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作者：Wu, Yihong; Yang, Pengkun
作者单位：Yale University; Princeton University
摘要：The method of moments (Philos. Trans. R. Soc. Lond. Ser. A 185 (1894) 71-110) is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially for the important case of mixture models, one frequently needs to contend with the difficulties of non-existence or nonuniqueness of statistically meaningful solutions, as well as the high computational cost of s...
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作者：Bagchi, Pramita; Dette, Holger
作者单位：George Mason University; Ruhr University Bochum
摘要：The assumption of separability is a simplifying and very popular assumption in the analysis of spatiotemporal or hypersurface data structures. It is often made in situations where the covariance structure cannot be easily estimated, for example, because of a small sample size or because of computational storage problems. In this paper we propose a new and very simple test to validate this assumption. Our approach is based on a measure of separability which is zero in the case of separability a...
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作者：Rousseau, Judith; Szabo, Botond
作者单位：University of Oxford; Leiden University - Excl LUMC; Leiden University
摘要：We investigate the frequentist coverage properties of (certain) Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To overcome this problem (in context of sieve type of priors), we introduce an extra assumption on the functional parameters, the so-called general polished tail condition. We then show that under standard assumptions, both the hierarchical and empirical B...
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作者：Ghoshdastidar, Debarghya; Gutzeit, Maurilio; Carpentier, Alexandra; von Luxburg, Ulrike
作者单位：Eberhard Karls University of Tubingen; Otto von Guericke University
摘要：The study of networks leads to a wide range of high-dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime, where the goal is to test between two populations of inhomogeneous random graphs defined on the same set of n vertices. The size of each population m is much smaller than n, and can even be a constant as small as 1. The critica...
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作者：Kutyniok, Gitta
作者单位：Technical University of Berlin
摘要：I would like to congratulate Johannes Schmidt-Hieber on a very interesting paper in which he considers regression functions belonging to the class of so-called compositional functions and analyzes the ability of estimators based on the multivariate nonparametric regression model of deep neural networks to achieve minimax rates of convergence. In my discussion, I will first regard such a type of result from the general viewpoint of the theoretical foundations of deep neural networks. This will ...
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作者：McGoff, Kevin; Nobel, Andrew B.
作者单位：University of North Carolina; University of North Carolina Charlotte; University of North Carolina; University of North Carolina Chapel Hill
摘要：A dynamical model consists of a continuous self-map T : chi -> chi of a compact state space chi and a continuous observation function f : chi -> R. This paper considers the fitting of a parametrized family of dynamical models to an observed real-valued stochastic process using empirical risk minimization. The limiting behavior of the minimum risk parameters is studied in a general setting. We establish a general convergence theorem for minimum risk estimators and ergodic observations. We then ...
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作者：Anderes, Ethan; Moller, Jesper; Rasmussen, Jakob G.
作者单位：University of California System; University of California Davis; Aalborg University
摘要：We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, that is, graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called th...
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作者：Aragam, Bryon; Dan, Chen; Xing, Eric P.; Ravikumar, Pradeep
作者单位：University of Chicago; Carnegie Mellon University
摘要：Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable by introducing a novel framework involving clustering overfitted parametric (i.e., misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature and are flexible enough to include, for example, mixtures of infinite Gaussian mixtures. In contrast to the recent literature, we allow for general nonparametr...
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作者：Ding, Shanshan; Qian, Wei; Wang, Lan
作者单位：University of Delaware; University of Miami
摘要：This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time T depends on a high-dimensional covariate vector X through low-dimensional linear combinations of covariates Gamma(T) X. The censoring time is allowed to be conditionally independent of the survival time given...
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作者：Kolassa, John E.; Kuffner, Todd A.
作者单位：Rutgers University System; Rutgers University New Brunswick; Washington University (WUSTL)
摘要：We consider a fundamental open problem in parametric Bayesian theory, namely the validity of the formal Edgeworth expansion of the posterior density. While the study of valid asymptotic expansions for posterior distributions constitutes a rich literature, the validity of the formal Edgeworth expansion has not been rigorously established. Several authors have claimed connections of various posterior expansions with the classical Edgeworth expansion, or have simply assumed its validity. Our main...
