Exploring Heterogeneity and Uncertainty for Graph-based Cognitive Diagnosis Models in Intelligent Education

Graph-based Cognitive Diagnosis (CD) has attracted much research interest due to its strong ability on inferring students' proficiency levels on knowledge concepts. While graph-based CD models have demonstrated remarkable performance, we contend that they still cannot achieve optimal performance due to the neglect of edge heterogeneity and uncertainty. Edges involve both correct and incorrect response logs, indicating heterogeneity. Meanwhile, a response log can have uncertain semantic meanings, e.g., a correct log can indicate true mastery or fortunate guessing, and a wrong log can indicate a lack of understanding or a careless mistake. In this paper, we propose an Informative Semantic-aware Graph-based Cognitive Diagnosis model (ISG-CD), which focuses on how to utilize the heterogeneous graph in CD and minimize effects of uncertain edges. Specifically, to explore heterogeneity, we propose a semantic-aware graph neural networks based CD model. To minimize effects of edge uncertainty, we propose an Informative Edge Differentiation layer from an information bottleneck perspective, which suggests keeping a minimal yet sufficient reliable graph for CD in an unsupervised way. We formulate this process as maximizing mutual information between the reliable graph and response logs, while minimizing mutual information between the reliable graph and the original graph. After that, we prove that mutual information maximization can be theoretically converted to the classic binary cross entropy loss function, while minimizing mutual information can be realized by the Hilbert-Schmidt Independence Criterion. Finally, we adopt an alternating training strategy for optimizing learnable parameters of both the semantic-aware graph neural networks based CD model and the edge differentiation layer. Extensive experiments on three real-world datasets have demonstrated the effectiveness of ISG-CD.