A Probabilistic Framework for Temporal Cognitive Diagnosis in Online Learning Systems

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.