Sparse Factor Analysis for Learning and Content Analytics
| dc.contributor.advisor | Baraniuk, Richard G. | |
| dc.contributor.committeeMember | Veeraraghavan, Ashok | |
| dc.contributor.committeeMember | Allen, Genevera | |
| dc.creator | Lan, Shiting | |
| dc.date.accessioned | 2014-09-22T19:55:24Z | |
| dc.date.available | 2014-09-22T19:55:24Z | |
| dc.date.created | 2014-05 | |
| dc.date.issued | 2014-04-23 | |
| dc.date.submitted | May 2014 | |
| dc.date.updated | 2014-09-22T19:55:24Z | |
| dc.description.abstract | 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. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | Lan, Shiting. "Sparse Factor Analysis for Learning and Content Analytics." (2014) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/77215">https://hdl.handle.net/1911/77215</a>. | |
| dc.identifier.uri | https://hdl.handle.net/1911/77215 | |
| dc.language.iso | eng | |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | |
| dc.subject | Factor analysis | |
| dc.subject | Sparse probit regression | |
| dc.subject | Sparse logistic regression | |
| dc.subject | Bayesian latent factor analysis | |
| dc.subject | Personalized learning | |
| dc.title | Sparse Factor Analysis for Learning and Content Analytics | |
| dc.type | Thesis | |
| dc.type.material | Text | |
| thesis.degree.department | Electrical and Computer Engineering | |
| thesis.degree.discipline | Engineering | |
| thesis.degree.grantor | Rice University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science |
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