Meta-knowledge dictionary learning on 1-bit response data for student knowledge diagnosis

This paper focuses on the problem of student knowledge diagnosis that is a basic task of realizing personalized education. Most traditional methods rely on the question-concept matrix empirically designed by experts. However, the expert concepts are expensive and inter-overlapping in their constructions, leading to ambiguous explanations. With the intuition that each student can master a part of the knowledge involved in all questions, in this paper, we propose a novel learning-based model for student knowledge diagnosis, dubbed Meta-knowledge Dictionary Learning (metaDL). MetaDL aims to learn a meta-knowledge dictionary from student responses, where any knowledge entity (e.g., student, question or expert concept) is a linear combination of a few atoms in the meta-knowledge dictionary. The resultant problem could be effectively solved by developing the alternating direction method of multipliers. This study has three innovations: learning independent meta-knowledges instead of traditional complex concepts, sparely representing knowledge entity instead of densely weighted representation, and interpreting expert concepts with the resulting meta-knowledges. For evaluation, the diagnosis results from metaDL are used to group students and predict responses on two public datasets and a private dataset from our institution. The experiment results show that metaDL delivers an effective student knowledge diagnosis and then results in good performances on the two applications in comparison with other methods. This technique could provide significant insights into student's knowledge state and facilitate the progress on personalized education.