高等数学学习方法指导的改革与实践

学习科学已经发展为一个学科群，作为学习科学的重要组成部分，高等数学学习方法指导的研究也警来越受到人们的重视，本文通过对高等数学学习方法指导的现状的剖析，提出高等数学学习方法改革的基本思路.     

Optimal incremental learning under covariate shift

Learning strategies under covariate shift have recently been widely discussed. The density of learning inputs under covariate shift is different from that of test inputs. Learning machines in such environments need to employ special learning strategies to acquire greater capabilities of generalizing through learning. However, incremental learning methods are also used for learning in non-stationary learning environments, which represent a kind of covariate shift. However, the relation between covariate-shift environments and incremental-learning environments has not been adequately discussed. This paper focuses on the covariate shift in incremental-learning environments and our re-construction of a suitable incremental-learning method. Then, the model-selection criterion is also derived, which is to be an essential object function for memetic algorithms to solve these kinds of learning problems.     

Rejoinder on “Imprecise probability models for learning multinomial distributions from data. Applications to learning credal networks”

In this paper we answer to the comments provided by Fabio Cozman, Marco Zaffalon, Giorgio Corani, and Didier Dubois on our paper ‘Imprecise Probability Models for Learning Multinomial Distributions from Data. Applications to Learning Credal Networks’. The main topics we have considered are: regularity, the learning principle, the trade-off between prior imprecision and learning, strong symmetry, and the properties of ISSDM for learning graphical conditional independence models.     

快速自底向上构造神经网络的方法

介绍了一种构造神经网络的新方法 .常规的瀑流关联 (Cascade-Correlation)算法起始于最小网络(没有隐含神经元 ) ,然后逐一地往网络里增加新隐含神经元并训练 ,结束于期望性能的获得 .我们提出一种与构造算法 (Constructive Algorithm)相关的快速算法 ,这种算法从适当的初始网络结构开始 ,然后不断地往网络里增加新的神经元和相关权值 ,直到满意的结果获得为止 .实验证明 ,这种快速方法与以往的常规瀑流关联方法相比 ,有几方面优点 :更好的分类性能 ,更小的网络结构和更快的学习速度 .     

Semi-Supervised Learning with the help of Parzen Windows

Semi-Supervised Learning is a family of machine learning techniques that make use of both labeled and unlabeled data for training, typically a small amount of labeled data with a large number of unlabeled data. In this paper we propose a Semi-Supervised regression algorithm by means of density estimator, generated by Parzen Windows functions under the framework of Semi-Supervised Learning. We conduct error analysis by capacity independent technique and obtain some satisfactory learning rates in terms of regularity of the target function and the decay condition on the marginal distribution near the boundary.     

Combining latent learning with dynamic programming in the modular anticipatory classifier system

Learning Classifier Systems (LCS) are rule based Reinforcement Learning (RL) systems which use a generalization capability. In this paper, we highlight the differences between two kinds of LCSs. Some are used to directly perform RL while others latently learn a model of the interactions between the agent and its environment. Such a model can be used to speed up the core RL process. Thus, these two kinds of learning processes are complementary. We show here how the notion of generalization differs depending on whether the system anticipates (like Anticipatory Classifier System (ACS) and Yet Another Classifier System (YACS)) or not (like XCS). Moreover, we show some limitations of the formalism common to ACS and YACS, and propose a new system, called Modular Anticipatory Classifier System (MACS), which allows the latent learning process to take advantage of new regularities. We describe how the model can be used to perform active exploration and how this exploration may be aggregated with the policy resulting from the reinforcement learning process. The different algorithms are validated experimentally and some limitations in presence of uncertainties are highlighted.     

生成学习系统的混沌与设计

认知学习是一种高度复杂的非线性现象.试图依据生成学习理论和经验学习的思想,建构含有记忆效应的生成学习系统动力学模型,探讨认知学习过程的复杂现象和变化特征,揭示学习系统波动的内生机制和学生认知的混沌规律,并在此基础上提出基于学习混沌的教学系统设计模式,期望能促进学生认知结构的发展.     

AN INVESTIGATION INTO THE BALANCE OF PRESCRIPTION,EXPERIMENT AND PLAY WHEN LEARNING ABOUT THE PROPERTIES OF QUADRATIC FUNCTIONS WITH ICT

This paper will draw on research being developed within the Teaching and Learning strand of the ESRC InterActive Education: Learning in the Information Age project which is examining the ways in which new technologies can be used in educational settings to enhance learning. It will focus on the learning and understanding of quadratic functions using a graphical software package and includes a discussion of how the structuring of the activities influences the nature of the learning environment. The potential affordance that the software provides for experiment and play is highlighted in relation to the teacher's role in shaping the tasks to effectively make good use of this mode of learning.     

Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.

ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.

Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.

In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.

In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.     

Lost in a black-box? Interpretable machine learning for assessing Italian SMEs default

Academic research and the financial industry have recently shown great interest in Machine Learning algorithms capable of solving complex learning tasks, although in the field of firms' default prediction the lack of interpretability has prevented an extensive adoption of the black-box type of models. In order to overcome this drawback and maintain the high performances of black-boxes, this paper has chosen a model-agnostic approach. Accumulated Local Effects and Shapley values are used to shape the predictors' impact on the likelihood of default and rank them according to their contribution to the model outcome. Prediction is achieved by two Machine Learning algorithms (eXtreme Gradient Boosting and FeedForward Neural Networks) compared with three standard discriminant models. Results show that our analysis of the Italian Small and Medium Enterprises manufacturing industry benefits from the overall highest classification power by the eXtreme Gradient Boosting algorithm still maintaining a rich interpretation framework to support decisions.     

Properties of learning models in collective action: Rationality of backward-looking players

This article intends to clarify properties of learning models in simulation studies and to conduct a comparison of preceding learning models. Learning models are often used in many simulation studies, but there is no uniform rule of learning. We introduce three technical properties (monotonicity, condition of probability, neutrality) and three rational properties (rationality is fixed situations, rationality in first order stochastic domination, rationality with risk preference in stocahstic situations). We examine Michael Macy's model, the Erev & Roth model, and some others. We find that these models have different properties. Though learning is treated as one of the solutions of social dilemma from the results of Macy's model (Kollock, 1998), Macy's model is peculiar learning model. Learning is not always a solution of social dilemma. A comparison of learning models from a uniform point of view clarifies the properties of each model, and helps to probe conformity of a learning model and human behavior.     

多因素分析的线性结构模型及其应用

线性结构模型是含有潜在因子的通径分析,该模型可以分析外生的潜在因子与内生的潜在因子之间相互影响的结构关系.研究应用线性结构模型探讨对《算法与数据结构》的学习兴趣有影响的主要因素,结果显示学生的专业基础和教学方式对学习兴趣的影响分别占各因素影响总和的49.56%和43.11%.注重专业基础课程的教学效果和采取通俗易懂的讲授方式是提高学生学习兴趣的有效途径.     

Simon’s team’s contributions to scientific progress in mathematics education: A commentary on the Learning Through Activity (LTA) research program

I discuss two ways in which the Learning Through Activity (LTA) research program contributes to scientific progress in mathematics education: (a) providing general and content-specific constructs to explain conceptual learning and instructional design that corroborate and/or elaborate on previous work and (b) raising new questions/issues. The general constructs include using instructional design as testable models of learning and using theoretical constructs to guide real-time, instructional adaptations. In this sense, the general constructs promote understanding of linkages between conceptual learning and instruction in mathematics. The concept-specific constructs consist of empirically-grounded, hypothetical learning trajectories (HLTs) for fractional and multiplicative reasoning. Each HLT consists of specific, intended conceptual changes and tasks that can bring them forth. Questions raised for me by the LTA work involve inconsistencies between the stance on learning and reported teaching-learning interactions that effectively led to students’ abstraction of the intended mathematical concepts.     

Basis function-based adaptive critic learning and its learning parameters selection

An adaptive critic learning (ACL) structure consists of two modules: the action and the critic ones. Learning occurs in both modules. The critic module learns to evaluate the system status. It transforms occasionally occurred failure signals into useful evaluation information. Utilizing such information, the action module can learn the control technique. In this paper, we investigate the technique of using basis functions (BFs) in ACL. One difficulty in the scheme is on selection of learning parameters. Without a guideline, the best set of learning parameters must be obtained from a large number of test simulations. This study investigated the effects of parameters through analysis and verified the analytical results by simulations. In addition to the problem of parameter selection, effects of measurement errors on the CMAC-based (one basis function technique) ACL have been also examined and reported.     

An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students’ initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students’ thinking and learning over time in relation to a set of tasks and activities developed to engender a view of exponential growth as a relation between two continuously covarying quantities. Developed out of two teaching experiments with early adolescents, the EGLT identifies three major stages of students’ conceptual development: prefunctional reasoning, the covariation view, and the correspondence view. The learning trajectory is presented along with three individual students’ progressions through the trajectory as a way to illustrate the variation present in how the participants made sense of ideas about exponential growth.     

A diverse human learning optimization algorithm

Human Learning Optimization is a simple but efficient meta-heuristic algorithm in which three learning operators, i.e. the random learning operator, the individual learning operator, and the social learning operator, are developed to efficiently search the optimal solution by imitating the learning mechanisms of human beings. However, HLO assumes that all the individuals possess the same learning ability, which is not true in a real human population as the IQ scores of humans, one of the most important indices of the learning ability of humans, follow Gaussian distribution and increase with the development of society and technology. Inspired by this fact, this paper proposes a Diverse Human Learning Optimization algorithm (DHLO), into which the Gaussian distribution and dynamic adjusting strategy are introduced. By adopting a set of Gaussian distributed parameter values instead of a constant to diversify the learning abilities of DHLO, the robustness of the algorithm is strengthened. In addition, by cooperating with the dynamic updating operation, DHLO can adjust to better parameter values and consequently enhances the global search ability of the algorithm. Finally, DHLO is applied to tackle the CEC05 benchmark functions as well as knapsack problems, and its performance is compared with the standard HLO as well as the other eight meta-heuristics, i.e. the Binary Differential Evolution, Simplified Binary Artificial Fish Swarm Algorithm, Adaptive Binary Harmony Search, Binary Gravitational Search Algorithms, Binary Bat Algorithms, Binary Artificial Bee Colony, Bi-Velocity Discrete Particle Swarm Optimization, and Modified Binary Particle Swarm Optimization. The experimental results show that the presented DHLO outperforms the other algorithms in terms of search accuracy and scalability.     

Modified optimization layer by layer algorithm for learning multilayer perceptrons

1. IntroductionThe feedforward Multilayer Perceptron (MLP) is one of the most widely used artificial neural networks among other network models. Its field of application includes patternrecognition, identification and control of dynamic systems, system modeling and nonlinearprediction of time series, etc. [1--41 founded on its nonlinear function approximation capability. Research of this type of networks has been stimulated since the discovery andpopularization of the Backpropagation learnin…     

Comparison of strategy learning methods in Farmer–Pest problem for various complexity environments without delays

In this paper effectiveness of several agent strategy learning algorithms is compared in a new multi-agent Farmer–Pest learning environment. Learning is often utilized by multi-agent systems which can deal with complex problems by means of their decentralized approach. With a number of learning methods available, a need for their comparison arises. This is why we designed and implemented new multi-dimensional Farmer–Pest problem domain, which is suitable for benchmarking learning algorithms. This paper presents comparison results for reinforcement learning (SARSA) and supervised learning (Naïve Bayes, C4.5 and Ripper). These algorithms are tested on configurations with various complexity with not delayed rewards. The results show that algorithm performances depend highly on the environment configuration and various conditions favor different learning algorithms.     

基于熵权TOPSIS-PSO-ELM的制造企业绿色创新能力评价模型及实证研究

为客观和准确地评价制造企业绿色创新能力,本文构建了制造企业绿色创新能力评价指标体系,提出了基于熵权TOPSIS的粒子群(PSO)优化极限学习机(ELM)集成学习算法的制造企业绿色创新能力评价模型。首先运用熵权法客观确定指标权重,结合TOPSIS测度并综合评价制造企业绿色创新能力,然后将评价值作为先验样本进行极限学习机的训练与测试,训练过程中利用PSO优化极限学习机的网络结构与连接权值,从而对绿色创新能力进行全面的分析和评价。最后以60家制造企业为例进行实证分析,并将熵权TOPSIS-PSO-ELM算法与极限学习机回归拟合算法对比,结果表明:基于熵权TOPSIS-PSO-ELM模型所得评价结果较已有方法更为准确可靠。此外,为进一步提高我国制造企业绿色创新发展能力提出了理论建议。     

Local systemic intervention

This paper reviews Local Systemic Intervention (LSI). LSI results from learning about Total Systems Intervention (TSI). Learning followed application of TSI and by putting TSI through a postmodern critique. LSI is a complementarist approach. It encourages diversity through local decision making about the relevance of designs, consideredness of decisions and astuteness of judgements. It encourages developing discourse around these three centres of learning and designing action accordingly. There is a regular stream of applications of LSI in many types of organisations.