

Thesis Defense 
Graduate and Postdoctoral Studies
Electrical and Computer Engineering

Speaker: 
Shiting Lan
Masters Candidate


SPARFA: Sparse Factor Analysis for Learning and Content Analytics 
Tuesday, April 15, 2014
9:00 AM
to 10:30 AM

2014 Duncan Hall


We develop a new model and algorithms for machine learningbased learning analytics, which estimate a learnerâ€™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 questionâ€™s intrinsic difficulty. We estimate these factors given the graded responses to a collection of questions. The underlying estimation problem is illposed in general, especially when only a subset of the questions are answered. The key observation that enables a wellposed solution is the fact that typical educational domains of interest involve only a small number of key concepts. Leveraging this observation, we develop a biconvex maximumlikelihood solution to the resulting SPARse Factor Analysis (SPARFA) problem. We also incorporate instructorspecified tags on questions and question text information to facilitate the interpretation of the estimated factors. Experiments with synthetic and realworld data demonstrate the efficacy of our approach. 


