Direct estimation of the minimum RSS value for training Bayesian Knowledge Tracing parameters

Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However, the most popular methods for training the parameters of BKT have some problems, such as identifiability, local minima, degenerate parameters and computational cost during fitting. In this paper we address some of the issues of one of these training models, BKT Brute Force. Instead of finding the parameter values that provide the lowest Residual Sum of Squares (RSS), we estimate this minimum RSS value from some a priori known values of the skill. From there we perform some preliminary analysis to improve our knowledge of the relationship between the RSS, from BKT-BF, and the four BKT parameters.