Probabilistic Graphical Models for Boosting Cardinal and Ordinal Peer Grading in MOOCs

Abstract

With the enormous scale of massive open online courses (MOOCs), peer grading is vital for addressing the assessment challenge for open-ended assignments or exams while at the same time providing students with an effective learning experience through involvement in the grading process. Most existing MOOC platforms use simple schemes for aggregating peer grades, e.g., taking the median or mean. To enhance these schemes, some recent research attempts have developed machine learning methods under either the cardinal setting (for absolute judgment) or the ordinal setting (for relative judgment). In this paper, we seek to study both cardinal and ordinal aspects of peer grading within a common framework. First, we propose novel extensions to some existing probabilistic graphical models for cardi- nal peer grading. Not only do these extensions give su- perior performance in cardinal evaluation, but they also outperform conventional ordinal models in ordinal eval- uation. Next, we combine cardinal and ordinal models by augmenting ordinal models with cardinal predictions as prior. Such combination can achieve further performance boosts in both cardinal and ordinal evaluations, suggesting a new research direction to pursue for peer grading on MOOCs. Extensive experiments have been conducted using real peer grading data from a course called “Science, Technology, and Society in China I” offered by HKUST on the Coursera platform.