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Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements

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Acta Mathematica Sinica,English Series 2019年第5期35卷 583-596页

作者： Robert PARKER Andrew ROSALSKY Department of Biostatistics University of Florida Department of Statistics University of Florida

For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.

关键词： Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type p Banach space convergence in Lp

PROXIMAL-PROXIMAL-GRADIENT METHOD

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Journal of Computational Mathematics 2019年第6期37卷 778-812页

作者： Ernest K.Ryu Wotao Yin Department of Mathematics University of CaliforniaLos AngelesCA 90095USA

In this paper,we present the proximal-proximal-gradient method(PPG),a novel optimization method that is simple to implement and simple to parallelize.PPG generalizes the proximal-gradient method and ADMM and is applicable to minimization problems written as a sum of many differentiable and many non-differentiable convex functions.The non-differentiable functions can be coupled.We furthermore present a related stochastic variation,which we call stochastic PPG(S-PPG).S-PPG can be interpreted as a generalization of Finito and MISO over to the sum of many coupled non-differentiable convex functions.We present many applications that can benefit from PPG and S-PPG and prove convergence for both methods.We demonstrate the empirical effectiveness of both methods through experiments on a CUDA GPU.A key strength of PPG and S-PPG is,compared to existing methods,their ability to directly handle a large sum of non-differentiable nonseparable functions with a constant stepsize independent of the number of functions.Such non-diminishing stepsizes allows them to be fast.

关键词： Proximal-gradient ADMM Finito MISO SAGA Operator splitting Firstorder methods Distributed optimization Stochastic optimization Almost sure convergence linear convergence

General decay asymptotic stability of neutral stochastic differential delayed equations with Markov switching

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Frontiers of Mathematics in China 2019年第4期14卷 793-818页

作者： Guangqiang LAN Fang XIA College of Mathematics and Physics Beijing University of Chemical Technology Beijing 100029 China

The p-th moment and almos t sure st ability with general decay rate of the exact solutions of neutral stochastic differential delayed equations with Markov switching are investigated under given conditions. Two exampl... 详细信息

关键词： Neutral stochastic differential delayed equations with Markov switching (NSDDEswMS) global solution general decay rate, p-th moment stability almost sure st ability

Feature Screening for Ultrahigh-dimensional Censored Data with Varying Coefficient Single-index Model

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 845-861页

作者： Yi LIU School of Mathematical Sciences Ocean University of China

In this paper, we study the sure independence screening of ultrahigh-dimensional censored data with varying coefficient single-index model. This general model framework covers a large number of commonly used survival models. The property that the proposed method is not derived for a specific model is appealing in ultrahigh dimensional regressions, as it is difficult to specify a correct model for ultrahigh dimensional predictors.Once the assuming data generating process does not meet the actual one, the screening method based on the model will be problematic. We establish the sure screening property and consistency in ranking property of the proposed method. Simulations are conducted to study the finite sample performances, and the results demonstrate that the proposed method is competitive compared with the existing methods. We also illustrate the results via the analysis of data from The National Alzheimers Coordinating Center(NACC).

关键词： censored data consistency in ranking property feature selection high-dimensional data sure screening property varying coefficient single-index model

Tournament screening cum EBIC for feature selection with high-dimensional feature spaces

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Science China Mathematics 2009年第6期52卷 1327-1341页

作者： CHEN ZeHua CHEN JiaHua Department of Statistics&Applied Probability National University of Singapore3 Science Drive 2117543Singapore Department of Statistics University of British ColumbiaVancouverBCV6T 1Z2Canada

The feature selection characterized by relatively small sample size and extremely high-dimensional feature space is common in many areas of contemporary statistics.The high dimensionality of the feature space causes serious diffculties:(i) the sample correlations between features become high even if the features are stochastically independent;(ii) the computation becomes intractable.These diffculties make conventional approaches either inapplicable or ine?cient.The reduction of dimensionality of the feature space followed by low dimensional approaches appears the only feasible way to tackle the problem.Along this line,we develop in this article a tournament screening cum EBIC approach for feature selection with high dimensional feature space.The procedure of tournament screening mimics that of a tournament.It is shown theoretically that the tournament screening has the sure screening property,a necessary property which should be satisfied by any valid screening procedure.It is demonstrated by numerical studies that the tournament screening cum EBIC approach enjoys desirable properties such as having higher positive selection rate and lower false discovery rate than other approaches.

关键词： extended Bayes information criterion feature selection penalized likelihood reduc-tion of dimensionality small-n-large-P sure screening

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sure算法在核磁共振信号去噪中的实现

地球物理学报 2010年第11期53卷 2776-2783页

作者：谢庆明肖立志廖广志中国石油大学油气资源与探测国家重点实验室北京102249

核磁共振产生的回波信号幅度比较低,容易受到噪声干扰.如何有效提高低场核磁共振回波信号的信噪比一直是核磁共振技术研究的关键课题之一.本文讨论了一种基于小波变换的Stein无偏风险估计(sure)算法,从相关系数图版中确定尺度因子和分... 详细信息

核磁共振产生的回波信号幅度比较低,容易受到噪声干扰.如何有效提高低场核磁共振回波信号的信噪比一直是核磁共振技术研究的关键课题之一.本文讨论了一种基于小波变换的Stein无偏风险估计(sure)算法,从相关系数图版中确定尺度因子和分解层次,依据噪声在不同分解层次上的差异取不同的阈值对回波信号去噪.该算法与传统的模极大值法和空域相关法相比,能获得更高的信噪比,为储层流体分析提供更准确的孔隙度信息.

关键词：核磁共振回波去噪 sure SVD反演小波变换

用sure引导自适应采样与采样颜色直方图重构

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计算机辅助设计与图形学学报 2016年第4期28卷 533-539页

作者：袁红亮吴付坤郑昌文中国科学院软件研究所天基综合信息系统重点实验室北京100190 中国科学院大学北京100190

针对现有采样颜色直方图重构缺少自适应采样方法的问题,提出一种基于Stein’s unbiased risk estimator(sure)的像素均方误差计算方法.首先对图像空间粗采样;然后在GPU上分块计算sure来评估图像每个像素的误差度量值,并用该值引导非均... 详细信息

针对现有采样颜色直方图重构缺少自适应采样方法的问题,提出一种基于Stein’s unbiased risk estimator(sure)的像素均方误差计算方法.首先对图像空间粗采样;然后在GPU上分块计算sure来评估图像每个像素的误差度量值,并用该值引导非均匀自适应采样;最后使用非局部多尺度滤波方法重构图像.实验结果表明,不论从图像噪声定量化指标还是视觉效果来看,该方法都极大地改进了图像绘制质量.

关键词： GPU加速自适应采样 sure 均方误差

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激光主动成像图像噪声分析与抑制

红外与激光工程 2011年第2期40卷 332-337页

作者：李晓峰徐军罗积军曹立佳张胜修第二炮兵工程学院陕西西安710025

分析了激光主动成像图像的噪声机理,针对强度像噪声抑制问题,提出了一种基于同态滤波和小波域sure(Stein′s Unbiased Risk Estimate)的激光主动成像图像降噪算法。该方法首先用同态变换将乘性散斑噪声转换为加性噪声;然后在小波域,没... 详细信息

分析了激光主动成像图像的噪声机理,针对强度像噪声抑制问题,提出了一种基于同态滤波和小波域sure(Stein′s Unbiased Risk Estimate)的激光主动成像图像降噪算法。该方法首先用同态变换将乘性散斑噪声转换为加性噪声;然后在小波域,没有将小波系数看作随机变量,而是以最小化均方误差MSE为目的,将图像降噪过程看作是一个小波系数的加权和,通过sure获得近似最优的小波系数的权值;最后再作相应的小波逆变换和同态逆变换,得到降噪后的图像。实验结果表明:该方法具有较好的噪声抑制效果,且计算量极小。

关键词：激光主动成像图像降噪小波变换 sure

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旅行的意义

疯狂英语（新读写） 2023年第3期 16-20,76页

作者：蒋建平四川

旅行可以缓解来自生活和学习方面的压力,使人的精神得到彻底的放松;旅行的过程虽然可能很累,但是它能给人带来精神上的愉悦感。For some people,travelling represents one of the essential goals in life because it is a perfect mix... 详细信息

旅行可以缓解来自生活和学习方面的压力,使人的精神得到彻底的放松;旅行的过程虽然可能很累,但是它能给人带来精神上的愉悦感。For some people,travelling represents one of the essential goals in life because it is a perfect mix of pleasure,curiosity,fun and recreation.It is considered by many to be a recreational activity,but for sure,it represents more than that.

关键词：愉悦感 some many 旅行 sure