Quantized Matrix Completion for Personalized Learning
This work addresses the practical challenge of parameter tuning in educational data analysis for learning and content analytics, though it is incremental as it builds on the SPARFA framework.
The paper tackles the problem of parameter selection in personalized learning models by introducing SPARFA-Lite, a convex optimization-based method that requires only a single parameter and automatically determines the number of concepts, achieving comparable prediction performance to existing methods like IRT and SPARFA while being more computationally efficient.
The recently proposed SPARse Factor Analysis (SPARFA) framework for personalized learning performs factor analysis on ordinal or binary-valued (e.g., correct/incorrect) graded learner responses to questions. The underlying factors are termed "concepts" (or knowledge components) and are used for learning analytics (LA), the estimation of learner concept-knowledge profiles, and for content analytics (CA), the estimation of question-concept associations and question difficulties. While SPARFA is a powerful tool for LA and CA, it requires a number of algorithm parameters (including the number of concepts), which are difficult to determine in practice. In this paper, we propose SPARFA-Lite, a convex optimization-based method for LA that builds on matrix completion, which only requires a single algorithm parameter and enables us to automatically identify the required number of concepts. Using a variety of educational datasets, we demonstrate that SPARFALite (i) achieves comparable performance in predicting unobserved learner responses to existing methods, including item response theory (IRT) and SPARFA, and (ii) is computationally more efficient.