PAC-Bayes Analysis Beyond the Usual Bounds
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Bibliographic record
Abstract
We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution is then used to make randomized predictions, and the high-level theme addressed here is guaranteeing the quality of predictions on examples that were not seen during training, i.e. generalization. In this setting the unknown quantity of interest is the expected risk of the data-dependent randomized predictor, for which upper bounds can be derived via a PAC-Bayes analysis, leading to PAC-Bayes bounds. Specifically, we present a basic PAC-Bayes inequality for stochastic kernels, from which one may derive extensions of various known PAC-Bayes bounds as well as novel bounds. We clarify the role of the requirements of fixed 'data-free' priors, bounded losses, and i.i.d. data. We highlight that those requirements were used to upper-bound an exponential moment term, while the basic PAC-Bayes theorem remains valid without those restrictions. We present three bounds that illustrate the use of data-dependent priors, including one for the unbounded square loss.
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.003 |
| 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