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作者：James, Lancelot F.
作者单位：Hong Kong University of Science & Technology
摘要：Statistical latent feature models, such as latent factor models, are models where each observation is associated with a vector of latent features. A general problem is how to select the number/types of features, and related quantities. In Bayesian statistical machine learning, one seeks (nonparametric) models where one can learn such quantities in the presence of observed data. The Indian Buffet Process (IBP), devised by Griffiths and Ghahramani (2005), generates a (sparse) latent binary matri...
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作者：Verzelen, Nicolas; Arias-Castro, Ery
作者单位：INRAE; University of California System; University of California San Diego
摘要：We consider Gaussian mixture models in high dimensions, focusing on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive minimax rates for the problems of testing and of variable selection. We find these rates to depend crucially on the knowledge of the covariance matrices and on whether the mixture is symmetric or not. We establish the performance of various procedures, including the top sparse eigenvalue of the sample covariance ...
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作者：Boistard, Helene; Lopuhaa, Hendrik P.; Ruiz-Gazen, Anne
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Delft University of Technology
摘要：For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz-Thompson empirical process and the Hajek empirical process centered by their finite population mean as well as by their super-population mean in a survey sampling framework. The results apply to single-stage unequal probability sampling designs and essentially only require conditions on higher order correlations. We apply our main results to a Hadamard differentiable statistical f...
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作者：Ernst, Philip A.; Shepp, Larry A.; Wyner, Abraham J.
作者单位：Rice University; University of Pennsylvania
摘要：In this paper, we resolve a longstanding open statistical problem. The problem is to mathematically prove Yule's 1926 empirical finding of nonsense correlation [J. Roy. Statist. Soc. 89 (1926) 1-63], which we do by analytically determining the second moment of the empirical correlation coefficient theta : = integral(1)(0) W-1(t) W-2(t) dt - integral(1)(0) W-1(t) dt integral(1)(0) W-2(t) dt/root integral(1)(0) W-1(2)(t) dt - (integral(1)(0) W-1(t) dt)(2) root integral(1)(0) W-2(2)(t) dt - (inte...
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作者：Liu, Song; Suzuki, Taiji; Relator, Raissa; Sese, Jun; Sugiyama, Masashi; Fukumizu, Kenji
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Institute of Science Tokyo; Tokyo Institute of Technology; University of Tokyo; National Institute of Advanced Industrial Science & Technology (AIST)
摘要：We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for successful change detection with respect to the sample size n(p), n(q), the dimension of data m and the number of changed edges d. When us...
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作者：Zhong, Ping-Shou; Lan, Wei; Song, Peter X. K.; Tsai, Chih-Ling
作者单位：Michigan State University; University of Michigan System; University of Michigan; University of California System; University of California Davis
摘要：In regression analysis with repeated measurements, such as longitudinal data and panel data, structured covariance matrices characterized by a small number of parameters have been widely used and play an important role in parameter estimation and statistical inference. To assess the adequacy of a specified covariance structure, one often adopts the classical likelihood-ratio test when the dimension of the repeated measurements (p) is smaller than the sample size (n). However, this assessment b...
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作者：Wang, Qinwen; Yao, Jianfeng
作者单位：University of Hong Kong
摘要：Consider two p-variate populations, not necessarily Gaussian, with covariance matrices Sigma 1 and Sigma 2, respectively. Let S-1 and S-2 be the corresponding sample covariance matrices with degrees of freedom m and n. When the difference Delta between Sigma l and Sigma 2 is of small rank compared to p, m and n, the Fisher matrix S := S2-1S1 is called a spiked Fisher matrix. When p, m and n grow to infinity proportionally, we establish a phase transition for the extreme eigenvalues of the Fish...
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作者：Wang, Jingshu; Zhao, Qingyuan; Hastie, Trevor; Owen, Art B.
作者单位：University of Pennsylvania; Stanford University
摘要：We consider large-scale studies in which thousands of significance tests are performed simultaneously. In some of these studies, the multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable( s) of interest (e.g., treatment variable, phenotype) and the outcome. Over the past decade, many statistical methods have been proposed to adjust for the confounders in hypothesis testing. We un...
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作者：Basu, Kinjal; Mukherjee, Rajarshi
作者单位：Stanford University
摘要：In a very recent work, Basu and Owen [Found. Comput. Math. 17 (2017) 467-496] propose the use of scrambled geometric nets in numerical integration when the domain is a product of s arbitrary spaces of dimension d having a certain partitioning constraint. It was shown that for a class of smooth functions, the integral estimate has variance O(n(-1-2/d) (log n)(s-1)) for scrambled geometric nets compared to O(n(-1)) for ordinaryMonte Carlo. The main idea of this paper is to expand on the work by ...
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作者：Toulis, Panos; Airoldi, Edoardo M.
作者单位：University of Chicago; Harvard University
摘要：Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradient descent procedures, which involve parameter updates that are implicitly defined. Intuitively, implicit updates shrink standard stochastic gradient descent updates. The amount o...
