Bounding Excess Minimum Risk via Rényi's Divergence
Bibliographic record
Abstract
Given finite dimensional random vectors$\boldsymbol{Y,X}$and$\boldsymbol{Z}$that form a Markov chain in that order$(\boldsymbol{Y}\rightarrow \boldsymbol{X}\rightarrow \boldsymbol{Z})$, we derive Rényi divergence based upper bounds for excess minimum risk, where$\boldsymbol{Y}$is a (target) vector that is to be estimated from an observed (feature) vector$\boldsymbol{X}$or its (stochastically) degraded version$\boldsymbol{Z}$. We define the excess minimum risk as the difference between the minimum expected loss in estimating$\boldsymbol{Y}$from$\boldsymbol{X}$and the minimum expected loss in estimating$\boldsymbol{Y}$from$\boldsymbol{Z}$. We obtain a family of bounds which generalize the bounds developed by Györfi et al. (2023) expressed in terms of Shannon's mutual information. Our bounds are similar to the bounds by Modak et al. (2021) obtained in the context of the generalization error of learning algorithms, but unlike the latter they do not involve fixed sub-Gaussian parameters and therefore hold for more general joint distributions of$\boldsymbol{Y,X}$, and$\boldsymbol{Z}$. We also provide an example with Bernoulli random variables where Rényi's divergence based upper bound are tighter than mutual information bounds.
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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 | 0.011 | 0.054 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.004 | 0.007 |
| Research integrity | 0.002 | 0.008 |
| Insufficient payload (model declined to judge) | 0.008 | 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".