BKT Brute Force (BKT-BF): grid-search parameter estimation minimizing Residual Sum of Squares¶

Theory · All theories
Evidence · no claims cited

Description¶

BKT-BF is an algorithm to estimate BKT parameter values by brute force: a grid of possible parameter values is set, and for each combination a Residual Sum of Squares (RSS) value is obtained; "the combination of values resulting in the lowest Residual Sum of Squares (RSS) value for a skill is the one that will be used in BKT." The RSS is computed from observed answers Oi,t and the BKT-derived likelihood of a correct answer Ci,j, normalized by students and dim. In this study, grids used values 0.05–0.95 (step 0.15) for L0 and T, and bounded 0.05–0.30 (step 0.05) for G and S to avoid model degeneracy, yielding 1764 RSS values per skill.

Design Implications¶

Context¶

Requirements¶

• A grid of candidate parameter values
• Student response data for skill-tagged questions
• Computation over all grid combinations to obtain RSS values

Constraints¶

• Very expensive in computational cost, as all brute force algorithms are
• Does not help the identifiability problem of BKT
• In this study a step much larger than the one recommended by the algorithm was used

Target Learners¶

• researchers and course designers fitting student models to skill-tagged response data

Target Learning Objectives¶

• estimating BKT parameters (L0, T, G, S) for knowledge inference

Claims¶

Related Theories¶

• Bayesian Knowledge Tracing: a two-state Hidden Markov Model inferring skill mastery from response histories

Examples¶

• Estimate a skill's minimum BKT-BF RSS a priori from dim, n, and percent_correct before running the full grid search

Key Sources¶

• Martori, F., Cuadros, J., & González-Sabaté, L. (2015). Direct estimation of the minimum RSS value for training Bayesian Knowledge Tracing parameters. Proceedings of the 8th International Conference on Educational Data Mining. https://www.educationaldatamining.org/EDM2015/proceedings/short364-367.pdf