Mean Absolute Deviations about the Mean, the Cut Norm and Taxicab Correspondence Analysis
Why this work is in the frame
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Bibliographic record
Abstract
Optimization has two faces, minimization of a loss function or maximization of a gain function. We show that the mean absolute deviation about the mean, d, maximizes a gain function based on the power set of the individuals; and nd, where n is the sample size, equals twice the value of the cut-norm of the deviations about the mean. This property is generalized to double-centered and triple-centered data sets. Furthermore, we show that among the three well known dispersion measures, standard deviation, least absolute deviation and d, d is the most robust based on the relative contribution criterion. More importantly, we show that the computation of each principal dimension of taxicab correspondence analysis (TCA) corresponds to balanced 2-blocks seriation. These ideas are applied on two data sets.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 it