Using Bayesian Networks to Manage Uncertainty in Student Modeling

When a tutoring system aims to provide students with interactive help, it needs to know what knowledge the student has and what goals the student is currently trying to achieve. That is, it must do both assessment and plan recognition. These modeling tasks involve a high level of uncertainty when students are allowed to follow various lines of reasoning and are not required to show all their reasoning explicitly. We use Bayesian networks as a comprehensive, sound formalism to handle this uncertainty. Using Bayesian networks, we have devised the probabilistic student models for Andes, a tutoring system for Newtonian physics whose philosophy is to maximize student initiative and freedom during the pedagogical interaction. Andes’ models provide long-term knowledge assessment, plan recognition, and prediction of students’ actions during problem solving, as well as assessment of students’ knowledge and understanding as students read and explain worked out examples. In this paper, we describe the basic mechanisms that allow Andes’ student models to soundly perform assessment and plan recognition, as well as the Bayesian network solutions to issues that arose in scaling up the model to a full-scale, field evaluated application. We also summarize the results of several evaluations of Andes which provide evidence on the accuracy of its student models.This revised version was published online in July 2005 with corrections to the author name VanLehn.     

A Bayesian Diagnostic Algorithm for Student Modeling and its Evaluation

In this paper, we present a new approach to diagnosis in student modeling based on the use of Bayesian Networks and Computer Adaptive Tests. A new integrated Bayesian student model is defined and then combined with an Adaptive Testing algorithm. The structural model defined has the advantage that it measures students' abilities at different levels of granularity, allows substantial simplifications when specifying the parameters (conditional probabilities) needed to construct the Bayesian Network that describes the student model, and supports the Adaptive Diagnosis algorithm. The validity of the approach has been tested intensively by using simulated students. The results obtained show that the Bayesian student model has excellent performance in terms of accuracy, and that the introduction of adaptive question selection methods improves its behavior both in terms of accuracy and efficiency.     

Beyond Tracking: Modelling Activity and Understanding Behaviour

In this work, we present a unified bottom-up and top-down automatic model selection based approach for modelling complex activities of multiple objects in cluttered scenes. An activity of multiple objects is represented based on discrete scene events and their behaviours are modelled by reasoning about the temporal and causal correlations among different events. This is significantly different from the majority of the existing techniques that are centred on object tracking followed by trajectory matching. In our approach, object-independent events are detected and classified by unsupervised clustering using Expectation-Maximisation (EM) and classified using automatic model selection based on Schwarz's Bayesian Information Criterion (BIC). Dynamic Probabilistic Networks (DPNs) are formulated for modelling the temporal and causal correlations among discrete events for robust and holistic scene-level behaviour interpretation. In particular, we developed a Dynamically Multi-Linked Hidden Markov Model (DML-HMM) based on the discovery of salient dynamic interlinks among multiple temporal processes corresponding to multiple event classes. A DML-HMM is built using BIC based factorisation resulting in its topology being intrinsically determined by the underlying causality and temporal order among events. Extensive experiments are conducted on modelling activities captured in different indoor and outdoor scenes. Our experimental results demonstrate that the performance of a DML-HMM on modelling group activities in a noisy and cluttered scene is superior compared to those of other comparable dynamic probabilistic networks including a Multi-Observation Hidden Markov Model (MOHMM), a Parallel Hidden Markov Model (PaHMM) and a Coupled Hidden Markov Model (CHMM). First online version published in February, 2006     

Blended Learning to Increase Student Satisfaction: An Exploratory Study

Undergraduate nursing research courses are often difficult to teach due to the challenging content and lack of student satisfaction. To address this issue, two nursing instructors and a librarian embedded online discussions into an accelerated format, introductory nursing research course. The study was conducted over two semesters with two different instructors. The researchers investigated if using the blended learning strategy of discussion boards enhanced the learning experience and tested their theory with two measures: a weekly qualitative questionnaire and a post-study survey. Results suggested that asynchronous online discussions increased student satisfaction in introductory nursing research course work.     

A Bayesian Method for the Induction of Probabilistic Networks from Data

This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.     

An enhanced Bayesian model to detect students' learning styles in Web-based courses

Abstract   Students acquire and process information in different ways depending on their learning styles. To be effective, Web-based courses should guarantee that all the students learn despite their different learning styles. To achieve this goal, we have to detect how students learn: reflecting or acting; steadily or in fits and starts; intuitively or sensitively. In a previous work, we have presented an approach that uses Bayesian networks to detect a student's learning style in Web-based courses. In this work, we present an enhanced Bayesian model designed after the analysis of the results obtained when evaluating the approach in the context of an Artificial Intelligence course. We evaluated the precision of our Bayesian approach to infer students' learning styles from the observation of their actions with a Web-based education system during three semesters. We show how the results from one semester enabled us to adjust our initial model and helped teachers improve the content of the course for the following semester, enhancing in this way students' learning process. We obtained higher precision values when inferring the learning styles with the enhanced model.     

基于贝叶斯网络的学生模型在测试系统的应用研究

在网络课程及虚拟课堂中,在线测试是一个重要组成部分。本文对贝叶斯网络及其概率推理进行了简述,提出了基于贝叶斯网络的学生模型,并将其应用于自适应在线测试系统中。该系统不仅能够因人施测,而且具有预测能力,同时还可以排除学生猜对试题答案的非真实能力。     

Student modelling in intelligent tutoring systems

Student modelling is a special type of user modelling which is relevant to the adaptability of intelligent tutoring systems. This paper reviews the basic techniques which have been used in student modelling and discusses issues and approaches of current interest. The role of a student model in a tutoring system and methods for representing information about students are discussed. The paper concludes with an overview of some unresolved issues and problems in student modelling.Electric Brain Company     

Behaviour modelling,instruction and exploration training approaches in group and individual contexts

Behaviour modelling has been associated with higher learning outcomes compared to other training approaches. These cumulative research findings create imperative to examine underlying causal mechanisms or contingency factors that may promote behaviour modelling's advantages even further. We propose group-based learning as one contingency factor because there exists greater opportunity for observation, imitation and feedback. We use a two-by-three experimental laboratory design involving 84 subjects to test for an interaction effect between training context (group-based, individual-based) and training approach (behaviour modelling, exploration, instruction) on several learning outcomes. We use hierarchical regression to show that, while the interaction effect was not significant, the training approach main effect was significant. Consistent with expectations, behaviour modelling outperformed exploration on task performance. There were no significant differences between behaviour modelling and instruction. We conclude that behaviour modelling is associated with higher task performance levels on a complex word-processing task when compared to exploration.     

概率逻辑模型与学习研究进展

近年来,概率逻辑学习研究取得了很大进展,已经提出各种不同的形式化方法和学习方法,包括概率关系模（PRMs）、贝叶斯逻辑程序（BLPs）、逻辑贝叶斯网络（LBNs）和随机逻辑程序（SLPs）等。文章重点介绍了贝叶斯网络与一阶逻辑的结合,并以PRMs、BLPs和LBNs为例,描述了基于贝叶斯网络的概率逻辑模型（PLMs）的知识表示方法,给出了此类PLMs一般使用的参数估计方法和结构学习方法,并给出了建议的研究方向。     

Probabilistic temporal reasoning and its application to fossil power plant operation

Many real-world applications, such as industrial diagnosis, require an adequate representation and inference mechanism that combines uncertainty and time. In this work, we propose a novel approach for representing dynamic domains under uncertainty based on a probabilistic framework, called temporal nodes Bayesian networks (TNBN). The TNBN model is an extension of a standard Bayesian network, in which each temporal node represents an event or state change of a variable and the arcs represent causal–temporal relationships between nodes. A temporal node has associated a probability distribution for its time of occurrence, where time is discretized in a finite number of temporal intervals; allowing a different number of intervals for each node and a different duration for the intervals within a node (multiple granularity). The main difference with previous probabilistic temporal models is that the representation is based on state changes at different times instead of state values at different times. Given this model, we can reason about the probability of occurrence of certain events, for diagnosis or prediction, using standard probability propagation techniques developed for Bayesian networks. The proposed approach is applied to fossil power plant diagnosis through two detailed case studies: power load increment and control level system failure. The results show that the proposed formalism could help to improve power plant availability through early diagnosis of events and disturbances.     

Empirical analysis of an on-line adaptive system using a mixture of Bayesian networks

An on-line reinforcement learning system that adapts to environmental changes using a mixture of Bayesian networks is described. Building intelligent systems able to adapt to dynamic environments is important for deploying real-world applications. Machine learning approaches, such as those using reinforcement learning methods and stochastic models, have been used to acquire behavior appropriate to environments characterized by uncertainty. However, efficient hybrid architectures based on these approaches have not yet been developed. The results of several experiments demonstrated that an agent using the proposed system can flexibly adapt to various kinds of environmental changes.     

Modelling the student in Pitagora 2.0

With the aim to individualise human-computer interaction, an Intelligent Tutoring System (ITS) has to keep track of what and how the student has learned. Hence, it is necessary to maintain a Student Model (SM) dealing with complex knowledge representation, such as incomplete and inconsistent knowledge and belief revision. With this in view, the main objective of this paper is to present and discuss the student modelling approach we have adopted to implement Pitagora 2.0, an ITS based on a co-operative learning model, and designed to support teaching-learning activities in a Euclidean Geometry context. In particular, this approach has led us to develop two distinct modules that cooperate to implement the SM of Pitagora 2.0. The first module resembles a classical student model, in the sense that it maintains a representation of the current student knowledge level, which can be used by the teacher in order to tune its teaching strategies to the specific student needs. In addition, our system contains a second module that implements a virtual partner, called companion. This module consists of a computational model of an average student which cooperates with the student during the learning process. The above mentioned module calls for the use of machine learning algorithms that allow the companion to improve in parallel with the real student. Computational results obtained when testing this module in simulation experiments are also presented.     

Representing Probabilistic Rules with Networks of Gaussian Basis Functions

There is great interest in understanding the intrinsic knowledge neural networks have acquired during training. Most work in this direction is focussed on the multi-layer perceptron architecture. The topic of this paper is networks of Gaussian basis functions which are used extensively as learning systems in neural computation. We show that networks of Gaussian basis functions can be generated from simple probabilistic rules. Also, if appropriate learning rules are used, probabilistic rules can be extracted from trained networks. We present methods for the reduction of network complexity with the goal of obtaining concise and meaningful rules. We show how prior knowledge can be refined or supplemented using data by employing either a Bayesian approach, by a weighted combination of knowledge bases, or by generating artificial training data representing the prior knowledge. We validate our approach using a standard statistical data set.     

Modelling of Complete Robot Dynamics Based on a Multi-Dimensional, RBF-like Neural Architecture

A neural network based identification approach of manipulator dynamics is presented. For a structured modelling, RBF-like static neural networks are used in order to represent and adapt all model parameters with their non-linear dependences on the joint positions. The neural architecture is hierarchically organised to reach optimal adjustment to structural apriori-knowledge about the identification problem. The model structure is substantially simplified by general system analysis independent of robot type. But also a lot of specific features of the utilised experimental robot are taken into account.A fixed, grid based neuron placement together with application of B-spline polynomial basis functions is utilised favourably for a very effective recursive implementation of the neural architecture. Thus, an online identification of a dynamic model is submitted for a complete 6 joint industrial robot.     

Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior landscape. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.     

Deterministic learning from neural control for uncertain nonlinear pure‐feedback systems by output feedback

The essence of intelligence lies in the acquisition/learning and utilization of knowledge. However, how to implement learning in dynamical environments for nonlinear systems is a challenging issue. This article investigates the deterministic learning (DL) control problem for uncertain pure‐feedback systems by output feedback, which achieves the human‐like learning and control in a simple way. To reduce the complexity of control design and analysis, first, by combining an appropriate system transformation, the original pure‐feedback system is transformed into a simple normal nonaffine system. An observer is then introduced to estimate the transformed system states. Based on the backstepping and dynamic surface control techniques, a simple adaptive neural control scheme is first developed to guarantee the finite time convergence of the tracking error using only one neural network (NN) approximator. Second, through DL, the exponential convergence of the NN weights is obtained with the satisfaction of partial persistent excitation condition. Thus, locally accurate approximation/learning of the transformed unknown system dynamics is achieved and stored as constant NNs. Finally, by utilizing the stored knowledge, an experience‐based controller is constructed and a novel learning control scheme is further proposed to improve the control performance without any further adaptation online for the estimate neural weights. Simulation results have been given to illustrate that the proposed scheme not only can learn and memorize knowledge like humans but also can utilize experience to achieve superior control performance.     

Application of Bayesian Network Learning Methods to Waste Water Treatment Plants

Bayesian Networks have been proposed as an alternative to rule-based systems in domains with uncertainty. Applications in monitoring and control can benefit from this form of knowledge representation. Following the work of Chong and Walley, we explore the possibilities of Bayesian Networks in the Waste Water Treatment Plants (WWTP) monitoring and control domain. We show the advantages of modelling knowledge in such a domain by means of Bayesian networks, put forth new methods for knowledge acquisition, describe their applications to a real waste water treatment plant and comment on the results. We also show how a Bayesian Network learning environment was used in the process and which characteristics of data in the domain suggested new ways of representing knowledge in network form but with uncertainty representations formalisms other than probability. The results of applying a possibilistic extension of current learning methods are also shown and compared.     

一种通过反馈提高神经网络学习性能的新算法

为了有效提高前向神经网络的学习性能,需要从一个新的角度考虑神经网络的学习训练．基于此,提出了一种基于结果反馈的新算法——FBBP算法．将神经网络输入调整与通常的权值调整的反向传播算法结合起来,通过调整权值和输入矢量值的双重作用来最小化神经网络的误差函数．并通过几个函数逼近和模式分类问题的实例仿真,将FBBP算法与加动量项BP算法、最新的一种加快收敛的权值更新的算法进行了比较,来验证所提出的算法的有效性．实验结果表明,所提出的算法具有训练速度快和泛化能力高的双重优点,是一种非常有效的学习方法．