A Closed-Form Solution for Fast and Reliable Adaptive Testing

Yan Zhuang, Chenye Ke, Zirui Liu, Qi Liu, Yuting Ning, Zhenya Huang, Weizhe Huang, Qingyang Mao, Shijin Wang

Keywords: Computerized Adaptive Testing, Human Assessment, Psychometrics, Ability Estimation, AI Education

TL;DR: A closed-form method for adaptive testing that selects questions efficiently and accurately without complex iterative optimization.

Abstract: Human ability estimation is essential for educational assessment, career advancement, and professional certification. Adaptive Testing systems can improve estimation efficiency by selecting fewer, targeted questions, and are widely used in exams, e.g., GRE, GMAT, and Duolingo English Test. However, selecting an optimal subset of questions remains a challenging nested optimization problem. Existing methods rely on costly approximations or data-intensive training, making them unsuitable for today's large-scale and complex testing environments. Thus, we propose a Closed-Form solution for question subset selection in Adaptive Testing. It directly minimizes ability estimation error by reducing ability parameter's gradient bias while maintaining Hessian stability, which enables a simple greedy algorithm for question selection. Moreover, it can quantify the impact of human behavioral perturbations on ability estimation. Extensive experiments on large-scale educational datasets demonstrate that it reduces the number of required questions by 10% compared to SOTA methods, while maintaining the same estimation accuracy.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Submission Number: 6782