Jeroen Donkers

Maastricht University

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*Student Model = A representation of learner’s

internal (hidden) variables and their relations

*Attitudes, preferences, predispositions

*Current knowledge, misconceptions

*Behaviour

*Level of development, skills

*Metacognitive factors

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*Wide range of application

*Adaptive systems

* Intelligent tutoring

*Computer adaptive testing

*Personalized feedback

*Games

*Models varying in content and complexity

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*We deal with unobserved or indirectly and

partially observed variables

*Many concepts are vaguely defined

*A large range of uncontrolled external

influences

*Calling for a probabilistic approach

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Structure

Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems:

Networks of Plausible Inference. Morgan Kaufmann Publishers.

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Conditional

probabilities

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Inference

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Millán, E., Loboda, T., & Pérez-de-la-Cruz, J. L. (2010). Bayesian networks

for student model engineering. Computers & Education, 55(4), 1663–1683.

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*PRO

*Robust, large scale

*Efficient, fast algorithms

*Many tools to build and run

*Human-Interpretable, explainable

*Can be learned/mined from data

*CON

*Difficult to create

*Fixed, non-flexible structure

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*Learner environment is complex and changing

*An ontology such as OWL can be used to

describe concepts and relations

*Classes and instances

*Subclasses (owl:Thing, owl:Nothing)

*Object properties (relations), with instances

*Data-type properties, with instances

https://www.w3.org/TR/owl2-overview/

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*Classes: Student, Task, Time, Competency

*Instances:

*student John, Lili; Time t1, t2, t3

*Task k1, k2, k3; Competency c1, c2, c3

*Object properties: k1 needsCompetency c2

*Datatype properties: John hasName “John

Adams”, c1 hasName “Communication”

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*Extend Bayesian networks with OWL concepts

*Add probabilistic relations and reasoning to

OWL

*Add flexibility to Bayesian networks

*Use a mathematically sound way of reasoning

under uncertainty (Bayesian logic)

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* Koller, D. & Pfeffer, A. (1997). Object-Oriented Bayesian

Networks. UAI-97, San Francisco, CA, USA.

* Costa, P. & Laskey, K. (2006). PR-OWL: A Framework for

Probabilistic Ontologies. FOIS 2006. Baltimore, USA.

* Laskey, K. B. (2008). MEBN : A Language for First-Order Bayesian

Knowledge Bases. Artificial Intelligence, 17(2-3).

* Carvalho, R. N., Laskey, K. B., & Costa, P. C. G. (2010). PR-OWL

2.0 - Bridging the gap to OWL semantics. URSW/ISWC 2010.

Shanghai, China.

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*Knowledge fragments (MFrags)

*Features of entities (data properties)

*Relations between entities (object properties)

*Both represented by random variables (RV)

*Together they form an MTheory

*Consistent, joint probability distribution for all

instances of RVs in all Mfrags

*An MTheory, together with observed evidence can

be compiled into a classic Bayesian network (SSBN)

Costa, P. C. G., & Laskey, K. B. (2006). Multi-Entity Bayesian Networks Without Multi-Tears

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Costa, P. C. G., & Laskey, K. B. (2006). Multi-Entity Bayesian Networks Without Multi-Tears

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Costa, P. C. G., & Laskey, K. B. (2006). Multi-Entity Bayesian Networks Without Multi-Tears

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Costa, P. C. G., & Laskey, K. B. (2006). Multi-Entity Bayesian Networks Without Multi-Tears

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Situation specific

Bayesian Network

(SSBN)

Costa, P. C. G., & Laskey, K. B. (2006). Multi-Entity Bayesian Networks Without Multi-Tears

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Costa, P. C. G., & Laskey, K. B. (2006). Multi-Entity Bayesian Networks Without Multi-Tears

A complete MTHeory

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*MEBN Entities, attributes and relations are

defined as OWL classes, data properties and

object properties

*MEBN structure/logic is also declared in OWL

(predefined classes)

*Probability functions are stored in OWL

annotations

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*Create OWL ontology in Protégé

*Create and maintain MEBN in UnBBayes

(includes Protégé plugin)

*Query using UnBBayes GUI or java-API

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