An Efficient Joint Learning Approach for Item Response Theory

Tanish Agarwal, Kaustubh Shivshankar Shejole, Arpit Agarwal
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:869-899, 2026.

Abstract

Item response theory (IRT) is widely used in areas such as recommender systems, education, psychology, and other fields. A popular model for IRT is the Rasch model. Under this model, if a user with ability $\theta$ performs a task with difficulty $\beta$ then its label $X \sim \text{Bernoulli} (1 / (1 + \exp(-(\theta - \beta)))$. Existing joint maximum likelihood estimation approaches for this problem do not perform well when the number of items is small and also lack theoretical guarantees. Recently, Nguyen and Zhang proposed a two step approach: (1) spectral method for estimation of task parameters, (2) likelihood optimization for estimation of user parameters. While this approach is theoretically sound, it is not computationally efficient. In this work, we propose an EM-based algorithm for joint estimation of item and user parameters by introducing Pólya-Gamma latent variables, which simplify the logistic log-likelihood. We show that our algorithm is both theoretically sound and consistently outperforms existing methods on synthetic and real-world datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-agarwal26d, title = {An Efficient Joint Learning Approach for Item Response Theory}, author = {Agarwal, Tanish and Shejole, Kaustubh Shivshankar and Agarwal, Arpit}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {869--899}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/agarwal26d/agarwal26d.pdf}, url = {https://proceedings.mlr.press/v306/agarwal26d.html}, abstract = {Item response theory (IRT) is widely used in areas such as recommender systems, education, psychology, and other fields. A popular model for IRT is the Rasch model. Under this model, if a user with ability $\theta$ performs a task with difficulty $\beta$ then its label $X \sim \text{Bernoulli} (1 / (1 + \exp(-(\theta - \beta)))$. Existing joint maximum likelihood estimation approaches for this problem do not perform well when the number of items is small and also lack theoretical guarantees. Recently, Nguyen and Zhang proposed a two step approach: (1) spectral method for estimation of task parameters, (2) likelihood optimization for estimation of user parameters. While this approach is theoretically sound, it is not computationally efficient. In this work, we propose an EM-based algorithm for joint estimation of item and user parameters by introducing Pólya-Gamma latent variables, which simplify the logistic log-likelihood. We show that our algorithm is both theoretically sound and consistently outperforms existing methods on synthetic and real-world datasets.} }
Endnote
%0 Conference Paper %T An Efficient Joint Learning Approach for Item Response Theory %A Tanish Agarwal %A Kaustubh Shivshankar Shejole %A Arpit Agarwal %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-agarwal26d %I PMLR %P 869--899 %U https://proceedings.mlr.press/v306/agarwal26d.html %V 306 %X Item response theory (IRT) is widely used in areas such as recommender systems, education, psychology, and other fields. A popular model for IRT is the Rasch model. Under this model, if a user with ability $\theta$ performs a task with difficulty $\beta$ then its label $X \sim \text{Bernoulli} (1 / (1 + \exp(-(\theta - \beta)))$. Existing joint maximum likelihood estimation approaches for this problem do not perform well when the number of items is small and also lack theoretical guarantees. Recently, Nguyen and Zhang proposed a two step approach: (1) spectral method for estimation of task parameters, (2) likelihood optimization for estimation of user parameters. While this approach is theoretically sound, it is not computationally efficient. In this work, we propose an EM-based algorithm for joint estimation of item and user parameters by introducing Pólya-Gamma latent variables, which simplify the logistic log-likelihood. We show that our algorithm is both theoretically sound and consistently outperforms existing methods on synthetic and real-world datasets.
APA
Agarwal, T., Shejole, K.S. & Agarwal, A.. (2026). An Efficient Joint Learning Approach for Item Response Theory. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:869-899 Available from https://proceedings.mlr.press/v306/agarwal26d.html.

Related Material