Bayesian Knowledge Tracing (BKT) is a probabilistic model that aims to understand a learner’s state of mastery for a specific knowledge component. The model considers this state as a hidden or latent variable and updates it based on the observed correctness of the learner’s responses using transition probabilities between states.
One of the challenges in implementing BKT is determining the parameters that govern the model. The Expectation-Maximization (EM) algorithm is commonly used to infer these parameters. However, the EM algorithm has its limitations, such as producing multiple valid sets of parameters, settling into local minima, and computationally expensive fitting.
This paper takes a unique approach by deriving constraints for the BKT parameter space, starting from fundamental mathematical principles and building up to the expected behaviors of parameters in real-world systems. By imposing these constraints prior to fitting, computational cost can be reduced, and issues arising from the EM procedure can be minimized.
What sets this paper apart is that it not only derives the constraints from first principles but also introduces a novel algorithm to estimate BKT parameters while respecting these constraints. Previous research has reported the issue of degenerate parameter values, but this is the first paper, to the best of our knowledge, that provides a derivation of constraints and presents an algorithm that adheres to them.
By incorporating these newly defined constraints into the parameter estimation process, researchers can have more confidence in the validity of the inferred parameters and the resulting model. This advancement has the potential to improve the accuracy and efficiency of BKT implementations in various educational and training contexts.