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作者：Camerlenghi, Federico; Lijoi, Antonio; Prunster, Igor
作者单位：University of Milano-Bicocca; Bocconi University; Bocconi University
摘要：Hierarchical nonparametric processes are popular tools for defining priors on collections of probability distributions, which induce dependence across multiple samples. In survival analysis problems, one is typically interested in modeling the hazard rates, rather than the probability distributions themselves, and the currently available methodologies are not applicable. Here, we fill this gap by introducing a novel, and analytically tractable, class of multivariate mixtures whose distribution...
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作者：Dobriban, Edgar; Sheng, Yue
作者单位：University of Pennsylvania; University of Pennsylvania
摘要：Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, send the results to a central server and take a weighted average of the parameters. Opti...
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作者：Belomestny, Denis; Goldenshluger, Alexander
作者单位：University of Duisburg Essen; University of Haifa; HSE University (National Research University Higher School of Economics)
摘要：In this paper, we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically, deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the characteristic function of the measurement errors does not have zeros on the real line. This assumption is rather strong and is not fulfilled in many cases of interest. In this paper, we develop a methodology for constructing optimal density deconvolution e...
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作者：Ghorbani, Behrooz; Mei, Song; Misiakiewicz, Theodor; Montanari, Andrea
作者单位：Stanford University; Stanford University; Stanford University
摘要：We consider the problem of learning an unknown function f(star) on the d-dimensional sphere with respect to the square loss, given i.i.d. samples {(y(i), x(i))}(i <= n) where x(i) is a feature vector uniformly distributed on the sphere and y(i) = f(star)(x(i)) + epsilon(i). We study two popular classes of models that can be regarded as linearizations of two-layers neural networks around a random initialization: the random features model of Rahimi-Recht (RF); the neural tangent model of Jacot-G...
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作者：Ding, Xiucai; Yang, Fan
作者单位：Duke University; University of Pennsylvania
摘要：We study a class of separable sample covariance matrices of the form (Q) over tilde (1) := (A) over tilde X-1/2 (B) over tilde BX*(B) over tilde (1/2). Here, (A) over tilde and (B) over tilde are positive definite matrices whose spectrums consist of bulk spectrums plus several spikes, that is, larger eigenvalues that are separated from the bulks. Conceptually, we call (Q) over tilde (1) a spiked separable covariance matrix model. On the one hand, this model includes the spiked covariance matri...
