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作者：Han, Yuefeng; Chen, Rong; Yang, Dan; Zhang, Cun-Hui
作者单位：University of Notre Dame; Rutgers University System; Rutgers University New Brunswick; University of Hong Kong
摘要：Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to Tucker tensor decomposition, except that the time dimension is treated as a dynamic process with a time dependent structure. In this paper, we introduce two approaches to estimate such a tensor factor model by using iterative orthogonal projections of the o...
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作者：Waudby-smith, Ian; Arbour, David; Sinha, Ritwik; Kennedy, Edward H.; Ramdas, Aaditya
作者单位：Carnegie Mellon University; Adobe Systems Inc.
摘要：Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under weak assumptions and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals, adding to the literature on confidence sequences (CS)-sequences of confidence intervals that ar...
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作者：Yang, Jun; Latuszynski, Krzysztof; Roberts, Gareth o.
作者单位：University of Copenhagen; University of Warwick
摘要：High-dimensional distributions, especially those with heavy tails, are results in empirically observed stickiness and poor theoretical mixing properties-lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high-dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk Metropolis type algorithms as well as versions of the Bouncy Particle Sampler that are uniformly...
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作者：Mesters, Geert; Zwiernik, Piotr
作者单位：Pompeu Fabra University; University of Toronto
摘要：A seminal result in the ICA literature states that for AY = s, if the components of s are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows (Signal Process. 36 (1994)). In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of s. We document new conditions that establish identification for several nonindependent component models, for example...
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作者：Cheng, Chen; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we revisit ridge regres...
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作者：Gu, Jia; Chen, Song xi
作者单位：Zhejiang University; Tsinghua University
摘要：This paper considers decentralized Federated Learning (FL) under heterogeneous distributions among distributed clients or data blocks for the Mestimation. The mean squared error and consensus error across the estimators from different clients via the decentralized stochastic gradient descent algorithm are derived. The asymptotic normality of the Polyak-Ruppert (PR) averaged estimator in the decentralized distributed setting is attained, which shows that its statistical efficiency comes at a co...
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作者：Kur, Gil; Gao, Fuchang; Guntuboyina, Adityanand; Sen, Bodhisattva
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Idaho; University of California System; University of California Berkeley; Columbia University
摘要：Under the usual nonparametric regression model with Gaussian errors, are shown to be suboptimal for estimating a d-dimensional convex function in squared error loss when the dimension d is 5 or larger. The specific function classes considered include: (i) bounded convex functions supported on a polytope (in random design), (ii) Lipschitz convex functions supported on any convex domain (in random design) and (iii) convex functions supported on a polytope (in fixed design). For each of these cla...
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作者：Rajaraman, Nived; Han, Yanjun; Jiao, Jiantao; Ramchandran, Kannan
作者单位：University of California System; University of California Berkeley; New York University; New York University
摘要：We consider the sequential decision-making problem where the mean outcome is a nonlinear function of the chosen action. Compared with the linear model, two curious phenomena arise in nonlinear models: first, in addition to the learning phase with a standard parametric rate for estimation or regret, there is an burn-in period with a fixed cost determined by the nonlinear function; second, achieving the smallest burn-in cost requires new exploration algorithms. For a special family of nonlinear ...
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作者：Lundborg, Anton rask; Kim, Ilmun; Shah, Rajen d.; Samworth, Richard j.
作者单位：University of Copenhagen; Yonsei University; University of Cambridge
摘要：Testing the significance of a variable or group of variables X for predicting a response Y, given additional covariates Z, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for X is nonzero. However, when the model is misspecified, the test may have poor power, for example, when X is involved in complex interactions, or lead to many false rejections. In this work, we study the problem of testing the m...
