A theory,a story,its analysis,and some implications

We present a refined form of a personal theory of learning which examines two distinct parts of the complex interaction between a learner's internal mental structures and his or her world of experience: what we call natural, conflicting, and alien experiences and the corresponding responses to them.In developing the theory we have come to realize that there are analogies between the experiences and the response of pupils, teachers, and researchers, and we suggest, therefore, that using the theory to analyze the learning of one group of learners can provide implications for the learning of others.The majority of the article concentrates on an example of analyzing for implications by describing the story of an incident in the authors' shared learning, an analysis of it, and some of the implications it provides for learning in general.     

Generalization bounds of ERM algorithm with Markov chain samples

One of the main goals of machine learning is to study the generalization performance of learning algorithms. The previous main results describing the generalization ability of learning algorithms are usually based on independent and identically distributed （i.i.d.） samples. However, independence is a very restrictive concept for both theory and real-world applications. In this paper we go far beyond this classical framework by establishing the bounds on the rate of relative uniform convergence for the Empirical Risk Minimization （ERM） algorithm with uniformly ergodic Markov chain samples. We not only obtain generalization bounds of ERM algorithm, but also show that the ERM algorithm with uniformly ergodic Markov chain samples is consistent. The established theory underlies application of ERM type of learning algorithms.     

建构主义下微积分教师的教学策略

建构主义主张学生是教学活动的认知主体,教师由传统的知识传授者转变为学生意义上建构的协助者和促进者,教学策略也发生显著变化.从教育者的角度出发,探讨了建构主义下微积分教师的教学策略.     

乘客策略行为下考虑需求学习的航空客运动态定价策略研究

研究航空公司在需求学习下的动态定价策略。通过假设乘客到达率不确定以及具有策略等待行为,运用贝叶斯理论和博弈论对航空公司需求学习下的多周期动态定价问题进行建模,探讨了机票最优定价策略的充分条件,并通过分析航空公司收益函数的性质,得到了最优定价随时间和已出售机票数量的变化趋势。最后应用算例分析了需求学习的效果,得出:需求学习能够缓解需求不确定带来的损失,但不能完全消除;乘客策略程度越大,需求学习效果越明显。     

On learning of Sigmoid Neural Networks

The Probably Approximately Correct (PAC) learning theory creates a framework to assess the learning properties of static models for which the data are assumed to be independently and identically distributed (i.i.d.). One important family of dynamic models to which the conventional PAC learning can not be applied is nonlinear Finite Impulse Response (FIR) models. The present article, using an extension of PAC learning that covers learning with m-dependent data, the learning properties of FIR modeling with sigmoid neural networks are evaluated. These results include upper bounds on the size of the data set required to train FIR sigmoid neural networks, provided that the input data are uniformly distributed. © 2001 John Wiley & Sons, Inc.     

Concrete representations and the procedural analogy theory

This paper describes a procedural analogy theory, which uses an isomorphism index to predict the likely learning outcomes when concrete materials are used in instruction in school mathematics. Literature from mathematics education and cognitive science are reviewed, the role of analogy in learning is considered, and examples of applications of the theory are provided.     

Learning study – promoting and hindering factors in mathematics teaching

This article focuses on presenting success factors for a group of teachers in carrying out a learning study in mathematics at their school. The research questions are: what are the actions of the school teaching community during development projects? What factors enable a group of teachers to carry out a learning study at their school? Activity theory provides a holistic framework to investigate relationships among the components present in a learning study. The results are based on analysis of interviews with teachers, students, principal organizers of schools and project coordinators, videotaped lessons, students’ tests and minutes taken at meetings of mathematics projects. The results show that the skills of facilitators, the time devoted to collaborative work, the link to learning theory and avoiding overly comprehensive content when teaching lessons are important promoting factors in mathematics teaching. The findings raise important questions about the way in which teacher work within universities.     

基于模糊粗糙样本的统计学习理论的理论基础

介绍模糊粗糙理论的基本内容;提出模糊粗糙经验风险泛函,模糊粗糙期望风险泛函,模糊粗糙经验风险最小化原则等概念;最后证明基于模糊粗糙样本的统计学习理论的关键定理并构建学习过程一致收敛速度的界.     

支持向量机及其在提高采收率潜力预测中的应用

提高采收率潜力分析的基础是进行提高采收率方法的潜力预测 .建立提高采收率潜力预测模型从统计学习的角度来看 ,实质是属于函数逼近问题 .本文首次将统计学习理论及支持向量机方法引入提高采收率方法的潜力预测中 .根据 Vapnik结构风险最小化原则 ,应尽量提高学习机的泛化能力 ,即由有效的训练集样本得到的小的误差能够保证对独立的测试集仍保持小的误差 .在本文所用较少样本条件下 ,支持向量机方法能够兼顾模型的通用性和推广性 ,具有较好的应用前景 .研究中采用的是综合正交设计法、油藏数值模拟和经济评价等方法生成的理论样本集     

Learning to rank: a ROC-based graph-theoretic approach

This note summarizes the main results presented in the author’s Ph.D. thesis, supervised by Luc Boullart and Bernard De Baets. The thesis was defended on 14th October 2008 at Universiteit Gent. It is written in English and available for download at . The work deals with preference learning, with emphasis on the ranking and ordinal regression machine learning settings and their connections to decision theory. Based on receiver operator characteristics analysis and graph theory, new performance measures are proposed to evaluate this type of models, and new algorithms are presented to compute and optimize these performance measures efficiently. Furthermore, the relationship with other settings like pairwise preference learning and multi-class classification is discussed.     

线性定常广义系统的D型迭代学习控制收敛性

给出了线性定常广义系统在D型学习律作用下的迭代控制收敛性结果,这一结果是全新的,其对时变系统也成立,而且,本文结果和方法大部分可以移植到线性定常广义离散时间系统.     

Vector-valued reproducing kernel Banach spaces with applications to multi-task learning

Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBSs). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RKBSs. The theory is then applied to multi-task machine learning. Especially, the representer theorem and characterization equations for the minimizer of regularized learning schemes in vector-valued RKBSs are established.     

The weight-decay technique in learning from data: an optimization point of view

The technique known as “weight decay” in the literature about learning from data is investigated using tools from regularization theory. Weight-decay regularization is compared with Tikhonov’s regularization of the learning problem and with a mixed regularized learning technique. The accuracies of suboptimal solutions to weight-decay learning are estimated for connectionistic models with a-priori fixed numbers of computational units. The Authors were partially supported by a PRIN grant from the Italian Ministry for University and Research, project “Models and Algorithms for Robust Network Optimization”.     

FIR Volterra kernel neural models and PAC learning

The probably approximately correct (PAC) learning theory creates a framework to assess the learning properties of static models for which the data are assumed to be independently and identically distributed (i.i.d.). The present article first extends the idea of PAC learning to cover the learning of modeling tasks with m‐dependent sequences of data. The data are assumed to be marginally distributed according to a fixed arbitrary probability. The resulting framework is then applied to evaluate learning of Volterra Kernel FIR models. © 2002 Wiley Periodicals, Inc.     

Integrating learning theories and application-based modules in teaching linear algebra

The research team of The Linear Algebra Project developed and implemented a curriculum and a pedagogy for parallel courses in (a) linear algebra and (b) learning theory as applied to the study of mathematics with an emphasis on linear algebra. The purpose of the ongoing research, partially funded by the National Science Foundation, is to investigate how the parallel study of learning theories and advanced mathematics influences the development of thinking of individuals in both domains. The researchers found that the particular synergy afforded by the parallel study of math and learning theory promoted, in some students, a rich understanding of both domains and that had a mutually reinforcing effect. Furthermore, there is evidence that the deeper insights will contribute to more effective instruction by those who become high school math teachers and, consequently, better learning by their students. The courses developed were appropriate for mathematics majors, pre-service secondary mathematics teachers, and practicing mathematics teachers. The learning seminar focused most heavily on constructivist theories, although it also examined socio-cultural and historical perspectives. A particular theory, Action-Process-Object-Schema (APOS) [10], was emphasized and examined through the lens of studying linear algebra. APOS has been used in a variety of studies focusing on student understanding of undergraduate mathematics. The linear algebra courses include the standard set of undergraduate topics. This paper reports the results of the learning theory seminar and its effects on students who were simultaneously enrolled in linear algebra and students who had previously completed linear algebra and outlines how prior research has influenced the future direction of the project.     

Expansive learning: lessons from one teacher’s learning journey

The provision of quality learning experiences for teachers is critical to mathematics reform agendas aimed at equitable and culturally responsive teaching. In this paper we use an activity theory framework to explore one teacher’s learning journey. Drawing on the teacher’s self-report of his journey 1 year after his participation in an intervention designed to support the introduction of mathematical inquiry practices we examine those factors that supported expansive learning. In seeking to understand our pedagogical stance within the intervention we gained new insights into the provision of research based tools to support learning, the provision of space for individual and collective learning, and the provision of a safe learning environment both within the programme, the class, and the wider professional community. These factors are important in understanding transformational changes associated with ambitious pedagogy.     

Learning horizon and optimal alliance formation

We develop a theoretical Bayesian learning model to examine how a firm’s learning horizon, defined as the maximum distance in a network of alliances across which the firm learns from other firms, conditions its optimal number of direct alliance partners under technological uncertainty. We compare theoretical optima for a ‘close’ learning horizon, where a firm learns only from direct alliance partners, and a ‘distant’ learning horizon, where a firm learns both from direct and indirect alliance partners. Our theory implies that in high tech industries, a distant learning horizon allows a firm to substitute indirect for direct partners, while in low tech industries indirect partners complement direct partners. Moreover, in high tech industries, optimal alliance formation is less sensitive to changes in structural model parameters when a firm’s learning horizon is distant rather than close. Our contribution lies in offering a formal theory of the role of indirect partners in optimal alliance portfolio design that generates normative propositions amenable to future empirical refutation.     

The Gender Confidence Gap in Fractions Knowledge: Gender Differences in Student Belief–Achievement Relationships

Recent research demonstrates that in many countries gender differences in mathematics achievement have virtually disappeared. Expectancy‐value theory and social cognition theory both predict that if gender differences in achievement have declined there should be a similar decline in gender differences in self‐beliefs. Extant literature is equivocal: there are studies indicating that the male over female advantage in self‐efficacy and beliefs about math learning is as strong as ever and there are studies reporting an absence of gender differences in belief. Using data from 996 grades 7–10 Canadian students, we found that gender differences in beliefs continued, even though gender differences in achievement were near zero. Gender differences, favoring males, were larger for self‐beliefs (math self‐efficacy and fear of failure) and weaker for functional and dysfunctional beliefs about math learning. There were also gender differences in the structure of a model linking beliefs about math, beliefs about self and achievement.     

Worker deployment in dual resource constrained systems with a task-type factor

This paper investigates worker learning and forgetting phenomenon in a dual resource constrained system (DRC) setting. Worker learning and forgetting in two and three stage DRC systems are modeled according to the dual-phase learning and forgetting model (DPLFM), which is based on the theory that a task has separate cognitive and motor requirements. Results show that the task-type (with respect to its learning rate and proportion of cognitive and motor requirements) affects the performance of training and deployment policies in DRC systems, and as such it should be included in future DRC research.     

基于网络混合学习策略的股市投资者行为演化模型及仿真

针对投资者有限理性决策行为的模仿学习等特质,运用复杂网络、贝叶斯学习和社会学习理论,分别对个人投资者和机构投资者的投资行为决策机制进行系统性分析,由此构建基于网络混合学习策略的投资者行为演化机理和数理模型,并进行数理解析和模拟仿真。研究发现,投资者金融关联网络的拓扑结构对个人投资者行为动态演变具有较强影响,但对机构投资者的影响较弱;个人投资者的学习策略偏好影响其行为动态演变均衡状态的稳定性较为显著;机构投资者获取的私有信息精确度与其行为动态演变的均衡状态之间存在显著的非线性关联;投资者的初始行为状态对其投资行为动态演变均衡状态的影响效应均较弱。