Approximations for Performance of Energy Detector and <inline-formula> <tex-math notation="LaTeX">$p$</tex-math></inline-formula>-Norm Detector
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Bibliographic record
Abstract
Although the approximations based on the central limit theorem (CLT) for the detection probability (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ) of the energy detector and of its more generalized cousin, the p-norm detector, are accurate for large sample sizes, their accuracy is poor otherwise. A recent work has addressed this problem by developing a cube-of-Gaussian approximation (CGA). However, CGA may not be the only option and thus this letter investigates five other classical approximations for deriving P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> . They tightly match the exact values even for few samples and thus are more accurate than CLT. These approximations have been unnoticed in the signal detection research community and this letter aims at making them known to a wider audience. Because the range of their potential applications could be diverse, to demonstrate their utility, we derive a novel expression for the area under the receiver operating characteristic curve of the p-norm detector.
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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 | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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