Dealbreaker: A Nonlinear Latent Variable Model for Educational Data

Andrew Lan, Tom Goldstein, Richard Baraniuk, Christoph Studer
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:266-275, 2016.

Abstract

Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i.e., the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-lan16, title = {Dealbreaker: A Nonlinear Latent Variable Model for Educational Data}, author = {Lan, Andrew and Goldstein, Tom and Baraniuk, Richard and Studer, Christoph}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {266--275}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/lan16.pdf}, url = {https://proceedings.mlr.press/v48/lan16.html}, abstract = {Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i.e., the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model.} }
Endnote
%0 Conference Paper %T Dealbreaker: A Nonlinear Latent Variable Model for Educational Data %A Andrew Lan %A Tom Goldstein %A Richard Baraniuk %A Christoph Studer %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-lan16 %I PMLR %P 266--275 %U https://proceedings.mlr.press/v48/lan16.html %V 48 %X Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i.e., the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model.
RIS
TY - CPAPER TI - Dealbreaker: A Nonlinear Latent Variable Model for Educational Data AU - Andrew Lan AU - Tom Goldstein AU - Richard Baraniuk AU - Christoph Studer BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-lan16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 266 EP - 275 L1 - http://proceedings.mlr.press/v48/lan16.pdf UR - https://proceedings.mlr.press/v48/lan16.html AB - Statistical models of student responses on assessment questions, such as those in homeworks and exams, enable educators and computer-based personalized learning systems to gain insights into students’ knowledge using machine learning. Popular student-response models, including the Rasch model and item response theory models, represent the probability of a student answering a question correctly using an affine function of latent factors. While such models can accurately predict student responses, their ability to interpret the underlying knowledge structure (which is certainly nonlinear) is limited. In response, we develop a new, nonlinear latent variable model that we call the dealbreaker model, in which a student’s success probability is determined by their weakest concept mastery. We develop efficient parameter inference algorithms for this model using novel methods for nonconvex optimization. We show that the dealbreaker model achieves comparable or better prediction performance as compared to affine models with real-world educational datasets. We further demonstrate that the parameters learned by the dealbreaker model are interpretable—they provide key insights into which concepts are critical (i.e., the “dealbreaker”) to answering a question correctly. We conclude by reporting preliminary results for a movie-rating dataset, which illustrate the broader applicability of the dealbreaker model. ER -
APA
Lan, A., Goldstein, T., Baraniuk, R. & Studer, C.. (2016). Dealbreaker: A Nonlinear Latent Variable Model for Educational Data. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:266-275 Available from https://proceedings.mlr.press/v48/lan16.html.

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