StanBKT: Rethinking Parameter Estimation in Bayesian Knowledge Tracing

2026-05-21

AI Summary

This work addresses the limitation of traditional Bayesian Knowledge Tracing (BKT), which relies on point estimates and thus fails to quantify parameter uncertainty, hindering reliable comparisons across students or experimental conditions. To overcome this, we propose StanBKT—an open-source Python toolkit built on Stan—that systematically integrates multiple Bayesian inference methods, including Hamiltonian Monte Carlo, variational inference, and Pathfinder, for the first time in BKT modeling. While preserving BKT’s interpretable hidden Markov structure, StanBKT supports standard, grouped, and hierarchical formulations. Through flexible prior specification and posterior predictive checks with diagnostic visualizations, it enables effective quantification of parameter uncertainty. Experiments on large-scale datasets such as ASSISTments 2020 demonstrate that these inference methods achieve comparable predictive performance while exhibiting trade-offs between computational efficiency and posterior fidelity, thereby facilitating credible comparisons of learning, forgetting, guessing, and slipping parameters in educational interventions.

Abstract

Bayesian Knowledge Tracing (BKT) is a widely used and interpretable student modeling approach in intelligent tutoring systems and educational data mining. However, most implementations rely on expectation-maximization or related optimization methods that yield only point estimates, limiting uncertainty quantification and principled comparisons across learners and conditions. We introduce StanBKT, an open-source Python package for estimating BKT models using Bayesian inference in Stan. StanBKT provides a unified framework supporting Hamiltonian Monte Carlo, variational inference, Pathfinder, and optimization-based estimation while preserving the hidden Markov structure and interpretability of classical BKT. It supports standard, grouped, and hierarchical BKT models, flexible prior specification, posterior predictive inference, and utilities for visualization and diagnostics. We evaluate StanBKT on large-scale observational and controlled educational datasets. On the ASSISTments 2020 dataset, we show that supported inference methods achieve comparable predictive performance while differing in computational efficiency and posterior fidelity. We further demonstrate how posterior inference enables principled comparison of condition-specific parameters in an educational intervention involving perceptual cue manipulations. Results illustrate how uncertainty quantification facilitates more reliable interpretation of differences in learning, forgetting, guessing, and slipping parameters across experimental conditions. Overall, StanBKT extends BKT beyond point estimation by providing a flexible framework for probabilistic student modeling, uncertainty quantification, and hierarchical inference in educational data mining.

Problem

• Bayesian Knowledge Tracing
• parameter estimation
• uncertainty quantification
• student modeling
• educational data mining

Innovation

• Bayesian Knowledge Tracing
• Bayesian inference
• Uncertainty quantification
• Hierarchical modeling
• Stan