Cognitive diagnosis is an important issue of intelligent education systems, which aims to estimate students’ proficiency on specific knowledge concepts. Most existing studies rely on the assumption of static student states and ignore the dynamics of proficiency in the learning process, which makes them unsuitable for online learning scenarios. In this paper, we propose a unified temporal item response theory (UTIRT) framework, incorporating temporality and randomness of proficiency evolving to get both accurate and interpretable diagnosis results. Specifically, we hypothesize that students’ proficiency varies as a Wiener process and describe a probabilistic graphical model in UTIRT to consider temporality and randomness factors. Furthermore, based on the relationship between student states and exercising answers, we hypothesize that the answering result at time k contributes most to inferring a student's proficiency at time k, which also reflects the temporality aspect and enables us to get analytical maximization (M-step) in the expectation maximization (EM) algorithm when estimating model parameters. Our UTIRT is a framework containing unified training and inferencing methods, and is general to cover several typical traditional models such as Item Response Theory (IRT), multidimensional IRT (MIRT), and temporal IRT (TIRT). Extensive experimental results on real-world datasets show the effectiveness of UTIRT and prove its superiority in leveraging temporality theoretically and practically over TIRT.

认知诊断是智能教育系统的一个重要问题，旨在评估学生对特定知识概念的熟练程度。现有研究大多依赖于静态学生状态的假设，而忽略了学习过程中熟练程度的动态变化，这使得它们不适合在线学习场景。在本文中，我们提出了一个统一的时间项目反应理论（UTIRT）框架，结合了熟练程度演变的时间性和随机性，以获得准确且可解释的诊断结果。具体来说，我们假设学生的熟练程度按照维纳过程变化，并在 UTIRT 中描述概率图形模型以考虑时间性和随机性因素。此外，根据学生状态和练习答案之间的关系，我们假设k时刻的答案结果对推断k时刻学生的熟练程度贡献最大，这也反映了时间性方面，使我们能够获得分析最大化（M 步） ）在估计模型参数时的期望最大化（EM）算法中。我们的UTIRT是一个包含统一训练和推理方法的框架，一般涵盖项目反应理论（IRT）、多维IRT（MIRT）和时间IRT（TIRT）等几种典型的传统模型。对真实世界数据集的大量实验结果表明了 UTIRT 的有效性，并证明了它在理论和实践上比 TIRT 在利用时间性方面的优越性。