Abstract
Bayesian networks are commonly used in cognitive student modeling and assessment. They typically represent the item-concepts relationships, where items are observable responses to questions or exercises and concepts represent latent traits and skills. Bayesian networks can also represent concepts-concepts and concepts-misconceptions relationships. We explore their use for modeling item-item relationships, in accordance with the theory of knowledge spaces. We compare two Bayesian frameworks for that purpose, a standard Bayesian network approach and a more constrained framework that relies on a local independence assumption. Their performance is compared over their respective ability to predict item outcome and through simulations over two data sets. The simulation results show that both approaches can effectively perform accurate predictions, but the constrained approach shows higher predictive power than a Bayesian Network. We discuss the applications of item to item structure for cognitive modeling within different contexts.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Trans. Information Theory 14(11), 462–467 (1968)
Conati, C., Gertner, A., Van Lehn, K.: Using Bayesian networks to manage uncertainty in student modeling. User Modeling and User-Adapted Interaction 12(4), 371–417 (2002)
Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)
Desmarais, M.C., Maluf, A., Liu, J.: User-expertise modeling with empirically derived probabilistic implication networks. User Modeling and User-Adapted Interaction 5(3-4), 283–315 (1996)
Desmarais, M.C., Pu, X.: A bayesian inference adaptive testing framework and its comparison with item response theory. International Journal of Artificial Intelligence in Education 15, 291–323 (2005)
Doignon, J.-P., Falmagne, J.-C.: Knowledge Spaces. Springer, Berlin (1999)
Domingos, P., Pazzani, M.: On the optimality of the simple Bayesian classifier under zero-one loss. Machine Learning 29, 103–130 (1997)
Dowling, C.E., Hockemeyer, C.: Automata for the assessment of knowledge. IEEE Transactions on Knowledge and Data Engineering (2001)
Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J.-P., Johannesen, L.: Introduction to knowledge spaces: How to build test and search them. Psychological Review 97, 201–224 (1990)
François, O., Leray, P.: Etude comparative d’algorithmes d’apprentissage de structure dans les réseaux bayésiens. In: RJCIA 2003, pp. 167–180 (2003)
Jensen, F.V.: An introduction to Bayesian Networks. UCL Press, London (1996)
Kambouri, M., Koppen, M., Villano, M., Falmagne, J.-C.: Knowledge assessment: tapping human expertise by the query routine. International Journal of Human-Computer Studies 40(1), 119–151 (1994)
Millán, E., Pérez-de-la-Cruz, J.-L., Suarez, E.: Adaptive bayesian networks for multilevel student modelling. In: Gauthier, G., VanLehn, K., Frasson, C. (eds.) ITS 2000. LNCS, vol. 1839, pp. 534–543. Springer, Heidelberg (2000)
Mislevy, R.J., Almond, R.G., Yan, D., Steinberg, L.S.: Bayes nets in educational assessment: Where the numbers come from. In: Laskey, K.B., Prade, H. (eds.) Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence (UAI 1999), pp. 437–446. Morgan Kaufmann Publishers, San Francisco (1999)
Murphy, K.P.: The Bayes net toolbox for MATLAB. Technical report, University of California at Berkeley; Berkeley, CA, October 12 (2001)
Neapolitan, R.E.: Learning Bayesian Networks. Prentice Hall, New Jersey (2004)
Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, 2nd edn. MIT Press, Cambridge (2000)
VanLehn, K., Niu, Z., Siler, S., Gertner, A.S.: Student modeling from conventional test data: A Bayesian approach without priors. In: Goettl, B.P., Halff, H.M., Redfield, C.L., Shute, V.J. (eds.) ITS 1998. LNCS, vol. 1452, pp. 434–443. Springer, Heidelberg (1998)
Vomlel, J.: Bayesian networks in educational testing. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 12(suppl. 1), 83–100 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Desmarais, M.C., Gagnon, M. (2006). Bayesian Student Models Based on Item to Item Knowledge Structures. In: Nejdl, W., Tochtermann, K. (eds) Innovative Approaches for Learning and Knowledge Sharing. EC-TEL 2006. Lecture Notes in Computer Science, vol 4227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11876663_11
Download citation
DOI: https://doi.org/10.1007/11876663_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45777-0
Online ISBN: 978-3-540-46234-7
eBook Packages: Computer ScienceComputer Science (R0)