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Graph theory and algorithms: various approaches to utilization of virtual learning environment

Graph theory and algorithms: various approaches to utilizati...

14th international conference on Interactive Collaborative learning (ICL)/11th international conference on Virtual-University (VU)

作者： Milkova, Eva Univ Hradec Kralove Fac Informat & Management Hradec Kralove Czech Republic

ISBN: (纸本)9781457717475

the paper focuses on experiences gained during the last years with the WebCT virtual learning environment together with multimedia applications supported education of three subjects. WebCT has been used at the Faculty of Informatics and Management since the beginning of this century. the author of the paper has been prepared with her students various multimedia applications dealing with objects appropriate to subject matter for more than 15 years. In the paper we discuss a benefit of multimedia applications and utilization of the WebCT courses used as a support of subjects dealing with graph theory and combinatorial optimization, i.e. Discrete Mathematics and Discrete Methods and Optimization. the paper also mentions the WebCT course prepared for the subject Algorithms and Data Structures aimed at the development of students' algorithmic thinking essential for the mentioned subjects.

关键词： algorithmic thinking graph theory combinatorial optimization virtual learning environment multimedia applications on-line testing team work

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An approach to intrinsic complexity of uniform learning

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thEORETICAL COMPUTER SCIENCE 2006年第1期364卷 42-61页

作者： Zilles, Sandra DFKI GmbH D-67608 Kaiserslautern Germany

Inductive inference is concerned with algorithmic learning of recursive functions. In the model of learning in the limit a learner successful for a class of recursive functions must eventually find a program for any function in the class from a gradually growing sequence of its values. this approach is generatised in uniform learning, where the problem of synthesising a successful learner for a class of functions from a description of this class is considered. A common reduction-based approach for comparing the complexity of learning problems in inductive inference is intrinsic complexity. Informally, if a learning problem (a class of recursive functions) A is reducible to a learning problem (a class of recursive functions) B, then a solution for B can be transformed into a solution for A. In the context of intrinsic complexity, reducibility between two classes is expressed via recursive operators transforming target functions in one direction and sequences of corresponding hypotheses in the other direction. the present paper is concerned with intrinsic complexity of uniform learning. the relevant notions are adapted and illustrated by several-examples. Characterisations of complete classes finally allow for various insightful conclusions. the connection to intrinsic complexity of non-uniform learning is revealed within several analogies concerning first the structure of complete classes and second the general interpretation of the notion of intrinsic complexity. (C) 2006 Elsevier B.V. All rights reserved.

关键词： inductive inference learning theory recursion theory

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From learning in the limit to stochastic finite learning

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thEORETICAL COMPUTER SCIENCE 2006年第1期364卷 77-97页

作者： Zeugmann, thomas Hokkaido Univ Div Comp Sci Sapporo Hokkaido 0600814 Japan

Inductive inference can be considered as one of the fundamental paradigms of algorithmic learning theory. We survey results recently obtained and show their impact to potential applications. Since the main focus is put on the efficiency of learning, we also deal with postulates of naturalness and their impact to the efficiency of limit learners. In particular, we look at the learnability of the class of all pattern languages and ask whether or not one can design a learner within the paradigm of learning in the limit that is nevertheless efficient. For achieving this goal, we deal with iterative learning and its interplay with the hypothesis spaces allowed. this interplay has also a severe impact to postulates of naturalness satisfiable by any learner. Furthermore, since a limit learner is only supposed to converge, one never knows at any particular learning stage whether or not the learner did already succeed. the resulting uncertainty may be prohibitive in many applications. We survey results to resolve this problem by outlining a new learning model, called stochastic finite learning. though pattern languages can neither be finitely inferred from positive data nor PAC-learned, our approach can be extended to a stochastic finite learner that exactly infers all pattern languages from positive data with high confidence. Finally, we apply the techniques developed to the problem of learning conjunctive concepts. (C) 2006 Elsevier B.V. All rights reserved.

关键词： inductive learning learning in the limit iterative learning pattern languages learning conjunctive concepts average-case analysis stochastic finite learning

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On generalized computable universal priors and their convergence

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thEORETICAL COMPUTER SCIENCE 2006年第1期364卷 27-41页

作者： Hutter, Marcus IDSIA CH-6928 Manno Lugano Switzerland

Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the posterior of the universal semimeasure M converges rapidly to the true sequence generating posterior it, if the latter is computable. Hence, M is eligible as a universal predictor in case of unknown mu. the first part of the paper investigates the existence and convergence of computable universal (semi) measures for a hierarchy of computability classes: recursive, estimable, enumerable, and approximable. For instance, M is known to be enumerable, but not estimable, and to dominate all enumerable semimeasures. We present proofs for discrete and continuous semimeasures. the second part investigates more closely the types of convergence, possibly implied by universality: in difference and in ratio, with probability 1, in mean sum, and for Martin-Lof random sequences. We introduce a generalized concept of randomness for individual sequences and use it to exhibit difficulties regarding these issues. In particular, we show that convergence fails (holds) on generalized-random sequences in gappy (dense) Bernoulli classes. (C) 2006 Elsevier B.V. All rights reserved.

关键词： sequence prediction algorithmic information theory Solomonoff's prior universal probability mixture distributions posterior convergence computability concepts Martin-Lof randomness

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Introducing a Framework for Code based Fairness Audits of learning Analytics Systems on the Example of Moodle learning Analytics 14

Introducing a Framework for Code based Fairness Audits of Le...

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14th international conference on Computer Supported Education (CSEDU)

作者： Tagharobi, Hassan Simbeck, Katharina Univ Appl Sci HTW Berlin Berlin Germany

ISBN: (纸本)9789897585623

Machine learning based predictive systems are increasingly used in various areas, including learning analytics (LA) systems. LA systems provide educators with an analysis of students' progress and offer predictions about their success. Although predictive systems provide new opportunities and convenience, studies show that they harbor risks for biased or even discriminatory outcomes. To detect and solve these discriminatory issues and examine algorithmic fairness, different approaches have been introduced. the majority of purposed approaches study the behavior of predictive systems using sample data. However, if the source code is available, e.g., for open-source projects, auditing it can further improve the examination of algorithmic fairness. In this paper, we introduce a framework for an independent audit of algorithmic fairness using all publicly available resources. We applied our framework on Moodle learning analytics and examined its fairness for a defined set of criteria. Our fairness audit shows that Moodle doesn't use protected attributes, e.g., gender, ethnicity, in its predictive process. However, we detected some issues in data distribution and processing, which could potentially affect the fairness of the system. Furthermore, we believe that the system should provide users with more detailed evaluation metrics to enable proper assessment of the quality of learning analytics models.

关键词： Code Audit algorithmic Fairness Moodle learning Analytics

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Well-calibrated predictions from on-line compression models

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thEORETICAL COMPUTER SCIENCE 2006年第1期364卷 10-26页

作者： Vovk, Vladimir Royal Holloway Univ London Dept Comp Sci Comp Learning Res Ctr Egham TW20 0EX Surrey England

It has been shown recently that transductive confidence machine (TCM) is automatically well-calibrated when used in the on-line mode and provided that the data sequence is generated by an exchangeable distribution. In this paper we strengthen this result by relaxing the assumption of exchangeability of the data-generating distribution to the much weaker assumption that the data agrees with a given "on-line compression model". (C) 2006 Elsevier B.V. All rights reserved.

关键词： transductive confidence machine confidence transducer on-line compression modelling Gaussian model Gauss linear model Markov model exchangeability model hypergraphical model

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Transductive confidence machine is universal 14th

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14th international conference on algorithmic learning theory

作者： Nouretdinov, I V'yugin, V Gammerman, A Univ London Comp Learning Res Ctr Royal Holloway Egham TW20 0EX Surrey England

ISBN: (纸本)3540202919

Vovk's Transductive Confidence Machine (TCM) is a practical prediction algorithm giving, in additions to its predictions, confidence information valid under the general iid assumption. the main result of this paper is that the prediction method used by TCM is universal under a natural definition of what "valid" means: any prediction algorithm providing valid confidence information can be replaced, without losing much of its predictive performance, by a TCM. We use as the main tool for our analysis the Kolmogorov theory of complexity and algorithmic randomness.

关键词： Forecasting

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learning a subclass of regular patterns in polynomial time

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thEORETICAL COMPUTER SCIENCE 2006年第1期364卷 115-131页

作者： Case, John Jain, Sanjay Reischuk, Ruediger Stephan, Frank Zeugmann, thomas Hokkaido Univ Div Comp Sci Sapporo Hokkaido 0600814 Japan Univ Delaware Dept Comp & Informat Sci Newark DE 19716 USA Natl Univ Singapore Sch Comp Singapore 117543 Singapore Med Univ Lubeck Inst Theoret Informat D-23538 Lubeck Germany Natl Univ Singapore Sch Comp Singapore 117543 Singapore Natl Univ Singapore Dept Math Singapore 117543 Singapore

An algorithm for learning a subclass of erasing regular pattern languages is presented. On extended regular pattern languages generated by patterns pi of the form x(0)alpha(1)x(1) ... alpha(m)x(m), where x(0),..., x(m) are variables and alpha(1), ..., alpha(m) strings of terminals of length c each, it runs with arbitrarily high probability of success using a number of examples polynomial in m (and exponential in c). It is assumed that m is unknown, but c is known and that samples are randomly drawn according to some distribution, for which we only require that it has certain natural and plausible properties. Aiming to improve this algorithm further we also explore computer simulations of a heuristic. (C) 2006 Elsevier B.V. All rights reserved.

关键词： algorithmic learning pattern languages average-case analysis probabilistically exact learning

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Formative Feedback in Mathematics Teacher Education: An Activity and Affordance theory Perspective 14

Formative Feedback in Mathematics Teacher Education: An Acti...

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14th international conference on Computer Supported Education (CSEDU)

作者： Hadjerrouit, Said Nnagbo, Celestine Ifeanyi Univ Agder Fac Engn & Sci Inst Math Sci Kristiansand Norway

ISBN: (纸本)9789897585623

the increasingly high number of students' enrolment has necessitated the recent attention on the use of computer-based assessment systems for feedback delivery to students for mathematical learning, such as Numbas. However, little is known about the affordances of Numbas in the research literature. the purpose of this study is to investigate the affordances of Numbas, their perception and actualization by students and teachers, and their effects on mathematical learning from an activity and affordance theory perspective. the study follows a qualitative research design using semi-structured interviews of six students and two teachers. the results reveal the perception and actualization of several affordances at the technological, mathematical, and pedagogical level. Conclusions and future work are drawn from the results to promote Numbas formative feedback for teaching and learning mathematics.

关键词： Activity theory (AT) Affordance Actualization Affordance Perception Affordance theory Computer-based Assessment System Constraint Formative Feedback Numbas

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Intrinsic complexity of uniform learning 14th

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14th international conference on algorithmic learning theory

作者： Zilles, S Univ Kaiserslautern FB Informat D-67653 Kaiserslautern Germany

ISBN: (纸本)3540202919

Inductive inference is concerned with algorithmic learning of recursive functions. In the model of learning in the limit a learner successful for a class of recursive functions must eventually find a program for any function in the class from a gradually growing sequence of its values. this approach is generalized in uniform learning, where the problem of synthesizing a successful learner for a class of functions from a description of this class is considered. A common reduction-based approach for comparing the complexity of learning problems in inductive inference is intrinsic complexity. In this context, reducibility between two classes is expressed via recursive operators transforming target functions in one direction and sequences of corresponding hypotheses in the other direction. the present paper is the first one concerned with intrinsic complexity of uniform learning. the relevant notions are adapted and illustrated by several examples. Characterizations of complete classes finally allow for various insightful conclusions. the connection to intrinsic complexity of non-uniform learning is revealed within several analogies concerning firstly the role and structure of complete classes and secondly the general interpretation of the notion of intrinsic complexity.

关键词： Recursive functions

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