Testing the Equality of Learning Rates Using a Linear Hypothesis
Bibliographic record
Abstract
For over a hundred years, psychologists have tried to describe and understand human learning. While many models disagree on the nature of the process, most agrees that the performance is well described by a power function (Newell and Rosenbloom, 1981). This equation has a curvature parameter as well as two scaling parameters. Recent models are making quantitative predictions on the learning rate, which is represented by the curvature parameter of the function. For example, Logan’s race model (Logan, 1988) predicts that standard deviations and means of response times will decrease at the same rate. The most intuitive way to test this hypothesis is to estimate the best-fitting parameters and to apply a statistical test on those estimations. The problem with this approach is that those estimations are highly biased (Cousineau, Helie and Lefebvre, in press). In the late fifties, Rao (1959) proposed a test of linear hypothesis. By assuming that the learning rates are equal, the power functions (or any other learning model postulated) become a linear combination of each other, irrespective of the scaling parameters. However, since learning data tends to be noisy, the power of Rao’s test was limited. In order to reduce the effects of noise, Cousineau, Helie and Lefebvre (in press) proposed to apply Rao’s test on block-average data.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.118 | 0.456 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.005 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.002 | 0.012 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.007 | 0.005 |
| Research integrity | 0.006 | 0.007 |
| Insufficient payload (model declined to judge) | 0.016 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".