Student Progress Modeling with Skills Deficiency Aware Kalman Filters

Carlotta Schatten, Lars Schmidt-Thieme

Abstract

One new usage of Learning Analytics in Intelligent Tutoring Systems (ITS) is sequencing based on performance prediction, which informs sequencers whether a student mastered or not a specific set of skills. Matrix Factorization (MF) performance prediction is particularly appealing because it does not require tagging involved skills in tasks. However, MF’s difficult interpretability does not allow to show the student’s state evolution, i.e. his/her progress over time. In this paper we present a novel progress modeling technique integrating the most famous control theory state modeler, the Kalman Filter, and Matrix Factorization. Our method, the Skill Deficiency aware Kalman State Estimation for Matrix Factorization, (1) updates at each interaction the student’s state outperforming the baseline both in prediction error and in computational requirements allowing faster online interactions; (2) models the individualized progress of the students over time that could be later used to develop novel sequencing policies. Our results are tested on data of a commercial ITS where other state of the art methods were not applicable.

References

  1. Cichocki, A., Zdunek, R., Phan, A. H., and Amari, S.-i. (2009). Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation. Wiley. com.
  2. Corbett, A. and Anderson, J. (1994). Knowledge tracing: Modeling the acquisition of procedural knowledge. UMAI.
  3. D Baker, R. S., Corbett, A. T., and Aleven, V. (2008). More accurate student modeling through contextual estimation of slip and guess probabilities in bayesian knowledge tracing. In ITS, pages 406-415. Springer.
  4. Janning, R., Schatten, C., and Lars, S.-T. (2014a). Feature analysis for affect recognition supporting task sequencing. In ECTEL.
  5. Janning, R., Schatten, C., and Schmidt-Thieme, L. (2014b). Multimodal affect recognition for adaptive intelligent tutoring systems. In FFMI EDM.
  6. Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Fluids Engineering, 82(1):35-45.
  7. Koren, Y., Bell, R., and Volinsky, C. (2009). Matrix factorization techniques for recommender systems. Computer, 42(8):30-37.
  8. Li, B., Zhu, X., Li, R., Zhang, C., Xue, X., and Wu, X. (2011). Cross-domain collaborative filtering over time. In Proceedings of the Twenty-Second international joint conference on Artificial IntelligenceVolume Volume Three, pages 2293-2298. AAAI Press.
  9. Manouselis, N., Drachsler, H., Vuorikari, R., Hummel, H., and Koper, R. (2011). Recommender systems in technology enhanced learning. In Recommender systems handbook, pages 387-415. Springer.
  10. Nielsen, J. (1994). Usability engineering. Elsevier.
  11. Pardos, Z. A. and Heffernan, N. T. (2010). Modeling individualization in a bayesian networks implementation of knowledge tracing. In UMAP. Springer.
  12. Pardos, Z. A. and Heffernan, N. T. (2011). Kt-idem: introducing item difficulty to the knowledge tracing model. In UMAP, pages 243-254. Springer.
  13. Pavlik, P., Cen, H., and Koedinger, K. (2009). Performance factors analysis-a new alternative to knowledge tracing. In AIED.
  14. Pilászy, I. and Tikk, D. (2009). Recommending new movies: Even a few ratings are more valuable than metadata. In RecSys.
  15. Rendle, S. and Schmidt-Thieme, L. (2008). Onlineupdating regularized kernel matrix factorization models for large-scale recommender systems. In Proceedings of the 2008 ACM conference on Recommender systems, pages 251-258. ACM.
  16. Schatten, C., Janning, R., and Schmidt-Thieme, L. (2014a). Vygotsky based sequencing without domain information: A matrix factorization approach. In Computer Supported Education, pages 35-51. Springer.
  17. Schatten, C., Janning, R., and Schmidt-Thieme, L. (2015). Integration and evaluation of a machine learning sequencer in large commercial its. In AAAI2015. Springer.
  18. Schatten, C., Mavrikis, M., Janning, R., and SchmidtThieme, L. (2014b). Matrix factorization feasibility for sequencing and adaptive support in its. In EDM.
  19. Schatten, C. and Schmidt-Thieme, L. (2014). Adaptive content sequencing without domain information. In CSEDU.
  20. Schatten, C., Wistuba, M., Schmidt-Thieme, L., and Gutirrez-Santos, S. (2014c). Minimal invasive integration of learning analytics services in its. In ICALT.
  21. Schilling, N., Wistuba, M., Drumond, L., and SchmidtThieme, L. (2015). Joint model choice and hyperparameter optimization with factorized multilayer perceptrons. In Tools with Artificial Intelligence (ICTAI), 2015 IEEE 27th International Conference on, pages 72-79. IEEE.
  22. Thai-Nghe, N., Drumond, L., Horvath, T., KrohnGrimberghe, A., Nanopoulos, A., and SchmidtThieme, L. (2011). Factorization techniques for predicting student performance. Educational Recommender Systems and Technologies: Practices and Challenges. IGI Global.
  23. Thai-Nghe, N., Drumond, L., Horvath, T., and SchmidtThieme, L. (2012). Using factorization machines for student modeling. In UMAP Workshops.
  24. Thai-Nghe, N., Drumond, L., Krohn-Grimberghe, A., and Schmidt-Thieme, L. (2010). Recommender system for predicting student performance. Procedia Computer Science, 1(2):2811-2819.
  25. Voss, L., Schatten, C., and Schmidt-Thieme, L. (2015). A transfer learning approach for applying matrix factorization to small its datasets. In EDM2015.
  26. Vygotsky, L. L. S. (1978). Mind in society: The development of higher psychological processes. HUP.
  27. Wang, Y. and Heffernan, N. T. (2012). The student skill model. In ITS2012.
  28. Wistuba, M., Schilling, N., and Schmidt-Thieme, L. (2015). Sequential model-free hyperparameter tuning. In Data Mining (ICDM), 2015 IEEE International Conference on, pages 1033-1038. IEEE.
  29. Xiong, L., Chen, X., Huang, T.-K., Schneider, J. G., and Carbonell, J. G. (2010). Temporal collaborative filtering with bayesian probabilistic tensor factorization. In SDM, volume 10, pages 211-222. SIAM.
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Paper Citation


in Harvard Style

Schatten C. and Schmidt-Thieme L. (2016). Student Progress Modeling with Skills Deficiency Aware Kalman Filters . In Proceedings of the 8th International Conference on Computer Supported Education - Volume 1: CSEDU, ISBN 978-989-758-179-3, pages 31-42. DOI: 10.5220/0005737200310042


in Bibtex Style

@conference{csedu16,
author={Carlotta Schatten and Lars Schmidt-Thieme},
title={Student Progress Modeling with Skills Deficiency Aware Kalman Filters},
booktitle={Proceedings of the 8th International Conference on Computer Supported Education - Volume 1: CSEDU,},
year={2016},
pages={31-42},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005737200310042},
isbn={978-989-758-179-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Computer Supported Education - Volume 1: CSEDU,
TI - Student Progress Modeling with Skills Deficiency Aware Kalman Filters
SN - 978-989-758-179-3
AU - Schatten C.
AU - Schmidt-Thieme L.
PY - 2016
SP - 31
EP - 42
DO - 10.5220/0005737200310042