Novel Spectral Algorithms for the Partial Credit Model

Duc Nguyen, Anderson Ye Zhang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:37840-37878, 2024.

Abstract

The Partial Credit Model (PCM) of Andrich (1978) and Masters (1982) is a fundamental model within the psychometric literature with wide-ranging modern applications. It models the integer-valued response that a subject gives to an item where there is a natural notion of monotonic progress between consecutive response values, such as partial scores on a test and customer ratings of a product. In this paper, we introduce a novel, time-efficient and accurate statistical spectral algorithm for inference under the PCM model. We complement our algorithmic contribution with in-depth non-asymptotic statistical analysis, the first of its kind in the literature. We show that the spectral algorithm enjoys the optimal error guarantee under three different metrics, all under reasonable sampling assumptions. We leverage the efficiency of the spectral algorithm to propose a novel EM-based algorithm for learning mixtures of PCMs. We perform comprehensive experiments on synthetic and real-life datasets covering education testing, recommendation systems, and financial investment applications. We show that the proposed spectral algorithm is competitive with previously introduced algorithms in terms of accuracy while being orders of magnitude faster.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-nguyen24k, title = {Novel Spectral Algorithms for the Partial Credit Model}, author = {Nguyen, Duc and Zhang, Anderson Ye}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {37840--37878}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/nguyen24k/nguyen24k.pdf}, url = {https://proceedings.mlr.press/v235/nguyen24k.html}, abstract = {The Partial Credit Model (PCM) of Andrich (1978) and Masters (1982) is a fundamental model within the psychometric literature with wide-ranging modern applications. It models the integer-valued response that a subject gives to an item where there is a natural notion of monotonic progress between consecutive response values, such as partial scores on a test and customer ratings of a product. In this paper, we introduce a novel, time-efficient and accurate statistical spectral algorithm for inference under the PCM model. We complement our algorithmic contribution with in-depth non-asymptotic statistical analysis, the first of its kind in the literature. We show that the spectral algorithm enjoys the optimal error guarantee under three different metrics, all under reasonable sampling assumptions. We leverage the efficiency of the spectral algorithm to propose a novel EM-based algorithm for learning mixtures of PCMs. We perform comprehensive experiments on synthetic and real-life datasets covering education testing, recommendation systems, and financial investment applications. We show that the proposed spectral algorithm is competitive with previously introduced algorithms in terms of accuracy while being orders of magnitude faster.} }
Endnote
%0 Conference Paper %T Novel Spectral Algorithms for the Partial Credit Model %A Duc Nguyen %A Anderson Ye Zhang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-nguyen24k %I PMLR %P 37840--37878 %U https://proceedings.mlr.press/v235/nguyen24k.html %V 235 %X The Partial Credit Model (PCM) of Andrich (1978) and Masters (1982) is a fundamental model within the psychometric literature with wide-ranging modern applications. It models the integer-valued response that a subject gives to an item where there is a natural notion of monotonic progress between consecutive response values, such as partial scores on a test and customer ratings of a product. In this paper, we introduce a novel, time-efficient and accurate statistical spectral algorithm for inference under the PCM model. We complement our algorithmic contribution with in-depth non-asymptotic statistical analysis, the first of its kind in the literature. We show that the spectral algorithm enjoys the optimal error guarantee under three different metrics, all under reasonable sampling assumptions. We leverage the efficiency of the spectral algorithm to propose a novel EM-based algorithm for learning mixtures of PCMs. We perform comprehensive experiments on synthetic and real-life datasets covering education testing, recommendation systems, and financial investment applications. We show that the proposed spectral algorithm is competitive with previously introduced algorithms in terms of accuracy while being orders of magnitude faster.
APA
Nguyen, D. & Zhang, A.Y.. (2024). Novel Spectral Algorithms for the Partial Credit Model. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:37840-37878 Available from https://proceedings.mlr.press/v235/nguyen24k.html.

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