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

Strategy · All strategies
Evidence · no claims cited

Description¶

The paper's proposed approach: rather than finding the parameter values that provide the lowest RSS by exhaustive search, estimate the minimum RSS value from a priori known skill variables. Three variables are used — dim (number of questions tagged with the skill), n (total responses, the product of students and dim), and percent_correct (pc) — chosen because they are "pieces of information that one may have easy access to before computing BKT-BF." A linear model trained on these variables predicts any skill's minimum RSS, enabling quicker convergence of a modified BKT-BF and reduced computational cost.

Design Implications¶

Context¶

Requirements¶

• Skill-level values of dim, n, and percent_correct before fitting
• A trained linear model (second-degree polynomial on pc) relating these variables to minimum RMSE/RSS

Constraints¶

• Model developed and validated on a single dataset (Psychology MOOC GT Spring 2013); authors state a different dataset is needed to be more certain
• Uses RMSE rather than RSS directly; conversion requires a transformation involving dim and n
• BKT-BF grid used a step much larger than recommended

Target Learners¶

• educational data mining researchers
• cognitive tutor system developers

Target Learning Goals¶

• reducing computational cost of BKT parameter fitting
• predicting minimum RSS for skill-level model training

Related Strategies¶

• Match the input-parameter estimation method (managerial estimates vs. time study) to the accuracy the simulation purpose requires

Examples¶

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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