A Hierarchical Probabilistic Framework for Incremental Knowledge Tracing in Classroom Settings
Journal:
arXiv
Published Date:
Jun 11, 2025
Abstract
Knowledge tracing (KT) aims to estimate a student's evolving knowledge state
and predict their performance on new exercises based on performance history.
Many realistic classroom settings for KT are typically low-resource in data and
require online updates as students' exercise history grows, which creates
significant challenges for existing KT approaches. To restore strong
performance under low-resource conditions, we revisit the hierarchical
knowledge concept (KC) information, which is typically available in many
classroom settings and can provide strong prior when data are sparse. We
therefore propose Knowledge-Tree-based Knowledge Tracing (KT$^2$), a
probabilistic KT framework that models student understanding over a
tree-structured hierarchy of knowledge concepts using a Hidden Markov Tree
Model. KT$^2$ estimates student mastery via an EM algorithm and supports
personalized prediction through an incremental update mechanism as new
responses arrive. Our experiments show that KT$^2$ consistently outperforms
strong baselines in realistic online, low-resource settings.
