Graduate and Postdoctoral Studies
Electrical and Computer Engineering
SPARFA: Sparse Factor Analysis for Learning and Content Analytics
Tuesday, April 15, 2014
to 10:30 AM
2014 George R. Brown Hall
We develop a new model and algorithms for machine learning-based learning analytics, which estimate a learner’s knowledge of the concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and those concepts. Our model represents the probability that a learner provides the correct response to a question in terms of three factors: their understanding of a set of underlying concepts, the concepts involved in each question, and each question’s intrinsic difficulty. We estimate these factors given the graded responses to a collection of questions. The underlying estimation problem is ill-posed in general, especially when only a subset of the questions are answered. The key observation that enables a well-posed solution is the fact that typical educational domains of interest involve only a small number of key concepts. Leveraging this observation, we develop a bi-convex maximum-likelihood solution to the resulting SPARse Factor Analysis (SPARFA) problem. We also incorporate instructor-specified tags on questions and question text information to facilitate the interpretation of the estimated factors. Experiments with synthetic and real-world data demonstrate the efficacy of our approach.