A Closed-Form Solution for Fast and Reliable Adaptive Testing

Zirui Liu (University of Minnesota - Twin Cities) · Shijin Wang (State Key Laboratory of Cognitive Intelligence) · Yan Zhuang (University Of Science And Technology Of China) · Qi Liu (Bytedance Inc.) · Chenye Ke (Anhui University) · Yuting Ning (Ohio State University, Columbus) · Zhenya Huang (University of Science and Technology of China) · Weizhe Huang (University of Science and Technology of China) · Qingyang Mao (University of Science and Technology of China)

ability estimation erroradaptive testingbehavioral perturbationsclosed-form solutioneducational assessmentestimation accuracygradient biasgreedy algorithmhessian stabilityhuman ability estimationlarge-scale datasets optimization problemprofessional certificationquestion subset selectionsota methods

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.