Minkowski deviation measures
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Bibliographic record
Abstract
Abstract We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink or deleverage a financial position for it to become acceptable. In particular, the Minkowski Deviation of a set which is convex, translation insensitive, and radially bounded at non-constants, is a generalized deviation measure in the sense of [R. T. Rockafellar, S. Uryasev and M. Zabarankin, Generalized deviations in risk analysis, Finance Stoch. 10 2006, 1, 51–74]. Furthermore, we explore the converse relations from properties of a Minkowski Deviation to its sub-level sets, introducing the notion of acceptance sets for deviations. Hence, we fill a gap existing in the literature, namely the lack of a well-defined concept of acceptance sets for deviation measures. Dual characterizations in terms of polar sets and support functionals are provided.
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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 | 0.003 | 0.003 |
| 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 | 0.000 | 0.000 |
| Open science | 0.000 | 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