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We propose VarFA, a variational inference factor analysis framework that extends existing factor analysis models for educational data mining to efficiently output uncertainty estimation in the model's estimated factors. Such uncertainty information is useful, for example, for an adaptive testing scenario, where additional tests can be administered if the model is not quite certain about a students' skill level estimation. Traditional Bayesian inference methods that produce such uncertainty information are computationally expensive and do not scale to large data sets. VarFA utilizes variational inference which makes it possible to efficiently perform Bayesian inference even on very large data sets. We use the sparse factor analysis model as a case study and demonstrate the efficacy of VarFA on both synthetic and real data sets. VarFA is also very general and can be applied to a wide array of factor analysis models. 

We investigate whether student comprehension and knowledge retention can be predicted from textbook annotations, specifically the material that students choose to highlight. Using a digital open-access textbook platform, Openstax, students enrolled in Biology, Physics, and Sociology courses read sections of their introductory text as part of required coursework, optionally highlighted the text to flag key material, and then took brief quizzes as the end of each section. We find that when students choose to highlight, the specific pattern of highlights can explain about 13% of the variance in observed quiz scores. We explore many different representations of the pattern of highlights and discover that a low-dimensional logistic principal component based vector is most effective as input to a ridge regression model. Considering the many sources of uncontrolled variability affecting student performance, we are encouraged by the strong signal that highlights provide as to a student’s knowledge state. 

Algorithms often carry out equally many computations for “easy” and “hard” problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the problem of finding a subset of O(k) points in a given set of points that contains the set of k nearest neighbors of a given query point. We pro- pose an algorithm based on adaptively estimating the distances, and show that it is essentially optimal out of algorithms that are only allowed to adaptively estimate distances. We then demonstrate both theoretically and experimentally that the algorithm can achieve significant speedups relative to the naive method.