Advertisement

Bayesian Student Models Based on Item to Item Knowledge Structures

  • Michel C. Desmarais
  • Michel Gagnon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4227)

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.

Keywords

Bayesian Network Directed Acyclic Graph Knowledge Structure Knowledge State Structural Learning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Trans. Information Theory 14(11), 462–467 (1968)MATHCrossRefGoogle Scholar
  2. 2.
    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)MATHCrossRefGoogle Scholar
  3. 3.
    Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)MATHGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Doignon, J.-P., Falmagne, J.-C.: Knowledge Spaces. Springer, Berlin (1999)MATHGoogle Scholar
  7. 7.
    Domingos, P., Pazzani, M.: On the optimality of the simple Bayesian classifier under zero-one loss. Machine Learning 29, 103–130 (1997)MATHCrossRefGoogle Scholar
  8. 8.
    Dowling, C.E., Hockemeyer, C.: Automata for the assessment of knowledge. IEEE Transactions on Knowledge and Data Engineering (2001)Google Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    François, O., Leray, P.: Etude comparative d’algorithmes d’apprentissage de structure dans les réseaux bayésiens. In: RJCIA 2003, pp. 167–180 (2003)Google Scholar
  11. 11.
    Jensen, F.V.: An introduction to Bayesian Networks. UCL Press, London (1996)Google Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    Murphy, K.P.: The Bayes net toolbox for MATLAB. Technical report, University of California at Berkeley; Berkeley, CA, October 12 (2001)Google Scholar
  16. 16.
    Neapolitan, R.E.: Learning Bayesian Networks. Prentice Hall, New Jersey (2004)Google Scholar
  17. 17.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, 2nd edn. MIT Press, Cambridge (2000)Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Vomlel, J.: Bayesian networks in educational testing. International Journal of Uncertainty, Fuzziness and Knowledge Based Systems 12(suppl. 1), 83–100 (2004)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michel C. Desmarais
    • 1
  • Michel Gagnon
    • 1
  1. 1.École Polytechnique de Montréal 

Personalised recommendations