Mixture Modeling of Individual Learning Curves.

We show that student learning can be accurately modeled using a mixture of learning curves, each of which specifies error probability as a function of time. This approach generalizes Knowledge Tracing [7], which can be viewed as a mixture model in which the learning curves are step functions. We show that this generality yields order-of-magnitude improvements in prediction accuracy on real data. Furthermore, examination of the learning curves provides actionable insights into how different segments of the student population are learning. To make our mixture model more expressive, we allow the learning curves to be defined by generalized linear models with arbitrary features. This approach generalizes Additive Factor Models [4] and Performance Factors Analysis [16], and outperforms them on a large, real world dataset.