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作者：Banerjee, Moulinath; Durot, Cecile; Sen, Bodhisattva
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We study how the divide and conquer principle works in non-standard problems where rates of convergence are typically slower than root n and limit distributions are non-Gaussian, and provide a detailed treatment for a variety of important and well-studied problems involving nonparametric estimation of a monotone function. We find that for a fixed model, the pooled estimator, obtained by averaging nonstandard estimates across mutually exclusive subsamples, outperforms the nonstandard monotonici...
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作者：Monard, Francois; Nickl, Richard; Paternain, Gabriel P.
作者单位：University of California System; University of California Santa Cruz; University of Cambridge
摘要：We consider the statistical inverse problem of recovering a function f : M -> R, where M is a smooth compact Riemannian manifold with boundary, from measurements of general X-ray transforms I-a(f) of f, corrupted by additive Gaussian noise. For M equal to the unit disk with flat geometry and a = 0 this reduces to the standard Radon transform, but our general setting allows for anisotropic media M and can further model local attenuation effects-both highly relevant in practical imaging problems...
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作者：Petersen, Alexander; Mueller, Hans-Georg
作者单位：University of California System; University of California Santa Barbara; University of California System; University of California Davis
摘要：Increasingly, statisticians are faced with the task of analyzing complex data that are non-Euclidean and specifically do not lie in a vector space. To address the need for statistical methods for such data, we introduce the concept of Frechet regression. This is a general approach to regression when responses are complex random objects in a metric space and predictors are in R-p, achieved by extending the classical concept of a Frechet mean to the notion of a conditional Frechet mean. We devel...
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作者：Lopes, Miles E.
作者单位：University of California System; University of California Davis
摘要：Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding when an ensemble is large enough-so that its accuracy is close to that of an ideal infinite ensemble. Due to the fact that bagging and random forests are randomized algorithms, the choice of ensemble size is closely related to the notion of algorithmic varianc...
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作者：Zhao, Qingyuan
作者单位：University of Pennsylvania
摘要：In observational studies, propensity scores are commonly estimated by maximum likelihood but may fail to balance high-dimensional pretreatment covariates even after specification search. We introduce a general framework that unifies and generalizes several recent proposals to improve covariate balance when designing an observational study. Instead of the likelihood function, we propose to optimize special loss functions-covariate balancing scoring rules (CBSR)-to estimate the propensity score....
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作者：Chang, Ming-Chung; Cheng, Shao-Wei; Cheng, Ching-Shui
作者单位：National Central University; National Tsing Hua University; Academia Sinica - Taiwan; University of California System; University of California Berkeley
摘要：Signal aliasing is an inevitable consequence of using fractional factorial designs. Unlike linear models with fixed factorial effects, for Gaussian random field models advocated in some Bayesian design and computer experiment literature, the issue of signal aliasing has not received comparable attention. In the present article, this issue is tackled for experiments with qualitative factors. The signals in a Gaussian random field can be characterized by the random effects identified from the co...
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作者：Drton, Mathias; Fox, Christopher; Wang, Y. Samuel
作者单位：University of Washington; University of Washington Seattle; University of Chicago
摘要：Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from nonlinear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is often required to avoid convergence issues. As an alternative approach, we propose a block-coordinate descent method that cycles through the considered variables, updating only the parameters related to a given variable in each step. We show that the resultin...
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作者：Schoen, Eric D.; Eendebak, Pieter T.; Goos, Peter
作者单位：KU Leuven; Netherlands Organization Applied Science Research; University of Antwerp
摘要：A conference design is a rectangular matrix with orthogonal columns, one zero in each column, at most one zero in each row and -1's and +1's elsewhere. A definitive screening design can be constructed by folding over a conference design and adding a row vector of zeroes. We prove that, for a given even number of rows, there is just one isomorphism class for conference designs with two or three columns. Next, we derive all isomorphism classes for conference designs with four columns. Based on o...
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作者：Cook, R. Dennis; Forzani, Liliana
作者单位：University of Minnesota System; University of Minnesota Twin Cities; National University of the Littoral
摘要：We study the asymptotic behavior of predictions from partial least squares (PLS) regression as the sample size and number of predictors diverge in various alignments. We show that there is a range of regression scenarios where PLS predictions have the usual root-n convergence rate, even when the sample size is substantially smaller than the number of predictors, and an even wider range where the rate is slower but may still produce practically useful results. We show also that PLS predictions ...
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作者：Zhang, Anru
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements to achieve recovery is not guaranteed to be optimal. In addition, the implementation of some previous methods are NP-hard. In this article, we propose a framework for low-rank tensor completion via a novel tensor measurement scheme that ...
