# Time-varying Learning and Content Analytics via Sparse Factor Analysis

arXiv: https://arxiv.org/abs/1312.5734 · HTML: https://mlsanity.com/paper/1312.5734/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2013.

## Built on by (most cited first, 6 of 6)

- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Domain Generalizable Knowledge Tracing via Concept Aggregation and Relation-Based Attention](https://mlsanity.com/paper/2407.02547/) (2024)
- [Lost in Translation: Reimagining the Machine Learning Life Cycle in Education](https://mlsanity.com/paper/2209.03929/) (2022)
- [A Conceptual Model for End-to-End Causal Discovery in Knowledge Tracing](https://mlsanity.com/paper/2305.16165/) (2023)
- [ast2vec: Utilizing Recursive Neural Encodings of Python Programs](https://mlsanity.com/paper/2103.11614/) (2021)
- [Dynamical Non-compensatory Multidimensional IRT Model Using Variational Approximation](https://mlsanity.com/paper/2609.10028/) (2026)

## Abstract (arXiv)

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.