Test-size Reduction Using Sparse Factor Analysis

Consider a large database of questions that test the knowledge of learners (e.g., students) about a range of different concepts. While the main goal of personalized learning is to obtain accurate estimates of each learner’s concept understanding, it is additionally desirable to reduce the number of questions to minimize each learner’s workload. In this paper, we propose a novel method to extract a small subset of questions (from a large question database) that still enables the accurate estimation of a learner’s concept understanding. Our method builds upon the SPARse Factor Analysis (SPARFA) framework and chooses a subset of questions that minimizes the entropy of the error in estimating the level of concept understanding. We approximate the underlying combinatorial optimization problem using a mixture of convex and greedy methods and demonstrate the efficacy of our approach on real educational data.