A note on cyclic shift permutation testing for large eigenvalues
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Bibliographic record
Abstract
Recent publications have described the problem of testing for the “significance” of large sample (empirical) matrix eigenvalues in the presence of modest variation of underlying true eigenvalues. This modest variation often can be ascribed to endemic dependence in one matrix dimension (e.g., rows), whereas the null hypothesis concerns the other dimension (columns). The need for such testing frequently arises in genomics, time‐series analysis, and a variety of other fields. However, the tools available for testing are underdeveloped, with statistical properties that may be sensitive to the true eigenvalues. The purpose of this note is to point the reader to this emerging literature and to suggest that the tool of cyclic shift permutation may be well‐suited to the problem.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.000 | 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