From PAC-Bayes Bounds to Quadratic Programs for Majority Votes
Bibliographic record
Abstract
We propose to construct a weighted majority vote on a set of basis functions by minimizing a risk bound (called the C-bound) that depends on the first two moments of the margin of the Q-convex combination realized on the data. This bound minimization algorithm turns out to be a quadratic program that can be efficiently solved. A first version of the algorithm is designed for the supervised inductive setting and turns out to be very competitive with AdaBoost, MDBoost and the SVM. The second version is designed for the transductive setting. It competes well against TSVM. We also propose a new PAC-Bayes theorem that bounds the difference between the true value of the C-bound and its empirical estimate and that, unexpectedly, contains no KL-divergence.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.039 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".