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作者：Dette, Holger; Liu, Xin; Yue, Rong-Xian
作者单位：Ruhr University Bochum; Donghua University; Shanghai Normal University
摘要：The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of the optimization problem and have been successfully applied for models with univariate predictors. In particular, several authors have developed sufficient conditions for the existence of minimally supported designs in univariate models, where the number of s...
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作者：Zhang, Anru R.; Cai, T. Tony; Wu, Yihong
作者单位：University of Wisconsin System; University of Wisconsin Madison; Duke University; University of Pennsylvania; Yale University
摘要：A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis on singular subspa...
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作者：Chen, Shuxiao; Liu, Sifan; Ma, Zongming
作者单位：University of Pennsylvania; Stanford University
摘要：In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or application scenario. Such datasets can be modeled by multi-layer networks where each layer is a separate network itself while different layers are associated and share some common information. The present paper studies community detection in a stylized yet informati...
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作者：Zhang, Tianyu; Simon, Noah
作者单位：University of Washington; University of Washington Seattle
摘要：The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. In nonparametric regression, one assumes that the regression function belongs to a prespecified infinite-dimensional function space (the hypothesis space). In the online setting, when the observations come in a stream, it is computationally-preferable to iteratively update an estimate rather than refitting an entire model repeatedly. Inspired by nonpara...
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作者：Kou, Jiyao; Walther, Guenther
作者单位：Stanford University
摘要：The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here, we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, for example, if the signal is clustered in many small blocks,...
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作者：Shao, Lingxuan; Lin, Zhenhua; Yao, Fang
作者单位：Peking University; National University of Singapore
摘要：A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from sparsely observed ...
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作者：Zhao, Anqi; Lee, Youjin; Small, Dylan S.; Karmakar, Bikram
作者单位：National University of Singapore; Brown University; University of Pennsylvania; State University System of Florida; University of Florida
摘要：Valid instrumental variables enable treatment effect inference even when selection into treatment is biased by unobserved confounders. When multiple candidate instruments are available, but some of them are possibly invalid, the previously proposed reinforced design enables one or more nearly independent valid analyses that depend on very different assumptions. That is, we can perform evidence factor analysis. However, the validity of the reinforced design depends crucially on the order in whi...
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作者：Celentano, Michael; Montanari, Andrea
作者单位：Stanford University
摘要：In high-dimensional regression, we attempt to estimate a parameter vector beta(0) is an element of R-P from n less than or similar to p observations {(y(i) , x(i))}(i <= n) , where x(i) is an element of R-P is a vector of predictors and y(i) is a response variable. A well-established approach uses convex regularizers to promote specific structures (e.g., sparsity) of the estimate (beta) over cap while allowing for practical algorithms. Theoretical analysis implies that convex penalization sche...
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作者：Gassiat, Elisabeth; Le Corff, Sylvain; Lehericy, Luc
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples are available to estimate it: the deconvolution problem is solved based only on observations of the corrupted signal. We establish the identifiability of the model up to translation when the signal has a Laplace transform with an exponential growth rho small...
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作者：Kuchibhotla, Arun K.; Patra, Rohit K.
作者单位：Carnegie Mellon University; State University System of Florida; University of Florida
摘要：We consider least squares estimation in a general nonparametric regression model where the error is allowed to depend on the covariates. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the error has a uniformly bounded conditional variance and has only finitely many moments. Our upper bound on the rate of convergence of the LSE depe...
