Abstract
Identifying the best network structure from a myriad of candidates is not an easy task, and we propose a supervised learning method for this task. We test the idea with an instance of learning student models from students’ responses to test items, because student models are very important for intelligent tutoring systems. The training data for the classifiers were simulated based on the expectation about students’ item responses when students learn in different ways, and the trained classifier was used to select the model from the list of candidate models based on the observed item responses. Experimental results indicate that, even when item responses do not faithfully reflect students’ competence in the concepts, our classifiers still help us differentiate very similar models with indirect observations.
Similar content being viewed by others
References
Ben-Zeev, T. & Ronald, J. (2002). Is procedure acquisition as unstable as it seems?, Contemporary Educational Psychology, 27(4), 529–550.
Bishop, C.M. (1995). Neural networks for pattern recognition. Oxford: Oxford University Press.
Carmona, C., Milian, E., Perez-de-la-Cruz, J.L., Trella, M., & Conejo, R. (2005). Introducing prerequisite relations in a multi-layered Bayesian student model, Proceedings of the tenth international conference on user modeling, 347–356.
Chang, C.-C. & Lin, C.-J. (2001). LIBSVM: A library for support vector machines. software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm.
Chickering, D.M., Heckerman, D., & Meek, C. (2004). Large-sample learning of Bayesian networks is NP-hard, Journal of Machine Learning Research, 5 (Oct), 1287–1330.
Cortes, C. & Vapnik, V. (1995). Support-vector network, Machine Learning, 20(3), 273–297.
Cover, T.M. & Thomas, J.A. (2006). Elements of information theory (second edition). New Jersey: John Wiley & Sons.
Desmarais, M.C., Meshkinfam, P., & Gagnon, M. (2006). Learned student models with item to item knowledge structures, User Modeling and User-Adapted Interaction, 16(5), 403–434.
Gierl, M.J., Leighton, J.P., & Hunka S.M. (2007). Using the attribute hierarchy method to make diagnostic inferences about examinees’ cognitive skills, In (Leighton & Gierl, 2007), 242–274.
Glymour, C. & Cooper, G.F. (Eds.) (1999). Computation, causation, and discovery. California: AAAI Press.
Guo, Y. & Schuurmans, D. (2006). Convex structure learning for Bayesian networks: Polynomial feature selection and approximate ordering, Proceedings of the twenty-second annual conference on uncertainty in artificial intelligence.
Heckerman, D. (1999). A tutorial on learning with Bayesian networks, In (Jordan, 1999), 301–354.
Jensen F.V. & Nielsen, T.D. (2007). Bayesian networks and decision graphs. New York: SpringerVerlag.
Jordan, M.I. (Ed.) (1999). Learning in graphical models. Massachusetts: The MIT Press.
Knuth, D.E. (1973). The art of computer programming: Fundamental algorithms, p.73. Massachusetts: Addison-Wesley.
Leighton, J.P. & Gierl, M.J. (2007). Cognitive diagnostic assessment for education. Cambridge: Cambridge University Press.
Liu, C.-L. (2005). Using mutual information for adaptive item comparison and student assessment, Journal of Educational Technology & Society, 8(4), 100–119.
Liu, C.-L. (2008). A simulation-based experience in learning structures of Bayesian networks to represent how students learn composite concepts, International Journal of Artificial Intelligence in Education, 18(3), 237–285.
Martin, J. & VanLehn, K. (1995). Student assessment using Bayesian nets, International Journal of Human-Computer Studies, 42(6), 575–591.
Millan, E. & Perez-de-la-Cruz, J.L. (2002). A Bayesian diagnostic algorithm for student modeling and its evaluation, User Modeling and User-Adapted Interaction, 12(2–3), 281–330.
Mislevy, R.J., Almond, R.G., Yan, D., & Steinberg, L.S. (1999). Bayes nets in educational assessment: Where do the numbers come from?, Proceedings of the fifteenth conference on uncertainty in artificial intelligence, 437–446.
Mislevy, R.J. & Gitomer, D.H. (1996). The role of probability-based inference in an intelligent tutoring system, User Modeling and User-Adapted Interaction, 5(4), 253–282.
Neapolitan, R.E. (2003). Learning Bayesian networks. New Jersey: Prentice Hall.
Nichols, P.D., Chipman, S.F., & Brennan, R.L. (Eds.) (1995). Cognitively diagnostic assessment. New Jersey: Lawrence Erlbaum.
Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. California: Morgan Kaufmann.
Russell, S.J. & Norvig, P. (2002). Artificial intelligence: A modern approach. New Jersey: Prentice Hall.
Silander, T. & Myllymaki, P. (2006). A simple approach for finding the globally optimal Bayesian network structure, Proceedings of the twenty-second annual conference on uncertainty in artificial intelligence, 445–452.
Sleeman, D., Kelly, A. E., Martinak, R., Ward, R.D., & Moore, J.L. (1989). Studies of diagnosis and remediation with high school algebra students, Cognitive Science, 13(4), 551–568.
Teyssier, M. & Koller, D. (2005). Ordering-based search: A simple and effective algorithm for learning Bayesian networks, Proceedings of the twenty-first annual conference on uncertainty in artificial intelligence, 584–590.
Tsamardinos, I., Brown, L.E., & Aliferis, C.F. (2006). The max-min hill-climbing Bayesian network structure learning algorithm, Machine Learning, 65(1), 31–78.
Tatsuoka, K.K. (1983). Rule space: An approach for dealing with misconceptions based on item response theory, Journal of Educational Measurement, 20(4), 345–354.
Tatsuoka, K.K. (1995). Architecture of knowledge structures and cognitive diagnosis: A statistical pattern recognition and classification approach, In (Nichols et al., 1995), 327–360.
Tatsuoka, K.K. & Tatsuoka, M.M. (1997). Computerized cognitive diagnostic adaptive testing: Effect on remedial instruction as empirical validation, Journal of Educational Measurement, 34(1), 3–20.
Van der Linden, W.J. & Hambleton, R.K. (Eds.) (1997). Handbook of modern item response theory. New York: Springer-Verlag.
Van Lehn, K., Ohlsson, S., & Nason, R. (1994). Applications of simulated students: An exploration, International Journal of Artificial Intelligence in Education, 5(2), 135–175.
Vomlel, J. (2004). Bayesian networks in educational testing. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(Supplement 1), 83–100.
Witten, I.H. & Frank, E. (2005). Data mining: Practical machine learning tools and techniques. California: Morgan Kaufmann.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Liu, CL. Selecting Baysian-Network Models Based on Simulated Expectation. Behaviormetrika 36, 1–25 (2009). https://doi.org/10.2333/bhmk.36.1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.2333/bhmk.36.1