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作者：Paul, Subhadeep; Chen, Yuguo
作者单位：University System of Ohio; Ohio State University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these intermediate fusion methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. However, the theoretical properties of these methods remain largely unexplored. In t...
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作者：Durmus, Alain; Moulines, Eric; Saksman, Eero
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); HSE University (National Research University Higher School of Economics); University of Helsinki
摘要：Hamiltonian Monte Carlo (HMC) is currently one of the most popular Markov Chain Monte Carlo algorithms to sample smooth distributions over continuous state space. This paper discusses the irreducibility and geometric ergodicity of the HMC algorithm. We consider cases where the number of steps of the Stormer-Verlet integrator is either fixed or random. Under mild conditions on the potential U associated with target distribution pi, we first show that the Markov kernel associated to the HMC algo...
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作者：Aue, Alexander; van Delft, Anne
作者单位：University of California System; University of California Davis; Ruhr University Bochum
摘要：Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, expli...
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作者：Meyer, Marco; Paparoditis, Efstathios; Kreiss, Jens-Peter
作者单位：Braunschweig University of Technology; University of Cyprus
摘要：Existing frequency domain methods for bootstrapping time series have a limited range. Essentially, these procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. In this paper we propose a new frequency domain bootstrap method-the hybrid periodogram bootstrap (HPB)-which is consistent for a much wider range of stationary, even nonlinear, processes and which can be applied to a large class of periodogram-based statistics...
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作者：Zhilova, Mayya
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a dimension explicitly. These results lead to improvements of accuracy of a weighted bootstrap procedure for general log-likelihood ratio statistics. The key element of our proofs of the bootstrap accuracy is a multivariate higher-order Berry-Esseen inequalit...
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作者：Dieuleveut, Aymeric; Durmus, Alain; Bach, Francis
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite PSL; Ecole Normale Superieure (ENS); Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the minimization of a strongly convex objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step size. While the detailed analysis was only performed for quadratic functions, we provide an explicit asymptotic expansion of the moments of the averaged SGD iterates that outlines the dependence on initial conditions, the effect of noise and the step size, as well as the lack of convergence in the general (nonquadra...
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作者：Mogensen, Soren Wengel; Hansen, Niels Richard
作者单位：University of Copenhagen
摘要：Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with m-separation provide classes of symmetric graphical independence models that are closed under marginalization. Asymmetric independence relations appear naturally for multivariate stochastic processes, for instance, in terms of local independence. However, no class of graphs representing such asymmetric independence relations, which is also closed under marg...
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作者：Baraud, Yannick; Birge, Lucien
作者单位：University of Luxembourg; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We observe n independent random variables with joint distribution P and pretend that they are i.i.d. with some common density s (with respect to a known measure mu) that we wish to estimate. We consider a density model (S) over bar for s that we endow with a prior distribution pi (with support in (S) over bar) and build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around s whenever the data are truly i.i.d. and their densit...
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作者：Zhu, Changbo; Zhang, Xianyang; Yao, Shun; Shao, Xiaofeng
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Texas A&M University System; Texas A&M University College Station
摘要：In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [In Advances in Neural Information Processing Systems (2008) 585-592]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert-Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates that the standard ...
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作者：Bertsimas, Dimitris; Van Parys, Bart
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes n and number of regressors p in the 100,000s, that is, two orders of magnitude better than the current state of the art, in seconds. The ability to solve the problem for very high dimensions allows us to observe new phase transi...
