PACMAN: PAC-style bounds accounting for the Mismatch between Accuracy and Negative log-loss
Bibliographic record
Abstract
Abstract The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) using a testing dataset, although these algorithms are optimized through the minimization of a typically different—more convenient—loss function using a training set. For classification tasks, this loss function is often the negative log-loss that yields the well-known cross-entropy risk that is typically better behaved (in terms of numerical behavior) than the 0-1 loss. Conventional studies on the generalization error do not usually take into account the underlying mismatch between losses at training and testing phases. In this work, we introduce a theoretical analysis based on a pointwise probably approximately correct (PAC) approach over the generalization gap considering the mismatch of testing on the accuracy metric and training on the negative log-loss, referred to as PACMAN. Building on the fact that the resulting mismatch can be written as a likelihood ratio, concentration inequalities can be used to obtain insights into the generalization gap in terms of PAC bounds, which depend on some meaningful information-theoretic quantities. An analysis of the obtained bounds and a comparison with available results in the literature is also provided.
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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 | 0.025 | 0.148 |
| Meta-epidemiology (narrow) | 0.004 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.007 | 0.015 |
| Open science | 0.007 | 0.009 |
| Research integrity | 0.005 | 0.012 |
| 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".