VarSKD: A Variational Student Knowledge Diagnosis for Efficiently Representing Student Latent Knowledge Space

Student knowledge diagnosis (SKD) is a fundamental and crucial task in educational data mining (EDM). SKD aims to diagnose student latent knowledge which is inferred from student's performance. The model used for SKD in EDM comes from two sources: variant classical psychometric approaches, and research on machine learning-based approaches. Tradition psychometric models and their variants diagnosis student knowledge state relying on the question-concept matrix (Q-matrix) empirically designed by experts. However, the expert concepts are expensive and inter-overlapping in their constructions, leading to ambiguous explanations. The recent model Meta-knowledge Dictionary Learning (MetaDL), a learning-based model, proposes a linear sparse dictionary method to mine Q-matrix without expert definition and student latent knowledge representation. MetaDL aims to learn a meta-knowledge dictionary from student responses, where any knowledge entity is a linear combination of a few atoms in the meta-knowledge dictionary. However, a linear model cannot capture complex features from the student learning process and MetaDL fails to solve the missing data. This paper proposes a novel Variational Student Knowledge Diagnosis (VarSKD) method that extends the linear sparse representation of student latent knowledge space into non-linear probabilistic sparse representation. This model based on variational sparse coding can obtain better student latent knowledge representation. Furthermore, extensive experimental results on real-world datasets demonstrate the prediction accuracy and effective power of VarSKD framework.