Unified Uncertainty Estimation for Cognitive Diagnosis Models

Cognitive diagnosis models have been widely used in different areas, especially intelligent education, to measure users' proficiency levels on knowledge concepts, based on which users can get personalized instructions. As the measurement is not always reliable due to the weak links of the models and data, the uncertainty of measurement also offers important information for decisions. However, the research on the uncertainty estimation lags behind that on advanced model structures for cognitive diagnosis. Existing approaches have limited efficiency and leave an academic blank for sophisticated models which have interaction function parameters (e.g., deep learning-based models). To address these problems, we propose a unified uncertainty estimation approach for a wide range of cognitive diagnosis models. Specifically, based on the idea of estimating the posterior distributions of cognitive diagnosis model parameters, we first provide a unified objective function for mini-batch based optimization that can be more efficiently applied to a wide range of models and large datasets. Then, we modify the reparameterization approach in order to adapt to parameters defined on different domains. Furthermore, we decompose the uncertainty of diagnostic parameters into data aspect and model aspect, which better explains the source of uncertainty. Extensive experiments demonstrate that our method is effective and can provide useful insights into the uncertainty of cognitive diagnosis.