ECE Theses and Dissertations

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Sparse Factor Analysis for Learning and Content Analytics
(2014-04-23) Lan, Shiting; Baraniuk, Richard G.; Veeraraghavan, Ashok; Allen, Genevera
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-defined tags on questions and question text to facilitate the interpretability of the estimated factors. Experiments with synthetic and real-world data demonstrate the efficacy of our approach.