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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：Biau, Gerard; Cadre, Benoit; Sangnier, Maxime; Tanielian, Ugo
作者单位：Universite Paris Cite; Sorbonne Universite; Ecole Normale Superieure de Rennes (ENS Rennes); Universite de Rennes
摘要：Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the-art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objective function through an adversarial game between a family of generators and a family of discriminators. In this paper, we offer a better theoretical understanding of GANs by analyzing some of their ma...
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作者：Cattaneo, Matias D.; Farrell, Max H.; Feng, Yingjie
作者单位：Princeton University; University of Chicago; Princeton University
摘要：We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics and machine learning. First, we obtain a general characterization of their leading asymptotic bias. Second, we establish integrated mean squared error approximations for the point estimator and propose feasible tuning parameter selection. Third, we develop point-wise inference methods based on undersmooth...
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作者：Johnstone, Iain M.; Onatski, Alexei
作者单位：Stanford University; University of Cambridge
摘要：We consider the five classes of multivariate statistical problems identified by James (Ann. Math. Stat. 35 (1964) 475-501), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of E-1 H where H and E are proportional to high-dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the noncentrality or the ...
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作者：Lee, Anthony; Singh, Sumeetpal S.; Vihola, Matti
作者单位：University of Bristol; University of Cambridge; University of Jyvaskyla
摘要：The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analys...
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作者：Han, Lei; Tan, Kean Ming; Yang, Ting; Zhang, Tong
作者单位：Tencent; University of Michigan System; University of Michigan; Hong Kong University of Science & Technology; Hong Kong University of Science & Technology
摘要：A major challenge for building statistical models in the big data era is that the available data volume far exceeds the computational capability. A common approach for solving this problem is to employ a subsampled dataset that can be handled by available computational resources. We propose a general subsampling scheme for large-scale multiclass logistic regression and examine the variance of the resulting estimator. We show that asymptotically, the proposed method always achieves a smaller va...
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作者：Kneip, Alois; Liebl, Dominik
作者单位：University of Bonn
摘要：We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression operators as a special case. We show the optimality of our reconstruction operator and demonstrate that the usually considered regression operators generally cannot be optimal reconstruction operators. Our estimation theory allows for autocorrelated functional ...
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作者：Cox, Gregory
作者单位：Columbia University
摘要：This paper establishes the argmin of a random objective function to be unique almost surely. This paper first formulates a general result that proves almost sure uniqueness without convexity of the objective function. The general result is then applied to a variety of applications in statistics. Four applications are discussed, including uniqueness of M-estimators, both classical likelihood and penalized likelihood estimators, and two applications of the argmin theorem, threshold regression an...
