Learning Analytics (LA) is a broad umbrella term used to describe statistical models and algorithms for understanding the relationship be- tween a set of learners and a set of questions. The end goal of LA is to understand the dynamics of the responses provided by each learner. LA models serve to answer important questions concerning learners and questions, such as which educational concepts a learner understands well, which ones they do not, and how these concepts relate to the individual question. LA models additionally predict future learning outcomes based on learner performance to date. This information can then be used to adapt learning to achieve specific educational goals.

In this thesis, we adopt a fully Bayesian approach to LA, which allows us both to have superior flexibility in modeling as well as achieve superior performance over methods based on convex optimization. We first develop novel models and algorithms for LA. We showcase the performance of these methods on both synthetic as well as real-world educational datasets.

Second, we apply our LA framework to the problem of collaboration– type detection in educational data sets. Collaboration amongst learners in educational settings is problematic for two reasons. First, such collaboration may be prohibited and considered a form of cheating. Detecting this form of collaboration is essential for maintaining fairness and academic integrity in a course. Finally, collaboration inhibits the ability of LA methods to accurately model learners. We develop several novel techniques for collaboration–type detection where we not only identify collaboration in a statistically principled way, but also classify the type of collaborative behavior.