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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