems. In some of his earliest work with Gil Hunt, he set out to prove that, in problems where invariant procedures have constant risk, any best invariant test would be minimax among all tests. Although finding it not quite true in general, this led to the legendary Hunt-Stein theorem, which established the result un...
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作者：Gao, Lan; Fan, Yingying; Lv, Jinchi; Shao, Qi-Man
作者单位：University of Southern California; Southern University of Science & Technology; Chinese University of Hong Kong
摘要：Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remain...
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作者：Kohler, Michael; Langer, Sophie
作者单位：Technical University of Darmstadt
摘要：Recent results in nonparametric regression show that deep learning, that is, neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this paper, we show that we can get similar results also for least squa...
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作者：Daudel, Kamelia; Douc, Randal; Portier, Francois
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
摘要：This paper introduces the (alpha, Gamma)-descent, an iterative algorithm which operates on measures and performs alpha-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used variational approximation by adding a prior on the variational parameters in the form of a measure. We prove that for a rich family of functions Gamma, this algorithm leads at each step to a systematic decrease in the alpha-divergence and derive convergence results. Our fra...
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作者：Mure, Joseph
作者单位：Electricite de France (EDF); Universite Paris Cite
摘要：In a seminal article, Berger, De Oliveira and Sanso [J. Amer. Statist. Assoc. 96 (2001) 1361-1374] compare several objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernel. The reference prior distribution stands out among them insofar as it always leads to a proper posterior. They prove this result for rough correlation kernels: Spherical, Exponential with power rho < 2, Matern with smoothness nu < 1. This paper provides a proof for smooth ...
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作者：Neykov, Matey; Balakrishnan, Sivaraman; Wasserman, Larry
作者单位：Carnegie Mellon University
摘要：We consider the problem of conditional independence testing of X and Y given Z where X, Y and Z are three real random variables and Z is continuous. We focus on two main cases-when X and Y are both discrete, and when X and Y are both continuous. In view of recent results on conditional independence testing [Ann. Statist. 48 (2020) 1514-1538], one cannot hope to design nontrivial tests, which control the type I error for all absolutely continuous conditionally independent distributions, while s...
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作者：Kulaitis, Gytis; Munk, Axel; Werner, Frank
作者单位：University of Gottingen; University of Wurzburg
摘要：As a general rule of thumb the resolution of a light microscope (i.e., the ability to discern objects) is predominantly described by the full width at half maximum (FWHM) of its point spread function (psf)-the diameter of the blurring density at half of its maximum. Classical wave optics suggests a linear relationship between FWHM and resolution also manifested in the well-known Abbe and Rayleigh criteria, dating back to the end of the 19th century. However, during the last two decades convent...
