We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education.

该论文提出了一种新的基于机器学习的框架SPARFA-Trace，用于教育应用的时间变化学习和内容分析，旨在从学习者的二元分级响应数据和每个时间点学习者执行的具体操作总结中估计学习者的知识转变，分析学习资源的质量和内容组织，问题概念关联及问题内在难度，提供个性化教育方案。两个在线课程数据集的实验结果表明SPARFA-Trace能够追踪每个学习者的概念知识演变，同时分析学习资源的质量和内容组织，问题概念关联及问题内在难度，以预测个性化的学习效果。

稀疏因子分析应用于时变学习和内容分析