interactive educational system for dynamic bayesian ... · interactive educational system for...

Interactive Educational System for DynamicBayesian Decision-making

EVGENIA SUZDALEVADepartment of Adaptive Systems

UTIA AV CRPod vodarenskou vezı 4, 18208 Prague

CZECH REPUBLIC

PETR NEDOMADepartment of Adaptive Systems

UTIA AV CRPod vodarenskou vezı 4, 18208 Prague

CZECH REPUBLIC

Abstract:The paper describes the extensive educational system for the field of Bayesian decision-making, based onthe tools of PDFLATEX andMATLAB R©. The system enables to familiarize with the tasks of Bayesian decision-making, related to the probability mixture models, and to learn the theoretical and algorithmic aspects of solutionof these tasks. The educational system is intended for the postgraduate students and researchers, beginning theactivity in this area. The paper summarizes the principles, used in design of the system, describes the teachingsession and provides the example of the realization of Bayesian decision-making task.

Key–Words:Educational system, Bayesian decision-making, probabilistic mixtures

1 Introduction

The paper describes the principles of creating theeducational means for dynamic Bayesian decision-making. Bayesian decision-making is a well-elaborated statistical methodology, applied in prac-tice for solving variety of problems, dealing with thedata mining.

The need for educational system has arisen,since the postgraduate students and the beginningresearchers were faced with difficulties in form oftremendous variety and volume of scientific materi-als to be studied. Then, the theoretical and algorith-mic basis of dynamic Bayesian decision-making hasbeen gathered in the book [1], and the interactive ed-ucational system, based on this book, has been devel-oped. Software support of the system has been pro-vided by the means of PDFLATEX, MATLAB R© [2],and especially by the toolbox Mixtools [3], whichis worth mentioning separately. Mixtools is the ex-tensive software toolbox, offering implementationof majority of the decision-making algorithms, pre-sented in [1], and finding successful application inmany areas (advisory system for operators of rollingmills [4], diagnostics of thyroid cancer [5], urbantraffic control [6], diagnostics and therapy of up-per limb lymphedema [7] etc.). Thus, using the al-gorithms of Mixtools, the educational system cov-ers both theoretical and programming aspects of dy-namic Bayesian decision-making. The basic facts of

this methodology are briefly described in Section 2.The main emphasis of the paper is on develop-

ing and design of the educational system, that is pro-vided in Section 3. Under developing the system anumber of principles was followed. One of them isconnectedness to theory. The paper describes, howthe access to theory is organized. Another importantprinciple is theuse of database, explaining the termsand meanings of variables. One of the basic featuresof the system is availability of educational tools bothin PDF format and by means ofMATLAB. Thepaper describes a structure of these tools, which ex-plain the decision-making tasks, and proposes theoriginal way of their specification. Navigation in-side the system allows to run the task inMATLABfrom the PDF format document, view aMATLABcode, open the corresponding theory, read about therecommended experiments etc. Section 3 describesin details the use and the functioning of the systemduring the teaching session.

Section 4 demonstrates one of the educationalexamples. Concluding remarks in Section 5 close thepaper.

2 Basic Facts of Bayesian Decision-making

To begin with, Bayesian decision-making requires tointroduce a concept ofdecision maker. In the context

Proceedings of the 3rd WSEAS/IASME International Conference on ENGINEERING EDUCATION, Vouliagmeni, Greece, July 11-13, 2006 (pp131-136)

of the educational system this concept means an user,working with the system, or a student. The next con-cept to be introduced is asystem, which the decisionmaker wants to describe or influence. The decisionmaker possesses some knowledge about the system –experience. It is clear, that there exists some knowl-edge about the system, which is not available to thedecision maker. It is denoted by a conceptignorance.The decision maker has a set ofadmissible strategies,which impose the physical restrictions on his actions.Naturally, there is aloss function, which quantifiesthe degree of reaching the decision maker’s aim. Un-der all these conditions the decision maker shouldmakedecision, which would lead to the reaching ofaim. In these words a scheme of decision-makingcan be briefly summarized.

To describe a system, the decision makerchooses a model. The probabilitymixture modelsproved themselves as a effective mean for solution ofBayesian decision-making tasks. The mixture modelis the conditional probability density function

f(data | previous data, parameters),

which is presented as the sum of the weighed com-ponents

ncom∑c=1

weightsc× (1)

K∏k=1

fk(data | previous data, parameters).︸︷︷︸kth parameterized factorwithin cth component︸︷︷︸

cth component

Let’s suppose, that the decision maker wants to de-scribe a system by the mixture. The system data,which should be preprocessed, are available to thedecision maker. Then, some prior knowledge aboutthe system might be available. For example, it canbe the knowledge whether the system is a static orthe dynamic one. This is theexperienceof the deci-sion maker for this moment of time.

For a start, the decision maker wishes to esti-mate a mixture structure. In other words, he has toperform themixture initialization, which represents aconstruction of prior estimate of the mixture. The re-sult of initialization gives the decision maker a mix-ture model structure.

After initialization it is necessary to perform themixture estimation, that results in a better qualitymixture with estimated parameters.

The mixture model obtained should be verifiedbefore its using in subsequent tasks. In other words,it is necessary to check whether the model provides

good description of system data or not. This task iscalledmodel validation.

The tasks mentioned, together with their varia-tions, belong to one of the basic branches of Bayesiandecision-making –learning, here learning with mix-tures. This is a schematic sequence of actions of thedecision maker, when the aim is only todescribethesystem. Naturally, this global aim can include manyvarious sub-aims.

In the case, when the aim is toinfluenceor con-trol the system, the task of the decision maker be-longs to another basic branch of Bayesian decision-making –design. It contains several types ofcontroldesignanddesign validation.

All these tasks have been described here verybriefly, only to give a general idea of decision-making process. To solve each of them, the varietyof techniques and algorithms are used. Most of thealgorithms have been implemented in toolbox Mix-tools, mentioned above. The problem has arisen,how to teach the students and young researchers thetheory and algorithms of Bayesian decision-making.

3 Design of the Educational System

The educational system is organized in the form ofcollection of the interactive case studies, each ofwhich explains a decision-making task, dependingon system data, model used, solution technique etc.The case studies are self-contained. They provideinformation enough for getting acquainted and un-derstanding the decision-making tasks. During theteaching session the educational system invites a stu-dent to play a role ofexternal decision maker, whilethe task is solved internally by the case study. Un-der developing the educational system the followingprinciples were conformed.Connectedness with theoryThe system is con-nected with a theoretical background both in a directand a figurative sense. The text of the case studies,the concepts and variables are based on the book [1]and correspond to the terminology, introduced in it.The case studies provide the hyperlinks to the arti-cles, or to the educational text with theoretical ma-terial, depending on the decision-making area, beingdiscussed. For example, the case study on mixtureestimation with one of the estimation algorithms al-lows to open the papers about algorithms and themixture estimation in general. There is no more needto look for the theoretical materials in the library.Use of the databaseThe system is connected with adecision-making database. It contains definitions ofthe decision-making terms and explains the meaning


of the variables. All the decision-making concepts(for example,system, experience, mixture etc) andthe variables, met in the text, are the hyperlinks tothe labels of database. Clicking on them shows thedefinition of the concept in new window.Use of PDFLATEX and MATLAB The educationalsystem was developed in PDFLATEX, which offersthe high-quality tools not only for typing the sci-entific documents, but also for using the hypertextreferences inside the system. Moreover, the hyper-links in such a PDF format document allow to runthe task inMATLAB. The educational system ex-ploits MATLAB to run the tasks, but any similarsoftware can be used. For example, the similar ed-ucational system [8] used GNU Octave [9]. In thissense the system has property ofuniversality. More-over, most of the processing functions of the tool-box Mixtools are re-coded in C-language and usedas MEX-functions.

Thus, the educational system unifies the text de-scription of the decision-making task and its programimplementation. It means, each case study is offeredas a text in the PDF format and asMATLAB script.Case study in the PDF formatEach case study hasits own page in PDF format. Example of such a pageis shown at Fig. 1.

Figure 1: Example of a case study page

At the beginning the page contains thespecifica-tion of the decision-making task. It consists of theconcepts defined in Section 2:◦ system,

◦ experience,

◦ ignorance,

◦ admissible strategy,

◦ loss function,

◦ decision.The specification allows the decision maker to have aclear idea of the task to be solved. With its help, thedecision maker understands what means (experience,admissible strategies, loss function) are available tohim for reaching the aim. This way of specificationof the decision-making task was introduced in [1].

Then, the page offers the solution of the task.The solution usually involves the algorithms of tool-box Mixtools. It is described from the position ofperformance of the algorithms with respect to theconcrete task. The description of the solution is il-lustrated by the figures, where primarily demonstratethe data, results of the individual iterations and thefinal result of the solution (for example, estimatedmodel). The description of the solution interprets theresults and gives an insight into performance of algo-rithms.

The important terms and the variables, met at thePDF page, are the color hypertext references to thedatabase of definitions.

At the bottom of the page there are several nav-igation buttons. They are worth describing in de-tails. The button “theory” refers to the articles de-pending on the decision-making area discussed. Thepurpose of the button “mixtools guide” is clear – itopens the manual [10] to the toolbox Mixtools at thechapter, related to the discussed area. The next but-ton is “function help”. It gives a description of thefunction from the toolbox Mixtools, which has beenused for solving the decision-making task. The but-ton “recommended experiments” informs the deci-sion maker, the changes of what values can influenceon the performance of the algorithms. It gives a listof experiments for the decision maker to fulfill. Thebutton “mainpage” returns the decision maker to themain page of the educational system. The mentionedbuttons always open the PDF document. It means,that the articles, the database, guide and descriptionof functions are of PDF format.

The rest of the buttons – “run example” and“view script” – are of another nature. The button“view script” shows aMATLAB script of the case


study in some simple text editor. The button “runexample” starts the task inMATLAB.Case study in MATLAB The case study inMATLAB represents a script, which uses thedecision-making algorithms of the toolbox Mixtools.This script produces theMATLAB dialog. The di-alog shows the elements of the specification of thedecision-making task already with certain values ofthe variables and settings of the algorithm (number ofiterations, options etc). The dialog asks whether thedecision maker wants to change something or not.Then the task is solved. The results of the solutionare plotted at the figures, which have been shown atthe PDF format page of the case study. It should benoted, that the PDF format page always contains theresults with default settings of the algorithm. ThenMATLAB shows the dialog with the changed val-ues and proposes to continue the solving, or to returnto the default values, or to stop.Teaching sessionThus, the educational system re-quires any PDF viewer andMATLAB installed onthe computer. The teaching session includes the fol-lowing actions of the decision maker. The decisionmaker opens the PDF format document and gets intothe system main page. It is necessary to choose thecase study with task of decision maker’s interest andto read the PDF format page. In the case of need thedecision maker uses the hyperlinks to the databaseof terms, to the theoretical materials and Mixtoolsguide. Then, with the help of button “run exam-ple”, the decision maker runs the task inMATLAB.MATLAB presents the solution with the defaultsettings. After getting acquainted with it, the deci-sion maker returns to the case study in PDF formatand obtains the list of experiments to be done withthe help of the button “recommended experiments”.He switches intoMATLAB, makes the experimentsand observes the influence of the changed values onthe performance of the algorithm. More advanceddecision maker can learn theMATLAB code of thecase study, which is demonstrated by means of thebutton “view script”. Having learned the task, thedecision maker returns to the main page of the sys-tem and chooses another one.

4 Example

To demonstrate the use of the educational system,one of the case studies has been chosen. It concernsthe task of themixture initialization, see Section 2.

The title of the case study at the main page of thesystems sounds:Static Mixture Initialization – “Ba-nana Shape” Benchmark. The aim of the example is

to show the result of initialization for one of the mosteasily visually verified form of mixture.

The PDF format page of the case study con-tains the following information (note, that all theterms typed by italics are the color hyperlinks to thedatabase of definitions).

System: ndatdata are generated by the staticnormalmixturewith ncomicomponents. The compo-nents are located in the shape of banana, whichcan be easily used for the visual model verifica-tion. Random generator is defined byseed. Thecommon covariance of components isdiac;

Experience: ndatdata; knowledge that the systemis a static one;

Ignorance: mixture structure; mixture parameters;initial setting of the initialization algorithm;

Admissible strategy:formulated only for designtasks, here it is not formulated;

Loss function:negativev-log-likelihood;

Decision: estimation of mixturestructureand pa-rameters.

The banana-shaped mixture is taken as the sim-ulator, see Fig. 2 (top left). The simulator generates

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Figure 2: Simulator, scaled data clusters, the initial-ized mixture and data, generated by it

the data. The order of data is randomized to eliminatepossible influence of the mixture-based data genera-tion. The data, scaled to zero mean and unit variance,


are displayed at Fig. 2 (top right). Then the initializa-tion of mixture is done, using the Mixtools functionmixinit, see Fig. 2 (bottom left). The performance ofthe initialization algorithm is influenced by a numberof components of the initial modelncomiand a num-ber of iterationsniter. The settings of the algorithmare defined by the variableopt.

The initialized mixture should be checkedwhether it provides a good description of data or not.Due to its shape this model can be verified visually.The initialized mixture is used as the simulator andgenerates the data of the same size, see Fig. 2 (bot-tom right). The good visual correspondence of thedata, used for initialization, and the data, generatedby the initialized mixture, validates the model. Fig.2 demonstrates the results with default settings of thealgorithm, that can be changed in running the casestudy inMATLAB.

Navigation button “function help” gives the de-scription of Mixtools functionmixinit and its param-eters. The button “run example” startsMATLAB,which produces the following dialog:

--- System ---------------------------number of components ncom = 40;diagonal of noise cov. diac = 0.5;

--- Data -----------------------------length of data ndat = 1500;seed seed = 1234;

--- Initialization -------------------prior No. of components ncomi = 10;number of repetitions niter = 3;options opt = ’pn1k3g3h100d100’

any changes?ENTER = no, or type a command: >

The default values of variables are shown. Notethe variableopt, description of which the decisionmaker obtains in the database. The variableopt in-cludes several options (herep, n1, k3, g3, h100,d100), which indicate the settings of the initializa-tion algorithm, in one default value.

The decision maker can change the values ofvariables according to recommendations, obtained inPDF format page by means of the button “recom-mended experiments”. It is recommended to observethe performance of the algorithm with the followingvalues:◦ number of mixture componentsncom= 10, 20;

◦ diagonal of noise covariancediac= 0.1, 0.5;

◦ data sizendat= 1000, 500;

◦ trajectory of random generatorseed= any integer;

◦ number of initial model componentsncomi= 30,10, 5;

◦ number of iterations of the initialization algorithmniter = 3, 5.

For example, the decision maker sets a value ofnumber of components of the simulatorncom = 20.The following results, see Fig. 3, are obtained. Note

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Figure 3: Simulator withncom = 20, data clusters,initialized mixture and data, generated by it

the difference between Fig. 2 (top left) and Fig. 3 (topleft).

The following dialog appears

ENTER:continue I: initial values S: stop C: >

The decision maker chooses among the options:◦ I – continue the experiment withncom = 20;

◦ S– return the default valuencom = 40;

◦ C – stop the experiment.

5 ConclusionThe paper described the interactive educational sys-tem for Bayesian decision-making, developed withthe help of tools of PDFLATEX and MATLAB.The system enables to familiarize with the tasksof Bayesian decision-making, related to themixturemodels, and to learn the theoretical and algorithmicaspects of their solution.


The system is intended for the postgraduate stu-dents and researchers, beginning their activity at thearea.

To the advantages of the system one may take,first of all, the combination of theoretical solutionand software implementation of the tasks. The uni-form way of specification of the decision-makingtasks is also important positive feature of the system.The property of the universality is one of the advan-tages of the educational system. It means, for thefirst, the principles of the creating of the system canbe used for another scientific area. For the second,any software, similar toMATLAB, can be used.For example, the educational system for Bayesianstatistics, directed at the undergraduate students ofthe Faculty of Transportation of the Czech TechnicalUniversity [8], was based on the same principles withOctave as a software for running the tasks.

Among the drawbacks of the presented educa-tional system one may note theclosed sourcecodeof the algorithms of the toolbox Mixtools. The de-cision maker only learns to use the functions of thetoolbox for working with mixture models.

The educational system is available on web(http://as.utia.cz/softwaretools/mixtools).

Acknowledgements: This work was supportedby GA CR grants No. 201/06/P434 and No.102/03/0049.

References:

[1] M. K arny, J. Bohm, T. V. Guy, L. Jirsa, I. Nagy,P. Nedoma, and L. Tesar, Optimized BayesianDynamic Advising: Theory and Algorithms,Springer, London, 2005.

[2] The Matlab Inc., Matlab documentation, vol.MA 01760-2098, Natick, 2000.

[3] P. Nedoma, M. Karny, T.V. Guy, I. Nagy, andJ. Bohm, Mixtools (Program), UTIA AV CR,Prague, 2003.

[4] P. Nedoma and P. Ettler, “Data-based adviser tooperators of complex processes”, inProceed-ings of the 2002 IEEE International Conferenceon Control Applications, M. J. Grimble, Ed.,Glasgow, September 2002, pp. 830–831, IEEE.

[5] Ladislav Jirsa, Anthony Quinn, and FerdinandVarga, “Identification of thyroid gland activityin radiotherapy”, inISBA Eighth World Meet-ing on Bayesian Statistics, Valencia, Spain,June 2006, accepted abstract.

[6] J. Kratochvılova and I. Nagy, “Traffic con-trol of microregion.”, in CMP’04: MUL-TIPLE PARTICIPANT DECISION MAKING,Theory, algorithms, software and applications,J. Andrysek, M. Karny, and J.. Kracık, Eds.,Adelaide, May 2004, pp. 161 – 171, AdvancedKnowledge International.

[7] P. Gebousky, M. Karny, H. Krızova, andM. Wald, “Relevance of quantification in com-bined lymphoscintigraphy diagnostics of up-per limb lymphedema”, Journal of NuclearMedicine, 2005, submitted.

[8] E. Suzdaleva, I. Nagy, L. Pavelkova, andM. Karny, EduKALIBRE EXAMPLES. (Pro-gram), UTIA AV CR, Praha, 2005.

[9] J. W. Eaton, GNU Octave Manual. A high-level interactive language for numerical com-putations, 3 edition, ISBN: 0-9541617-2-6.

[10] P. Nedoma, M. Karny, J. Bohm, and T. V. Guy,“Mixtools Interactive User’s Guide”, Tech.Rep. 2143,UTIA AV CR, Praha, 2005.


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