基于间隔迁移的多视角支持向量机

针对同一对象从不同途径或不同层面获得的特征数据被称为多视角数据. 多视角学习是利用事物的多视角数据进行建模求解的一种新的机器学习方法. 大量研究表明, 多视角数据共同学习可以显著提高模型的学习效果, 因此许多相关模型及算法被提出. 多视角学习一般需遵循一 致性原则和互补性原则. 基于一致性原则,Farquhar 等人成功地将支持向量机(Support Vector Machine, SVM)和核典型相关分析(Kernel Canonical Correlation Analysis, KCCA)整合成一个单独的优化问题, 提出SVM-2K模型. 但是, SVM-2K模型并未充分利用多视角数据间的互补信息. 因此, 在SVM-2K模型的基础之上, 提出了基于间隔迁移的多视角支持向量机模型(Margin transfer-based multi-view support vector machine, M^2SVM), 该模型同时满足多视角学习的一致性和互补 性两原则. 进一步地, 从一致性的角度对其进行理论分析, 并 与SVM-2K比较, 揭示了 M^2SVM 比SVM-2K 更为灵活. 最后, 在大量的多视角数据集上验证了M^2SVM模型的有效性.     

一种基于多视角学习的多元函数型聚类方法

函数型数据多以多变量的形式出现,目前的多元函数型聚类方法常以数据贴合的方式进行处理,不能充分提取各变量的共同信息及不同变量间的互补信息。为了进一步提取各变量中蕴含的聚类特征信息,本文在多视角学习框架下讨论多元函数型数据的聚类方法:构建了一个能够将多元函数型数据生成过程和各视角数据聚类特征提取统一进行的目标函数;借助非负矩阵分解的聚类特性,提出了一个基于半非负矩阵分解的多元函数型聚类模型;给出了交替迭代更新的求解算法。模拟实验结果显示,与现有的多元函数型聚类方法相比较,该聚类方法的聚类性能显著提高;以北京市空气质量监测站点应用为例,其聚类结果表明,多视角方法在聚类精度和信息提取方面具有优势。     

虚拟企业合作伙伴选择的综合评判方法

在虚拟企业合作伙伴选择的基本原则及合作伙伴选择步骤研究的基础上，提出了一种新的虚拟企业合作伙伴选择的方法，将所有候选伙伴按其投标的核心能力类型进行分类并组成虚拟企业组合方案，根据总成本最低原则、敏捷性原则和风险最小化原则，对虚拟企业组合进行综合评判。     

Banach空间中求解线性反问题的对偶梯度流方法

本文考虑求解不适定问题Ax=y,并确定该问题的R-极小解,其中A:X→Y是Banach空间X到Hilbert空间Y的有界线性算子, R:X→(-∞,∞]为强凸函数.针对数据带噪声的情形,本文研究一种对偶梯度流方法.由于问题的不适定性会导致方法产生半收敛现象,需要选择合适的停止时间以保证重构解的正则性.本文讨论不同的选取方式(如先验选取、偏差原则和启发式偏差原则)下相应的收敛结果,并且基于解的变分源条件建立方法的收敛阶.数值实验结果展示了对偶梯度流方法在求解线性反问题中的有效性.     

高中数学教学中示错教学的策略

“示错教学法”是高中数学教学中常用的一种有效的教学方法．所谓“示错教学法”,是指教师在数学课堂教学中能根据学生认知的情况,针对学生学习数学中容易出现的问题,通过各种不同形式把错误理解、错误解法等展现、暴露在学生面前,引发学生去思考、讨论,去分析错因,并加以纠错,从而形成正确认识,准确把握数学概念的本质,掌握解题方法的要领,避免学生走弯路或重蹈覆辙的一种授课方式．在数学教学中,要遵循“目的性原则、探究性原则、针对性原则、及时性原则”等示错教学的原则,把握好示错教学的时机、选择合理的示错方式,进行有效教学,才能充分发挥示错教学独特的教育功效,提高对错误的免疫力,优化思维品质．     

基于算法稳定的ERM原则一致性的研究

通过对变一误差估计下算法稳定的研究,提出了不依赖于样本分布的CO稳定的概念,证明了CO稳定不仅是变一误差估计条件下ERM原则一致性的充要条件,而且也是学习算法具有推广性的充分条件.     

基于批量-时间原则的VMI Hub配送柔性

批量-时间原则是一种既考虑配送经济批量又考虑配送时间要求的配送原则,基于此原则,本文对VMIHub运作模式下的配送柔性进行了研究,引入加权配送松弛时间(Weighted Slack Time,WST)以度量配送柔性。验证了VMI Hub运作模式在原材料配送方面的优势:VMI Hub运作模式具有配送上的集聚效应(Pooling Effect)和统一配送的特点,可以有效解决多供应商配送存在交叉时间而使加权配送松弛时间减少的问题,从而保证了稳定的配送松弛时间,体现了良好的配送柔性。     

建构主义学习理论下的数学教学原则与策略

本文从建构主义学习理论出发，分析了传统数学教学中存在的弊端。提出了建构主义学习理论下的数学教学原则和策略，对于充分认识建构主义学习、教学理论，对促进数学教学改革，提高数学教学质量具有重要的意义．     

基于合理粒度原则的多层模糊规则模型构建

模糊IF-THEN规则模型因其可产生具有较好解释性的推理结果受到了广泛的关注。对于高维、复杂的问题,模糊IF-THEN规则模型却未充分利用数据特征中包含的层次信息,对数据的多水平表征能力较弱。此外,模糊模型的构建往往受到数据质量、专家知识等因素的影响导致数值输出伴随着不确定性。本文基于合理粒度原则提出了一种具有多层结构的Takagi-Sugeno(T-S)模糊模型的建模方法。该方法在粒计算框架下将模糊技术与多层学习策略相结合,并在数据子空间内部采取逐层划分的方法进一步挖掘数据中隐含的结构信息,使模型具有良好的可解释性,同时以信息粒为输出体现了主要的预测范围。最后,在公开数据集上进行数据实验,检验了所提方法的有效性。     

数学创新教育中的教学原则探微

创新问题已经成为社会各界共同关注的热点 ,创新教育已成为我国教育改革的主旋律 .教育理论和教育实践工作者对创新教育的一系列研究均取得了丰硕成果 ,但对创新教育中的教学原则的研究却论及较少 .本文就此问题谈谈自己的浅见 ,并希望对数学创新教育研究有所裨益 .我们认为数学创新教育中应包括以下几个原则 :1　创设情境　自觉学习情感教育理论认为 ,情感作为主要的非认知因素 ,制导着认知学习 .实践也证明了良好的情感可推动人趋向学习目标 ,激发想象力 ,使创造性思维得到充分发挥 ,反之则会压抑学生学习的主动性和创造性 .创设情境可有…     

Learning from imprecise and fuzzy observations: Data disambiguation through generalized loss minimization

Methods for analyzing or learning from “fuzzy data” have attracted increasing attention in recent years. In many cases, however, existing methods (for precise, non-fuzzy data) are extended to the fuzzy case in an ad-hoc manner, and without carefully considering the interpretation of a fuzzy set when being used for modeling data. Distinguishing between an ontic and an epistemic interpretation of fuzzy set-valued data, and focusing on the latter, we argue that a “fuzzification” of learning algorithms based on an application of the generic extension principle is not appropriate. In fact, the extension principle fails to properly exploit the inductive bias underlying statistical and machine learning methods, although this bias, at least in principle, offers a means for “disambiguating” the fuzzy data. Alternatively, we therefore propose a method which is based on the generalization of loss functions in empirical risk minimization, and which performs model identification and data disambiguation simultaneously. Elaborating on the fuzzification of specific types of losses, we establish connections to well-known loss functions in regression and classification. We compare our approach with related methods and illustrate its use in logistic regression for binary classification.     

Balancing principle in supervised learning for a general regularization scheme

We discuss the problem of parameter choice in learning algorithms generated by a general regularization scheme. Such a scheme covers well-known algorithms as regularized least squares and gradient descent learning. It is known that in contrast to classical deterministic regularization methods, the performance of regularized learning algorithms is influenced not only by the smoothness of a target function, but also by the capacity of a space, where regularization is performed. In the infinite dimensional case the latter one is usually measured in terms of the effective dimension. In the context of supervised learning both the smoothness and effective dimension are intrinsically unknown a priori. Therefore we are interested in a posteriori regularization parameter choice, and we propose a new form of the balancing principle. An advantage of this strategy over the known rules such as cross-validation based adaptation is that it does not require any data splitting and allows the use of all available labeled data in the construction of regularized approximants. We provide the analysis of the proposed rule and demonstrate its advantage in simulations.     

TO LEARN OR TO CHANGE: OPTIMAL R&D INVESTMENTS UNDER UNCERTAINTY IN THE CASE OF CLIMATE CHANGE

When studying R&D investments in technologies that address potential damage from climate change (termed as “research to change” or RTC), current literature overlooks the effects of purchased learning (i.e., learn through scientific research, termed as “research to learn” or RTL) about climate change. We investigate interactions between optimal R&D investments in RTC and RTL under uncertainty in climate change and research outcomes, while accounting for the positive impact that successful RTL may have on RTC outcome. We find that simultaneously investing in both RTL and RTC may be optimal when the probability that climate change imposes a specific level of damage is either moderate or very high and when RTL cost is relatively low. Whenever RTL and RTC are conducted simultaneously, then they substitute. However, when it is not optimal to conduct RTC and RTL simultaneously, then an increase in RTC cost decreases, at least weakly, RTL investment (i.e., RTL and RTC complement). When the probability that climate change imposes damage increases, then the optimal RTL investment may first decrease and then increase. Moreover, we identify conditions under which either the precautionary principle or the learn‐then‐act principle should be followed regarding R&D investments.     

Multi-parameter Tikhonov Regularization—An Augmented Approach

We study multi-parameter regularization （multiple penalties） for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.     

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Variance related premium principle is one of the most important principles not only in practice applications but also in research field of actuarial science. In this paper, the Bayesian models are established under variance related premium principle. The Bayesian estimate and credibility estimate of risk premium are derived. Furthermore, some statistical properties of estimators are discussed. In the models with multitude contract data, the unbiased consistent estimates of the structure parameters are proposed. Finally, the empirical Bayes estimator are proved to be asymptotically optimal.     

奇异椭圆方程多重解的存在性

在这篇论文中,首先给出了奇异椭圆方程(1.1)正解在零点附近的一个精确的估计.然后,结合这个估计式,利用Ekeland变分原理和山路引理,在一定条件下得到了方程(1.1)多重正解的存在性.     

最小二乘原理在隧道施工安全质量预测预报中的应用

土建工程的安全质量控制的本质,就是运用数理统计原理,归纳、分析实测得到的有关数据,从而达到对现场安全作出准确诊断、对施工质量作出正确评价之目的,其中最常涉及的数学理论知识点是最小二乘原理.通过一隧道工程实例,阐明了最小二乘原理在其安全质量预测预报中的作用及使用,颇具实用性操作性地实现了数学理论与工程实际的密切结合.     

Multi-parameter Tikhonov regularization and model function approach to the damped Morozov principle for choosing regularization parameters

In this paper, we study the multi-parameter Tikhonov regularization method which adds multiple different penalties to exhibit multi-scale features of the solution. An optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters. Some theoretical results of the regularization solution about the dependence on regularization parameters are presented. Then, an a posteriori parameter choice, i.e., the damped Morozov discrepancy principle, is introduced to determine multiple regularization parameters. Five model functions, i.e., two hyperbolic model functions, a linear model function, an exponential model function and a logarithmic model function, are proposed to solve the damped Morozov discrepancy principle. Furthermore, four efficient model function algorithms are developed for finding reasonable multiple regularization parameters, and their convergence properties are also studied. Numerical results of several examples show that the damped discrepancy principle is competitive with the standard one, and the model function algorithms are efficient for choosing regularization parameters.