UMP invariance in adaptive detection: kernels that preserve monotone likelihood ratio
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Bibliographic record
Abstract
We consider the question of optimality for the adaptive coherence estimator (ACE), which is an adaptive detection statistic for the problem in which noise in the training data is not constrained to have same power level as noise in the test data. Having previously shown that ACE is a maximal invariant statistic, we complete a proof that a threshold test on ACE is uniformly-most-powerful (UMP) invariant. This requires a second result, that the statistic possesses a monotone likelihood ratio (MLR). We establish the MLR property by relating it to the property of the density being a positive kernel. By repeatedly applying a basic composition formula for such kernels, we show that the density for ACE is totally positive. Thus the density has MLR, and a simple threshold test on ACE has the strict optimality property of being UMP-invariant.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| 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