Abstract
The Knowledge Tracing model is broadly used in various intelligent tutoring systems. As it estimates the knowledge of the student, it is important to get an accurate estimate. The most common approach for fitting the model is Expected Maximization (EM), which normally stops iterating when there is minimal model improvement as measured by log-likelihood. Even though the model’s predictive accuracy has converged, EM may not have come up with the right parameters when it stops, because the convergence of the log-likelihood value does not necessarily mean the convergence of the parameters. In this work, we examine the model fitting process in more depth and answer the research question: when should EM stop, specifically for the Knowledge Tracing model. While typically EM runs for approximately 7 iterations, in this work we forced EM to run for 50 iterations for a simulated dataset and a real dataset. By recording the parameter values and convergence states at each iteration, we found that stopping EM earlier leads to problems, as the parameter estimates continue to noticeably change after the convergence of the log-likelihood scores.
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Cen, H., Koedinger, K.R., Junker, B.: Learning Factors Analysis - A General Method for Cognitive Model Evaluation and Improvement. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) ITS 2006. LNCS, vol. 4053, pp. 164–175. Springer, Heidelberg (2006)
Corbett, A., Anderson, J.: Knowledge Tracing: Modeling the Acquisition of Procedural Knowledge. User Modeling and User-Adapted Interaction 4, 253–278 (1995)
Gong, Y., Beck, J.E., Heffernan, N.T.: Comparing Knowledge Tracing and Performance Factor Analysis by Using Multiple Model Fitting. In: Aleven, V., Kay, J., Mostow, J. (eds.) ITS 2010, Part I. LNCS, vol. 6094, pp. 35–44. Springer, Heidelberg (2010)
Murphy, K.P.: The Bayes Net Toolbox for Matlab. Computing Science and Statistics (2007) DOI= http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html
Wang, Y., Heffernan, N.T.: The Student Skill Model. In: Cerri, S.A., Clancey, W.J., Papadourakis, G., Panourgia, K. (eds.) ITS 2012. LNCS, vol. 7315, pp. 399–404. Springer, Heidelberg (2012)
Wikipedia, http://en.wikipedia.org/wiki/Expectation-maximization_algorithm
Beck, J.E., Chang, K.-m.: Identifiability: A Fundamental Problem of Student Modeling. In: Conati, C., McCoy, K., Paliouras, G. (eds.) UM 2007. LNCS (LNAI), vol. 4511, pp. 137–146. Springer, Heidelberg (2007)
Cen, H., Koedinger, K.R., Junker, B.: Comparing two IRT models for conjunctive skills. In: Woolf, B.P., Aïmeur, E., Nkambou, R., Lajoie, S. (eds.) ITS 2008. LNCS, vol. 5091, pp. 796–798. Springer, Heidelberg (2008)
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Gu, J., Cai, H., Beck, J.E. (2014). Investigate Performance of Expected Maximization on the Knowledge Tracing Model. In: Trausan-Matu, S., Boyer, K.E., Crosby, M., Panourgia, K. (eds) Intelligent Tutoring Systems. ITS 2014. Lecture Notes in Computer Science, vol 8474. Springer, Cham. https://doi.org/10.1007/978-3-319-07221-0_19
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DOI: https://doi.org/10.1007/978-3-319-07221-0_19
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