Spectral BKT: a BKT variant combining feature compensation (3-gram observations) with model compensation (four latent states)¶

Theory · All theories
Evidence · no claims cited

Description¶

Spectral BKT is a reconceptualization of Bayesian Knowledge Tracing as a first-order HMM that applies two noise-handling paradigms from speech processing. Feature compensation replaces single binary observations with "n-grams of the consecutive original unary observations of correct and incor rect skill application" (3-grams, giving 8 spectral observations), and model compensation adds two intermediate latent states between unknown and known, for 4 states and 37 parameters per skill. A sparsity structure in the transition matrix forces forward progression from unknown to known and prevents the EM algorithm from learning degenerate models. Predictions over 8 spectral observations are mapped back to binary correct/incorrect via regular, strict, or relaxed rules.

Design Implications¶

Context¶

Requirements¶

• Skills must be fine-grained enough that 3-grams of observations suffice to identify the true model, per the paper's information-theoretic argument
• Predictions must be mapped from the 8-probability spectral distribution back to 2 values for fair comparison with standard BKT

Constraints¶

• The paper's setup (4 states, 3-grams) is one of several conceivable configurations and was chosen empirically
• Predictions for the first two original observations must be back-predicted because 3-grams only yield predictions from the third observation

Target Learners¶

• mathematics students practicing skills in the Cognitive Tutor (KDD Cup 2010 Bridge to Algebra population)

Target Learning Objectives¶

• modeling student skill acquisition and latent mastery in intelligent tutoring systems

Claims¶

Related Theories¶

• Bayesian Knowledge Tracing: a two-state Hidden Markov Model inferring skill mastery from response histories
• Two hypotheses for the meaning of Spectral BKT's intermediate states: a stages-of-mastery account and a mastery-by-metacognition interaction account
• Bayesian Knowledge Tracing as a model of changing skill mastery during game-based assessment

Examples¶

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Key Sources¶

• Falakmasir, M., Yudelson, M., Ritter, S., & Koedinger, K. (2015). Spectral Bayesian Knowledge Tracing. Proceedings of the 8th International Conference on Educational Data Mining. http://pslcdatashop.web.cmu.edu/KDDCup